General chemistry: textbook / A. V. Zholnin; edited by V. A. Popkova, A. V. Zholnina. - 2012. - 400 pp.: ill.

Chapter 2. BASICS OF CHEMICAL REACTION KINETICS

Chapter 2. BASICS OF CHEMICAL REACTION KINETICS

The difference between breathing and combustion is only in the speed of the process.

A.-L. Lavoisier

2.1. CHEMICAL KINETICS. SUBJECT AND BASIC CONCEPTS OF CHEMICAL KINETICS. SPEED REACTION

The direction, depth and fundamental possibility of the process occurring are judged by the magnitude of the change in free energy (ΔG ≤0). However, this value does not indicate the real possibility of the reaction occurring under these conditions.

For example, the reaction between nitrous oxide and oxygen occurs instantly at room temperature:

At the same time, 2H 2 (g) + O 2 (g) = 2H 2 O (l), Δ °G= -286.8 kJ/mol - a reaction characterized by a significantly greater decrease in free energy; under normal conditions the interaction does not occur, but at 700 °C or in the presence of a catalyst the process occurs instantly. Consequently, thermodynamics does not answer the question of the conditions and speed of the process. This reveals the limitations of the thermodynamic approach. To describe a chemical reaction, it is also necessary to know the patterns of its occurrence over time, which are studied by kinetics.

Kinetics is a branch of chemistry that studies the rate, mechanism of chemical reactions and the influence of various factors on them.

Depending on whether the reaction components are in one or more phases, the kinetics of homogeneous and heterogeneous reactions are distinguished. According to the mechanism, reactions are divided into simple and complex, therefore the kinetics of simple and complex reactions are distinguished.

The basic concept of reaction kinetics is rate of chemical reaction. Determining the rate of chemical reactions is of biological and economic importance.

The rate of a chemical reaction is determined by the amount of substance reacted per unit time per unit volume (in the case of homogeneous reactions, when the reactants are in the same phase) or per unit interface(in the case of heterogeneous reactions, when the reactants are in different phases).

The reaction rate is characterized by a change in the concentration of any of the initial or final reaction products as a function of time. Equation describing the dependence of the reaction rate (v) on concentration (With) reactants are called kinetic. The reaction rate is often expressed in mol/l-s, in biochemistry in mg/100 ml-s, or in mass fraction, in %/100 ml-s. A distinction is made between the average reaction rate over a time interval and the true reaction rate at a certain point in time. If in the time interval t 1 And t 2 the concentration of one of the starting substances or reaction products is equal to c 1 and c 2, respectively, then the average reaction rate (v) in the time interval t 1 And t 2 can be expressed:

Since in this case we are talking about a decrease in the concentration of the starting substance, i.e. the change in the concentration of the substance is taken in this case with a minus sign (-). If the reaction rate is assessed by a change (increase) in the concentration of one of the reaction products, then with a plus sign (+):

Using equation (2.2) we determine average speed chemical reaction. True (instantaneous) speed reactions are determined graphically. Construct a graph of the concentration of the starting substance or reaction product (Ca) versus time (t) - the kinetic curve of the reaction Ca - f(t) for a nonlinear process (Fig. 2.1).

At every point in time (for example, t 1) the true reaction rate is equal to the tangent of the tangent to the kinetic curve at the point corresponding to a given time. According to the graph, the instantaneous reaction rate will be calculated using the formula:

In biochemistry, it is used to describe the kinetics of enzymatic reactions. Michaelis-Menten equation, which shows the dependence of the rate of reaction catalyzed by an enzyme on the concentration of substrate and enzyme. The simplest kinetic scheme for which the Michaelis equation is valid: E+ S↔ES→E+ P:

Rice. 2.1. Kinetic curve

Where Vm- maximum reaction speed; Km is the Michaelis constant, equal to the substrate concentration at which the reaction rate is half the maximum; S- substrate concentration.

Studying the rate of a chemical reaction allows us to obtain information about its mechanism. In addition to concentration, the reaction rate depends on the nature of the reagents, external conditions and the presence of a catalyst.

2.2. MOLECULARITY AND ORDER OF REACTION. HALF-LIFE

In kinetics, chemical reactions differ in terms of molecularity and reaction order. Molecularity of the reaction determined by the number of particles (atoms, molecules or ions) simultaneously participating in the elementary act of chemical transformation. One, two or three molecules can take part in an elementary reaction. The probability of more particles colliding is very small. Based on this feature, monomolecular, bimolecular and trimolecular reactions are distinguished. Experimentally, the molecularity of a reaction can be determined only for elementary (simple) reactions occurring in one stage in accordance with the stoichiometric equation. For most of these reactions to occur, a large activation energy is required (150-450 kJ/mol).

Most of the reactions are complex. The set of elementary stages that make up a complex reaction is called reaction mechanism

tions. Therefore, to characterize the reaction kinetics, the concept is introduced reaction order, which is determined by the stoichiometric equation.

The sum of the stoichiometric parameters of all starting substances included in the reaction equation (2.5) (a+ b), determines the general order of the reaction. The indicator with which a given reagent enters into the equation is called the reaction order for the substance (partial reaction order), for example, the indicator A- reaction order for substance A, b- for substance B. The reaction order and molecularity are the same only for simple reactions. The order of a reaction is determined by those substances that affect the rate of the reaction.

Monomolecular reactions include decomposition and isomerization reactions.

Reactions whose rate equation includes the concentration of one reactant to the first power are called first-order reactions.

The kinetic equation includes substances whose concentration changes during the reaction. The concentrations of substances that are in significant excess do not change during the reaction.

Water in the hydrolysis reaction of sodium carbonate is in significant excess and is not included in the kinetic equation.

In heterogeneous systems, particle collisions occur at the interface, so the mass of the solid phase does not affect the reaction rate and is therefore not taken into account in the reaction rate expression.

Bimolecular reactions include dimerization reactions and substitution reactions that occur through the stage activated complex.

Reactions whose rate is proportional to the product of the concentrations of two substances to the first power or the square of the concentration of one substance are called second-order reactions.

Trimolecular reactions are rare, and four-molecular reactions are unknown.

Among biochemical processes, third-order reactions do not occur.

Reactions whose rate does not depend on the concentration of the starting substances are called zero-order reactions (v = k).

An example of zero-order reactions is catalytic reactions, the rate of which depends only on the concentration of the catalyst. A special case of such reactions are enzymatic reactions.

As a rule, several reagents (substrate, coenzyme, cofactor) are involved in biochemical processes. Sometimes not all of them are known. Therefore, the progress of the process is judged on one substance. In this case, a quantitative characteristic of the course of reactions over time is half-life period (time) reagent - the time during which the amount or concentration of the starting substance is halved (by 50%) or half of the reaction products are formed. In particular, the decay of radionuclides is characterized in this way, since their half-life does not depend on the initial amount.

By analyzing the dependence of the reaction half-life on the initial concentration, the order of the reaction can be determined (Ostwald-Noyes method). The constancy of the half-life period (at a given temperature) is characteristic of many decomposition reactions and, in general, first-order reactions. As the concentration of the reagent increases, the half-conversion period decreases for second-order reactions and increases for zero-order reactions.

2.3. REACTION RATE CONSTANT, ITS DEFINITION. LAW OF THE ACTING MASSES

The rate of homogeneous reactions depends on the number of encounters of reacting particles per unit time in a unit volume. The probability of collision of interacting particles is proportional to the product of the concentrations of the reacting substances. Thus, the reaction rate is directly proportional to the product of the concentrations of the reacting substances, taken in powers equal to the stoichiometric coefficients of the corresponding substances in the reaction equation. This pattern is called law of mass action(chemical reaction rate law), which is

the basic law of chemical kinetics. The law of mass action was established by Norwegian scientists K. Guldberg and P. Vahe in 1867.

For example, for a reaction proceeding in general form, according to the scheme

the kinetic equation will be valid:

Where v- rate of chemical reaction; with A And with B- concentrations of substances A And IN[mol/l]; v a And v b- order indicators for reagents A and B; k- rate constant of a chemical reaction - a coefficient that does not depend on the concentration of reactants.

Chemical reaction rate constant (k) represents the rate of a chemical reaction under conditions where the product of the concentrations of the reactants is 1 mol/l. In this case v = k.

For example, if in the reaction H 2 (g) + I 2 (g) = 2HI (g) c(H 2) and c(I 2) are equal to 1 mol/l or if c(H 2) is equal to 2 mol/l , and c(I 2) 0.5 mol/l, then v= k.

The units of equilibrium constant are determined by the stoichiometry of the reaction. It is incorrect to compare the rate constants of reactions of different orders with each other, since they are different quantities with different meanings and have different dimensions.

2.4. MECHANISM OF CHEMICAL REACTIONS. CLASSIFICATION OF COMPLEX REACTIONS

The reaction mechanism considers all collisions of individual particles that occur simultaneously or sequentially. The mechanism gives a detailed stoichiometric picture of each reaction step, i.e. understanding the mechanism means establishing the molecularity of each reaction step. Studying the mechanism of chemical reactions is a very difficult task. After all, we cannot carry out direct observations of the progress of the interaction of molecules. The results obtained sometimes depend on the size and shape of the vessel. In some cases, the same results can be explained using different mechanisms.

The reaction of hydrogen gas with iodine H 2 (g) + I 2 (g) = 2HI (g) was considered a classic example of a bimolecular reaction of the second

order, but in 1967 N.N. Semenov, G. Eyring and J. Sullivan showed that it is complex and consists of 3 elementary reactions: I 2 = 2I; 2I = I 2 ; 2I + H2 = 2HI. Although the reaction can formally be classified as trimolecular, its rate is described by a kinetic equation reminiscent of the second-order reaction equation:

In complex reactions, molecularity and reaction order usually do not coincide. An unusual - fractional or negative - order of a reaction clearly indicates its complex mechanism.

The kinetic equation for the oxidation of carbon monoxide with oxygen 2CO (g) + O 2 (g) = CO 2 (g) has a negative (minus first) order with respect to CO:

As the carbon monoxide concentration increases, the reaction rate decreases.

According to the mechanism of reaction, reactions can be divided into several types.

Consistent reactions are called complex reactions, in each of which the product (X 1) of the first elementary stage reacts with the product of the second stage, the product (X 2) of the second stage enters into the third, etc., until the final product is formed:

Where S- substrate (initial reagent); k 1, k 2, k 3 ... - rate constant 1, 2, etc. reaction stages; P- final product.

The stages of successive reactions occur at different rates. The stage whose rate constant is minimal is called limiting. It determines the kinetic pattern of the reaction as a whole. Substances formed in intermediate stages are called intermediate products or intermediates, which are substrates for subsequent stages. If an intermediate forms slowly and quickly decomposes, then its concentration does not change for a long time. Almost all metabolic processes are sequential reactions (for example, glucose metabolism).

Parallel reactions are reactions that have the same starting reagents and which correspond to different products. WITH The speed of parallel reactions is equal to the sum of the speeds of individual reactions. This rule also applies to bimolecular parallel chemical reactions.

Series-parallel reactions are called reactions that have the same initial reagents, which can react along two or more pathways (mechanisms), including with a different number of intermediate stages. This case underlies the phenomenon catalysis, when an intermediate in one of the pathways will increase the speed of other pathways.

Competing reactions called complex reactions in which the same substance A simultaneously interacts with one or more reagents B 1, B 2 etc., participates in simultaneously occurring reactions: A+ B 1 → X 1 ; A+ B 2 → X 2. These reactions compete with each other for the reagent A.

Conjugate reactions are complex reactions in which one reaction occurs only in the presence of another. In coupled reactions, the intermediate substance serves as a link between the primary and secondary processes and determines the occurrence of both.

A living cell needs energy to exist. A universal source of energy in living organisms is adenosine triphosphoric acid (ATP). This compound acts as an energy accumulator, since when it interacts with water, i.e. hydrolysis, adenosine diphosphoric (ADP) and phosphoric (P) acids are formed and energy is released. That's why it's called ATP macroergic compound, and the P-O-P bond that breaks during its hydrolysis is high-energy. Macroergic connection is a chemical bond that, when broken as a result of a hydrolysis reaction, releases significant energy:

As you know, breaking any connection (including high-energy ones) always requires energy expenditure. In the case of ATP hydrolysis, in addition to the process of breaking the bond between phosphate groups, for which Δ G>0, the processes of hydration, isomerization and neutralization of products formed during hydrolysis occur. As a result of all these processes, the total change in the Gibbs energy is negative

meaning. Consequently, it is not the breaking of a bond that is macroergic, but the energetic result of its hydrolysis.

In order for endergonic reactions (ΔG >0) to occur in living systems, it is necessary that they be coupled with exergonic reactions (ΔG<0). Такое сопряжение возможно, если обе реакции имеют какое-либо общее промежуточное соединение, и на всех стадиях сопряженных реакций суммарный процесс характеризуется отрицательным значением изменения энергии Гиббса (∑ΔG сопр.р <0). Например, синтез сахарозы является эндэргонической реакцией и самопроизвольно происходить не может:

However, the coupling of this reaction with the exergonic reaction of ATP hydrolysis, accompanied by the formation of a common intermediate compound glucose-1-phosphate, leads to the fact that the overall process has ∑ΔG<0:

Chain reactions are chemical and nuclear reactions in which the appearance of an active particle (a free radical or atom in chemical processes, a neutron in nuclear processes) causes a large number (chain) of successive transformations of inactive molecules or nuclei. Chain reactions are common in chemistry. Many photochemical reactions, oxidation processes (combustion, explosion), polymerization, and cracking occur via a chain mechanism. The theory of chain reactions was developed by academician H.H. Semenov, S.N. Hinshelwood (England) and others. The main stages of chain reactions are: origin (initiation), continuation (elongation) and chain termination (termination). There are two types of chain reactions: reactions with unbranched and branched chains. The peculiarity of chain reactions is that one primary act of activation leads to the transformation of a huge number of molecules of the starting substances. Biochemical reactions of free radical oxidation are chain reactions.

Periodic (self-oscillating) reactions are complex multi-stage autocatalytic reactions involving several substances in which periodic fluctuations in the concentrations of oxidized and reduced forms occur. Oscillatory reactions discovered by B.P. Belousov, studied by A.M. Zhabotinsky and others. The frequency and shape of vibrations depend on the concentrations of the starting substances, acids

ness, temperature. An example of such reactions is the interaction of bromomalonic acid with potassium bromate in an acidic environment, the catalyst being a cerium (III) salt. Periodic reactions are of great importance for biological objects, where reactions of this kind are widespread.

Solid-phase combustion reactions(reactions of self-propagating high-temperature synthesis, SHS) were discovered in 1967 at the Institute of Chemical Physics of the USSR Academy of Sciences by A.G. Merzhanov and I.G. Borovinskaya. The essence of the SHS method is that after local initiation of the interaction reaction of the reagents, the front of the combustion reaction spontaneously spreads throughout the system due to heat transfer from hot products to the starting substances, initiating the occurrence of the interaction reaction in them. Thus, the combustion process occurs, which is both the cause and the consequence of the reaction. The mechanism of SHS reactions is quite complex and includes the processes reaction diffusion. The term “reactive diffusion” defines a set of phenomena that occur during the interaction of two chemically different components capable of forming chemical compounds in the form of solid phases. The products of chemical interaction form a continuous layer that differs in structure from the original components, but does not interfere with further interaction.

2.5. THEORY OF ACTIVE COLLISIONS. ACTIVATION ENERGY. DEPENDENCE OF THE RATE OF REACTION ON THE NATURE OF REACTING SUBSTANCES AND TEMPERATURE

In order for an elementary act of chemical interaction to take place, the reacting particles must collide with each other. However, not every collision results in a chemical reaction. The latter occurs when particles approach distances at which redistribution of electron density and the emergence of new chemical bonds are possible. The interacting particles must have sufficient energy to overcome the repulsive forces that arise between their electron shells.

Transition state- a state of the system in which the destruction and creation of connections are balanced. In a transition state the system

is located for a short (10 -15 s) time. The energy that must be expended to bring the system into a transition state is called activation energy. In multistep reactions that include several transition states, the activation energy corresponds to the highest energy value. After overcoming the transition state, the molecules scatter again with the destruction of old bonds and the formation of new ones or with the transformation of the original bonds. Both options are possible, as they occur with the release of energy. There are substances that can reduce the activation energy for a given reaction.

Active molecules A 2 and B 2 upon collision combine into an intermediate active complex A 2 ... B 2 with weakening and then breaking of the A-A and B-B bonds and strengthening of the A-B bonds.

The “activation energy” of the reaction for the formation of HI (168 kJ/mol) is significantly less than the energy required to completely break the bond in the initial molecules H 2 and I 2 (571 kJ/mol). Therefore, the reaction path through the formation active (activated) complex energetically more favorable than the path through the complete rupture of bonds in the original molecules. The vast majority of reactions occur through the formation of intermediate active complexes. The principles of the theory of the active complex were developed by G. Eyring and M. Polyani in the 30s of the 20th century.

Activation energy represents the excess kinetic energy of particles relative to the average energy required for the chemical transformation of colliding particles. Reactions are characterized by different activation energies (Ea). In most cases, the activation energy of chemical reactions between neutral molecules ranges from 80 to 240 kJ/mol. For biochemical processes, the values ​​of E a are often lower - up to 20 kJ/mol. This is explained by the fact that the vast majority of biochemical processes proceed through the stage of enzyme-substrate complexes. Energy barriers limit the reaction. Due to this, in principle, possible reactions (with G<0) практически всегда не протекают

or slow down. Reactions with activation energies above 120 kJ/mol are so slow that their occurrence is difficult to detect.

For a reaction to occur, the molecules must be oriented in a certain way and have sufficient energy when they collide. The probability of proper collision orientation is characterized by activation entropyΔ S a. The redistribution of electron density in the active complex is favored by the condition when, upon collision, molecules A 2 and B 2 are oriented, as shown in Fig. 2.2, a, whereas with the orientation shown in Fig. 2.2, b, the probability of reaction is even much less - in Fig. 2.2, c.

Rice. 2.2. Favorable (a) and unfavorable (b, c) orientations of A 2 molecules

and B 2 in a collision

The equation characterizing the dependence of the rate and reaction on temperature, activation energy and activation entropy has the form:

Where k- reaction rate constant; A is, to a first approximation, the total number of collisions between molecules per unit of time (second) per unit volume; e is the base of natural logarithms; R- universal gas constant; T- absolute temperature; E a- activation energy; Δ S a- change in activation entropy.

Equation (2.8) was derived by Arrhenius in 1889. The pre-exponential factor A is proportional to the total number of collisions between molecules per unit time. Its dimension coincides with the dimension of the rate constant and, therefore, depends on the total order of the reaction. The exponent is equal to the proportion of active collisions from their total number, i.e. colliding molecules must have sufficient

exact interaction energy. The probability of their desired orientation at the moment of impact is proportional to e ΔSa/R

When discussing the law of mass action for speed (2.6), it was specifically stated that the rate constant is a constant value that does not depend on the concentrations of the reactants. It was assumed that all chemical transformations occur at a constant temperature. At the same time, it is well known that the rate of chemical transformation can change significantly with decreasing or increasing temperature. From the point of view of the law of mass action, this change in speed is due to the temperature dependence of the rate constant, since the concentrations of the reacting substances change only slightly due to thermal expansion or compression of the liquid.

The most well-known fact is that the rate of reactions increases with increasing temperature. This type of temperature dependence of speed is called normal (Fig. 2.3, a). This type of dependence is characteristic of all simple reactions.

Rice. 2.3. Types of temperature dependence of the rate of chemical reactions: a - normal; b - abnormal; c - enzymatic

However, chemical transformations are now well known, the rate of which decreases with increasing temperature. An example is the gas-phase reaction of nitrogen (II) oxide with bromine (Fig. 2.3, b). This type of temperature dependence of speed is called anomalous.

Of particular interest to physicians is the temperature dependence of the rate of enzymatic reactions, i.e. reactions involving enzymes. Almost all reactions occurring in the body belong to this class. For example, during the decomposition of hydrogen peroxide in the presence of the enzyme catalase, the rate of decomposition depends on temperature. In the range of 273-320 °K, the temperature dependence is normal. As the temperature increases, the speed increases, and as the temperature decreases, it decreases. When the temperature rises above

At 320 °K, a sharp anomalous drop in the rate of peroxide decomposition is observed. A similar picture occurs for other enzymatic reactions (Fig. 2.3, c).

From the Arrhenius equation for k it is clear that, since T included in the exponent, the rate of a chemical reaction is very sensitive to temperature changes. The dependence of the rate of a homogeneous reaction on temperature can be expressed by the van’t Hoff rule, according to which with every 10° increase in temperature, the reaction rate increases by 2-4 times; a number showing how many times the rate of a given reaction increases with an increase in temperature by 10° is called temperature coefficient of reaction rate- γ.

Where k- rate constant at temperature t°C. Knowing the value of γ, it is possible to calculate the change in reaction rate when the temperature changes from T 1 before T 2 according to the formula:

As the temperature increases in an arithmetic progression, the speed increases in a geometric progression.

For example, if γ = 2.9, then with an increase in temperature by 100° the reaction rate increases by 2.9 10 times, i.e. 40 thousand times. Deviations from this rule are biochemical reactions, the speed of which increases tens of times with a slight increase in temperature. This rule is only valid to a rough approximation. Reactions involving large molecules (proteins) are characterized by a large temperature coefficient. The rate of denaturation of protein (egg albumin) increases 50 times with an increase in temperature by 10 °C. After reaching a certain maximum (50-60 °C), the reaction rate sharply decreases as a result of thermal denaturation of the protein.

For many chemical reactions the law of mass action for speed is unknown. In such cases, the expression can be used to describe the temperature dependence of the conversion rate:

Pre-exponent And with does not depend on temperature, but depends on concentration. The unit of measurement is mol/l s.

The theoretical dependence allows the speed to be calculated in advance at any temperature if the activation energy and pre-exponential are known. Thus, the influence of temperature on the rate of chemical transformation is predicted.

2.6. REVERSABLE AND IRREVERSIBLE REACTIONS. STATE OF CHEMICAL EQUILIBRIUM. REACTION ISOTHERM EQUATION

A chemical reaction does not always “reach completion”; in other words, the starting substances are not always completely converted into reaction products. This occurs because as reaction products accumulate, conditions may be created for the reaction to proceed in the opposite direction. Indeed, if, for example, you mix iodine vapor with hydrogen at a temperature of ~200 °C, the reaction will occur: H 2 + I 2 = 2HI. However, it is known that hydrogen iodide, even when heated to 180 ° C, begins to decompose into iodine and hydrogen: 2HI = H 2 + I 2.

Chemical reactions that, under the same conditions, can proceed in opposite directions are called reversible. When writing equations for reversible reactions, instead of the equal sign, two oppositely directed arrows are used. A reaction that occurs from left to right is called straight(forward reaction rate constant k 1), from right to left - reverse(back reaction rate constant k 2).

In reversible reactions, the rate of the direct reaction initially has a maximum value, and then decreases due to a decrease in the concentration of the starting substances. Conversely, the reverse reaction at the initial moment has a minimum speed, which increases as the concentration of reaction products increases. Finally, a moment comes when the rates of the forward and reverse reactions become equal. The state in which the rate of the reverse reaction becomes equal to the rate of the forward reaction is called chemical equilibrium.

The state of chemical equilibrium of reversible processes is quantitatively characterized equilibrium constant. At the moment of reaching a state of chemical equilibrium, the rates of forward and reverse reactions are equal (kinetic condition).

where K - equilibrium constant, which is the ratio of the rate constants of the forward and reverse reactions.

On the right side of the equation are those concentrations of interacting substances that are established at equilibrium - equilibrium concentrations. This equation is a mathematical expression of the law of mass action in chemical equilibrium. It should be especially noted that, in contrast to the law of mass action for the reaction rate in this equation, the exponents a, b, d, f and etc. are always equal to the stoichiometric coefficients in the equilibrium reaction.

The numerical value of the equilibrium constant of a given reaction determines its yield. Reaction output they call the ratio of the amount of product actually obtained to the amount that would have been obtained if the reaction had proceeded to completion (usually expressed as a percentage). Thus, at K >>1 the reaction yield is high and, conversely, at K<<1 выход реакции очень мал.

The equilibrium constant is related to standard Gibbs energy reactions with the following ratio:

Using equation (2.12), we can find the value of the Gibbs energy of the reaction through equilibrium concentrations:

This equation is called chemical reaction isotherm equation. It allows you to calculate the change in the Gibbs energy during the process and determine the direction of the reaction:

at ΔG<0 - реакция идет в прямом направлении, слева направо;

At ΔG = 0 - the reaction has reached equilibrium (thermodynamic condition);

when ΔG >0, the reaction proceeds in the opposite direction.

It is important to understand that the equilibrium constant does not depend on the concentrations of substances. The opposite statement is true: in a state of equilibrium, the concentrations themselves take such values ​​that the ratio of their products in powers of stoichiometric coefficients

turns out to be a constant value at a given temperature. This statement corresponds to the law of mass action and can even be used as one of its formulations.

As mentioned above, reversible reactions do not proceed to completion. However, if one of the products of a reversible reaction leaves the reaction sphere, then the essentially reversible process proceeds almost to completion. If electrolytes are involved in a reversible reaction and one of the products of this reaction is a weak electrolyte, precipitate or gas, then in this case the reaction also proceeds almost to completion. Irreversible reactions These are reactions whose products do not interact with each other to form the starting substances. Irreversible reactions, as a rule, “reach the end”, i.e. until at least one of the starting substances is completely consumed.

2.7. LE CHATELIER'S PRINCIPLE

The state of chemical equilibrium under constant external conditions can theoretically be maintained indefinitely. In reality, when the temperature, pressure or concentration of reagents changes, the equilibrium can “shift” to one side or another of the process.

Changes occurring in the system as a result of external influences are determined by the principle of moving equilibrium - Le Chatelier's principle.

An external influence on a system that is in a state of equilibrium leads to a shift in this equilibrium in a direction in which the effect of the effect is weakened.

In relation to the three main types of external influence - changes in concentration, pressure and temperature - Le Chatelier's principle is interpreted as follows.

When the concentration of one of the reactants increases, the equilibrium shifts towards the consumption of this substance; when the concentration decreases, the equilibrium shifts towards the formation of this substance.

The effect of pressure is very similar to the effect of changing the concentrations of reacting substances, but it affects only gas systems. Let us formulate a general statement about the effect of pressure on chemical equilibrium.

With increasing pressure, the equilibrium shifts towards decreasing amounts of gaseous substances, i.e. in the direction of decreasing pressure; as pressure decreases, equilibrium shifts toward increasing

quantities of gaseous substances, i.e. towards increasing pressure. If the reaction proceeds without changing the number of molecules of gaseous substances, then pressure does not affect the equilibrium position in this system.

When temperature changes, both forward and reverse reactions change, but to varying degrees. Therefore, to clarify the effect of temperature on chemical equilibrium, it is necessary to know the sign of the thermal effect of the reaction.

As the temperature increases, the equilibrium shifts towards the endothermic reaction, and as the temperature decreases, towards the exothermic reaction.

In relation to biosystems, Le Chatelier's principle states that in a biosystem, for each action, a reaction of the same strength and nature is formed, which balances biological regulatory processes and reactions and forms a conjugate level of their disequilibrium.

In pathological processes, the existing closedness of the regulatory circuit is disrupted. Depending on the level of disequilibrium, the quality of intersystem and interorgan relations changes; they become increasingly nonlinear. The structure and specificity of these relationships is confirmed by the analysis of the relationship between the indicators of the lipid peroxidation system and the level of antioxidants, between harmonic indicators in conditions of adaptation and pathology. These systems are involved in maintaining antioxidant homeostasis.

2.8. QUESTIONS AND TASKS FOR SELF-CHECKING PREPARATION FOR CLASSES AND EXAMINATIONS

1.Which reactions are called homogeneous and which heterogeneous? Give one example of each type of reaction.

2.Which reactions are called simple and which complex? Give two examples each of simple and complex reactions.

3. In what case can the molecularity and order of the kinetic equation numerically coincide?

4. The speed of a certain reaction does not change over time. Will the half-life of this reaction change over time, and if so, how? Give an explanation.

5. In what case can the true (instantaneous) speed and the average reaction speed (in a sufficiently large time interval) coincide?

6. Calculate the rate constant of the reaction A + B → AB, if at concentrations of substances A and B equal to 0.5 and 0.1 mol/l, respectively, its rate is 0.005 mol/l min.

7. The half-life of a certain first-order reaction is 30 minutes. What fraction of the initial amount of the substance will remain after an hour?

8.Give the concept of the general reaction order and the reaction order by substance.

9.Methods for determining the reaction rate.

10.Basic law of chemical kinetics.

11.Give the concept of the mechanism of chemical reactions.

12.Simple and complex reactions.

13.Conjugate reactions. On what factors does the rate constant of chemical reactions depend?

14. Is the reaction rate really proportional to the product of the concentrations of the reacting substances to the power of their stoichiometric coefficients?

15.What experimental data are required to determine the order of reactions?

16. Write the kinetic equation for the reaction H 2 O 2 + 2HI → I 2 + + 2H 2 O if equal volumes of 0.02 mol/L H 2 O 2 solution and 0.05 mol/L HI solution are mixed. Rate constant 0.05 l/mol s.

17. Write the kinetic equation for the reaction H 2 O 2 + 2HI → I 2 + + 2H 2 O, taking into account that it is characterized by a first-order reaction in the concentrations of both starting substances.

18.Prove that the rate of a chemical reaction is maximum at a stoichiometric ratio of components.

19.List possible explanations for the effect of temperature on the reaction rate.

2.9. TEST TASKS

1. According to Van't Hoff's rule, when the temperature increases by 10°, the rate of many reactions:

a) decreases by 2-4 times;

b) decreases by 5-10 times;

c) increases 2-4 times;

d) increases 5-10 times.

2. The number of elementary acts of interaction per unit of time determines:

a) reaction order;

b) reaction speed;

c) molecularity of the reaction;

d) half-life.

3. What factors influence the increase in reaction rate?

a) the nature of the reacting substances;

b) temperature, concentration, catalyst;

c) only catalyst;

d) concentration only;

e) only temperature.

4. How many times will the rate of reaction 2A(g) + B(g) increase?→A 2 B(g) when the concentration of substance A is doubled?

a) the speed will not change;

b) will increase 18 times;

c) will increase 8 times;

d) will increase 4 times;

d) will increase by 2 times.

5. Elementary reaction A(s) + 2B(g)→AB 2 (d). Specify the correct kinetic equation for this reaction:

a)k[A][B] 2 ;

b)k[A][B];

c)k[B];

d)k[B] 2;

d)k[A].

6. How to change the pressure in the system to increase the rate of reaction A(s) + 2B(g)→AB 2 (d) 9 times?

a) increase the pressure 9 times;

b) reduce the pressure by 9 times;

c) increase the pressure 3 times;

d) reduce the pressure by 3 times.

7. What is the temperature coefficient of the reaction?γ 10 , if when the reaction mixture is cooled by 30°, the reaction rate decreases 8 times?

a)16;

b)8;

at 6;

d)4;

D 2.

8. Which reaction is faster?

A) E act= 40 kJ/mol;

b) E act = 80 kJ/mol;

V) E act = 160 kJ/mol;

G) E act = 200 kJ/mol.

Chemical reaction rate

Chemical reaction rate is defined as the change in the molar concentration of one of the reactants per unit time. The rate of a chemical reaction is always a positive value, so if it is determined by the starting substance (the concentration of which decreases during the reaction), then the resulting value is multiplied by -1.
For example, for a reaction, the speed can be expressed as follows:

In 1865 N.N. Beketov and in 1867 K.M. Guldberg and P. Waage formulated the law of mass action, according to which the rate of a chemical reaction at each moment of time is proportional to the concentrations of the reagents raised to certain powers. In addition to concentration, the rate of a chemical reaction is influenced by the following factors: the nature of the reacting substances, the presence of a catalyst, temperature (van't Hoff's rule) and the surface area of ​​the reacting substances.

Order of chemical reaction

ORDER OF REACTION for a given substance is the exponent at the concentration of this substance in the kinetic equation of the reaction.

Transition state

Catalysis

Catalysis is a process that involves changing the rate of chemical reactions in the presence of substances called catalysts.
Catalysts are substances that change the rate of a chemical reaction, which can participate in a reaction, be part of intermediate products, but are not part of the final reaction products and remain unchanged after the end of the reaction.
Catalytic reactions are reactions that occur in the presence of catalysts.

Catalysis is called positive when the reaction rate increases, and negative (inhibition) when it decreases. An example of positive catalysis is the oxidation of ammonia on platinum to produce nitric acid. An example of a negative is the reduction in corrosion rate when sodium nitrite, potassium chromate and dichromate are introduced into the liquid in which the metal is used.
Catalysts that slow down a chemical reaction are called inhibitors.
Depending on whether the catalyst is in the same phase as the reactants or forms an independent phase, we speak of homogeneous or heterogeneous catalysis.
An example of homogeneous catalysis is the decomposition of hydrogen peroxide in the presence of iodine ions. The reaction occurs in two stages:
H O + I = H O + IO
H O + IO = H O + O + I
In homogeneous catalysis, the action of the catalyst is due to the fact that it interacts with reacting substances to form intermediate compounds, this leads to a decrease in activation energy.
In heterogeneous catalysis, the acceleration of the process usually occurs on the surface of a solid body - the catalyst, therefore the activity of the catalyst depends on the size and properties of its surface. In practice, the catalyst is usually supported on a solid porous support. The mechanism of heterogeneous catalysis is more complex than that of homogeneous catalysis.
The mechanism of heterogeneous catalysis includes five stages, all of which are reversible.
1. Diffusion of reacting substances to the surface of a solid.
2. Physical adsorption on the active centers of the surface of a solid substance of reacting molecules and then their chemisorption.
3. Chemical reaction between reacting molecules.
4. Desorption of products from the catalyst surface.
5. Diffusion of the product from the surface of the catalyst into the general flow.
An example of heterogeneous catalysis is the oxidation of SO to SO over a VO catalyst in the production of sulfuric acid (contact method).
Promoters (or activators) are substances that increase the activity of the catalyst. In this case, promoters themselves may not have catalytic properties.
Catalytic poisons are foreign impurities in the reaction mixture, leading to partial or complete loss of catalyst activity. Thus, traces of arsenic and phosphorus cause a rapid loss of VO activity by the catalyst (contact method for the production of HSO).
Many important chemical productions, such as the production of sulfuric acid, ammonia, nitric acid, synthetic rubber, a number of polymers, etc., are carried out in the presence of catalysts.
Biochemical reactions in plant and animal organisms are accelerated by biochemical catalysts - enzymes.
Process speed is an extremely important factor determining the productivity of chemical production equipment. Therefore, one of the main tasks posed to chemistry by the scientific and technological revolution is the search for ways to increase the rate of reactions. Another important task of modern chemistry, due to the sharply increasing scale of production of chemical products, is increasing the selectivity of chemical transformations into useful products, reducing the amount of emissions and waste. This is also related to environmental protection and more rational use of unfortunately depleting natural resources.
To achieve all these goals, the right means are needed, and such means are primarily catalysts. However, finding them is not so easy. In the process of understanding the internal structure of the things around us, scientists have established a certain gradation, a hierarchy of levels of the microworld. The world described in our book is the world of molecules, the mutual transformations of which constitute the subject of chemistry. We will not be interested in all of chemistry, but only in part of it, devoted to the study of the dynamics of changes in the chemical structure of molecules. Apparently there is no need to say that molecules are built from atoms, and the latter are made from a nucleus and the electron shell surrounding it; that the properties of molecules depend on the nature of their constituent atoms and the sequence of their connection with each other; that the chemical and physical properties of substances depend on the properties of molecules and the nature of their interconnection. We will assume that all this is generally known to the reader, and therefore the main emphasis will be on issues related to the idea of ​​\u200b\u200bthe rate of chemical reactions.
Mutual transformations of molecules occur at very different rates. The rate can be changed by heating or cooling the mixture of reacting molecules. When heated, the reaction rate usually increases, but this is not the only means of accelerating chemical transformations. There is another, more effective method - catalytic, widely used in our time in the production of a wide variety of products.
The first scientific ideas about catalysis arose simultaneously with the development of the atomic theory of the structure of matter. In 1806, a year after Dalton, one of the founders of modern atomic theory, formulated the law of multiple ratios in the Proceedings of the Manchester Literary and Philosophical Society, Clément and Desormes published detailed data on the acceleration of the oxidation of sulfur dioxide in the presence of nitrogen oxides at room temperature. production of sulfuric acid. Six years later, in the Technology Journal, Kirchhoff presented the results of his observations on the accelerating effect of dilute mineral acids on the hydrolysis of starch to glucose. These two observations opened the era of experimental study of chemical phenomena unusual for that time, to which the Swedish chemist Berzelius gave the general name “catalysis” in 1835 from the Greek word “kataloo” - to destroy. This, in a nutshell, is the history of the discovery of catalysis, which with good reason should be classified as one of the fundamental phenomena of nature.
Now we should give the modern and most generally accepted definition of catalysis, and then some general classification of catalytic processes, since this is where any exact science begins. As you know, “physics is what physicists do (the same can be said about chemistry).” Following this instruction from Bergman, one could confine oneself to the statement that “catalysis is something that both chemists and physicists do.” But, naturally, such a humorous explanation is not enough, and since the time of Berzelius, many scientific definitions have been given to the concept of “catalysis.” In our opinion, the best definition is formulated by G.K. Vereskov: “Phenomenologically, catalysis can be defined as the excitation of chemical reactions or a change in their speed under the influence of substances - catalysts that repeatedly enter into intermediate chemical interactions with reaction participants and restore their chemical composition after each cycle of intermediate interactions "
The strangest thing about this definition is its final part - the substance that accelerates the chemical process is not consumed. If it is necessary to accelerate the movement of a heavy body, it is pushed and, therefore, energy is expended on this. The more energy spent, the greater the speed the body acquires. Ideally, the amount of energy expended will be exactly equal to the kinetic energy acquired by the body. This reveals the fundamental law of nature - conservation of energy.

Prominent figures in chemistry on catalysis

I. Berzelius (1837): “Known substances, when in contact with other substances, have such an influence on the latter that a chemical effect occurs - some substances are destroyed, others are formed again without the body, whose presence causes these transformations, taking on any -participation. We call the cause that produces these phenomena the catalytic force.”

M. Faraday (1840). “Catalytic phenomena can be explained by the known properties of matter, without supplying it with any new force.”

P. Raschig (1906): “Catalysis is a change in the structure of a molecule caused by external factors, resulting in a change in chemical properties.”

E. Abel (1913): “I have come to the conclusion that catalysis is effected by a reaction and not by the mere presence of a substance.”

L. Gurvich (1916): “Catalytically acting bodies, attracting moving molecules to themselves much stronger than bodies lacking catalytic action, thereby increasing the impact force of molecules hitting their surface.”

G.K. Boreskov (1968): “Once upon a time, catalysis was considered as a special, slightly mysterious phenomenon, with specific laws, the disclosure of which was supposed to immediately solve the selection problem in a general form. Now we know that this is not so. Catalysis in its essence is a chemical phenomenon. The change in the reaction rate during catalytic action is due to the intermediate chemical interaction of the reactants with the catalyst.”

If we do not take into account Berzelius's unsuccessful attempt to connect the observed phenomena with the action of a hidden "catalytic force", then, as can be seen from the above speeches, the discussion was mainly around the physical and chemical aspects of catalysis. For a long time, the energy theory of catalysis was especially popular, linking the process of excitation of molecules with resonant migration of energy. The catalyst interacts with reacting molecules, forming unstable intermediate compounds that decompose to release the reaction product and the chemically unchanged catalyst. Our modern knowledge is best reflected in Boreskov's statement. Here, however, the question arises: could the catalyst, since it itself chemically participates in the reaction, create a new equilibrium state? If this were so, then the idea of ​​the chemical participation of the catalyst would immediately conflict with the law of conservation of energy. To avoid this, scientists were forced to accept and then experimentally prove that the catalyst accelerates the reaction not only in the forward but also in the reverse direction. Those compounds that change both the rate and equilibrium of a reaction are not catalysts in the strict sense of the word. It remains for us to add that usually in the presence of a catalyst there is an acceleration of chemical reactions, and this phenomenon is called “positive” catalysis in contrast to “negative”, in which the introduction of a catalyst into the reaction system causes a decrease in the rate. Strictly speaking, catalysis always increases the rate of a reaction, but sometimes the acceleration of one of the stages (for example, the emergence of a new chain termination pathway) leads to the observed inhibition of a chemical reaction.

We will consider only positive catalysis, which is usually divided into the following types:

a) homogeneous, when the reaction mixture and catalyst are either in a liquid or gaseous state; b) heterogeneous - the catalyst is in the form of a solid substance, and the reacting compounds are in the form of a solution or gaseous mixture; (This is the most common type of catalysis, carried out, therefore, at the interface between two phases.) c) enzymatic - complex protein formations serve as catalysts, accelerating the course of biologically important reactions in organisms of the plant and animal world. (Enzyme catalysis can be either homogeneous or heterogeneous, but due to the specific features of the action of enzymes, it is advisable to separate this type of catalysis into an independent area.) Homogeneous catalysis

Among the numerous catalytic reactions, catalysis occupies a special place in chain reactions. “Chain reactions, as is known, are those chemical and physical processes in which the formation of some active particles (active centers) in a substance or in a mixture of substances leads to the fact that each of the active particles causes a whole series (chain) of sequential transformations of the substance” ( Emanuel, 1957).

This mechanism for the development of the process is possible due to the fact that the active particle interacts with the substance, forming not only reaction products, but also a new active particle (one, two or more), capable of a new reaction of converting the substance, etc. The resulting chain transformations of the substance continue until the active particle disappears from the system (the “death” of the active particle and the chain break occur). The most difficult stage in this case is the nucleation of active particles (for example, free radicals), but after nucleation the chain of transformations occurs easily. Chain reactions are widespread in nature. Polymerization, chlorination, oxidation and many other chemical processes follow a chain, or rather, a radical-chain (with the participation of radicals) mechanism. The mechanism of oxidation of organic compounds (in early stages) has now been established quite thoroughly. If we denote the oxidizing substance R-H (where H is the hydrogen atom that has the lowest bond strength with the rest of the R molecule), then this mechanism can be written in the following form:

Catalysts, such as compounds of variable valence metals, can influence any of the considered stages of the process. Let us now dwell on the role of catalysts in processes of degenerate chain branching. The interaction of hydroperoxide with a metal can lead to both acceleration and inhibition of the oxidation reaction of organic substances by metal compounds of variable valency, depending on the nature of the products formed during the decomposition of hydroperoxide. Metal compounds form a complex with hydroperoxides, which disintegrates in the “cage” of the solvent medium; if the radicals formed during the decomposition of the complex manage to leave the cell, then they initiate the process (positive catalysis). If these radicals do not have time to leave and recombine in the cell into molecular inactive products, then this will lead to a slowdown of the radical chain process (negative catalysis), since in this case hydroperoxide, a potential supplier of new radicals, is wasted.

So far we have considered only shallow stages of oxidation processes; at deeper stages, for example in the case of the oxidation of hydrocarbons, acids, alcohols, ketones, and aldehydes are formed, which can also react with the catalyst and serve as an additional source of free radicals in the reaction, i.e. in this case there will be additional degenerate chain branching.

Heterogeneous catalysis

Unfortunately, until now, despite a fairly large number of theories and hypotheses in the field of catalysis, many fundamental discoveries have been made by chance or as a result of a simple empirical approach. As you know, a mercury catalyst for the sulfonation of aromatic hydrocarbons was accidentally discovered by M.A. Ilyinsky, who accidentally broke a mercury thermometer: mercury entered the reactor, and the reaction began. In a similar way, the now well-known Ziegler catalysts, which at one time opened a new era in the polymerization process, were discovered. Naturally, this path of development of the doctrine of catalysis does not correspond to the modern level of science, and this explains the increased interest in the study of the elementary stages of processes in heterogeneous catalytic reactions. These studies are a prelude to creating a strictly scientific basis for the selection of highly efficient catalysts. In many cases, the role of heterogeneous catalysts in the oxidation process is reduced to the adsorption of an organic compound and oxygen with the formation of an adsorbed complex of these substances on the surface of the catalyst. This complex loosens the bonds of the components and makes them more reactive. In some cases, the catalyst adsorbs only one component, which dissociates into radicals. For example, propylene on cuprous oxide dissociates to form an allylic radical, which then easily reacts with oxygen. It turned out that the catalytic activity of metals of variable valence largely depends on the filling of d-orbitals in cations of metal oxides.

According to the catalytic activity in the decomposition reaction of many hydroperoxides, metal compounds are arranged in the following order:

We considered one of the possible ways to initiate the process - the interaction of hydroperoxide with the catalyst. However, in the case of oxidation, the reaction of heterogeneous chain initiation can occur both through decomposition into hydroperoxide radicals and through the interaction of the hydrocarbon with oxygen activated by the catalyst surface. The initiation of chains may be due to the participation of the charged form of the organic compound RH+, formed during the interaction of RH with the catalyst. This is the case with catalysis in chain initiation (nucleation and branching) reactions. The role of heterogeneous catalysts in chain continuation reactions is especially clearly emphasized by changes in the rate and direction of isomerization of peroxide radicals.

Catalysis in biochemistry

Enzymatic catalysis is inextricably linked with the life activity of plant and animal organisms. Many of the vital chemical reactions that occur in a cell (something like ten thousand) are controlled by special organic catalysts called enzymes or enzymes. The term “special” should not be given close attention, since it is already known what these enzymes are made of. Nature chose for this purpose one single building material - amino acids and connected them into polypeptide chains of various lengths and in different sequences

This is the so-called primary structure of the enzyme, where R are side residues, or the most important functional groups of proteins, possibly acting as active centers of enzymes. These side groups bear the main load during the operation of the enzyme, while the peptide chain plays the role of a supporting skeleton. According to the Pauling-Corey structural model, it is folded into a helix, which in the normal state is stabilized by hydrogen bonds between acidic and basic centers:

For some enzymes, the complete amino acid composition and sequence of their location in the chain, as well as a complex spatial structure, have been established. But this still very often cannot help us answer two main questions: 1) why enzymes are so selective and accelerate the chemical transformations of molecules only of a well-defined structure (which is also known to us); 2) how the enzyme reduces the energy barrier, i.e., chooses an energetically more favorable path, so that reactions can proceed at normal temperatures.

Strict selectivity and high speed are two main features of enzymatic catalysis that distinguish it from laboratory and industrial catalysis. None of the man-made catalysts (with the possible exception of 2-hydroxypyridine) can compare with enzymes in the strength and selectivity of their action on organic molecules. The activity of an enzyme, like any other catalyst, also depends on temperature: with increasing temperature, the rate of the enzymatic reaction also increases. At the same time, attention is drawn to the sharp decrease in activation energy E compared to the non-catalytic reaction. True, this does not always happen. There are many cases where the speed increases due to an increase in the temperature-independent pre-exponential factor in the Arrhenius equation.

Equilibrium

Chemical equilibrium constant

Free energy

Links

Chemical kinetics and catalysis Lectures by A. A. Kubasov, PhD in Chemistry. n, Associate Professor of the Department of Physical Chemistry, Faculty of Chemistry, Moscow State University.

see also

• Collision theory
• Transition state theory

Wikimedia Foundation. 2010.

See what “Chemical kinetics” is in other dictionaries:

A branch of physical chemistry, the study of the rates and mechanisms of chemical reactions. Chemical kinetics is the scientific basis for creating new and improving existing processes in chemical technology. Chemical kinetics methods are used in biology and... ... Big Encyclopedic Dictionary

Physical field chemistry, in which they study the mechanisms and speeds of chemistry. reactions. K. x. includes three main tasks: studying the patterns of chemical flow. reactions over time and the dependence of their rates on the concentrations of reagents, temperature and other factors;... ... Physical encyclopedia

CHEMICAL KINETICS- (from the Greek kinesis movement), a department of theoretical chemistry devoted to the study of the laws of chemistry. reactions. Several types of chemicals can be identified. interactions and, first of all, to distinguish reactions occurring in a homogeneous (homogeneous) medium from reactions... ... Great Medical Encyclopedia

Chemical kinetics- - a branch of physical chemistry that studies the rate and mechanisms of chemical reactions, patterns of changes over time in the concentrations of initial, intermediate components and final products of reactions described by kinetic curves. [Usherov... ... Encyclopedia of terms, definitions and explanations of building materials

Section of physical chemistry; the study of the rates and mechanisms of chemical reactions. Chemical kinetics is the scientific basis for creating new and improving existing processes in chemical technology. Chemical kinetics methods are used in biology and... encyclopedic Dictionary

Kinetics of chemical reactions, the study of chemical processes, the laws of their occurrence in time, speeds and mechanisms. The most important areas of modern chemistry and chemical science are associated with studies of the kinetics of chemical reactions... ... Great Soviet Encyclopedia

- (from the Greek kinetikos moving), section physical. chemistry, studying chemistry. ration as a process occurring over time, the mechanism of this process, its dependence on the conditions of implementation. K. x. establishes temporary patterns of chemical flow. r tions,… … Chemical encyclopedia

The doctrine of speeds and mechanisms (the totality and sequence of stages) of chemistry. reactions; section of physical chemistry. Chem. speed reactions in closed systems is determined by changes in the concentration of initial, intermediate or final molecules (molecules ... Big Encyclopedic Polytechnic Dictionary

Thermodynamics makes it possible to predict with great accuracy the fundamental possibility of a process occurring and the final state of the system, but it does not provide any information about the methods of actual implementation of the process and the time of its occurrence. In reality, some processes occur so quickly that they appear to be instantaneous, while others proceed so slowly that virtually no changes in the system are observed. There is no relationship between the magnitude of chemical affinity and the rate of reaction. Reactions between substances with high chemical affinity can occur slowly, and conversely, substances with low chemical affinity can react very quickly. Thus, according to thermodynamics, a mixture of hydrogen and oxygen gases at ordinary temperatures should almost completely transform into water (for this reaction D G o = –450 kJ), however, practically no water formation is observed in the experiment. The chemical potential of diamond under normal conditions is greater than the chemical potential of graphite and, therefore, diamond should spontaneously transform into graphite, but in reality such a transformation does not occur.

This apparent contradiction between theoretical predictions and practical results is due to the fact that in thermodynamics only the initial and final states of the system are taken into account, but the transition mechanism is not considered and such a practically important factor as time does not appear. In reality, every transformation is associated with overcoming a certain energy barrier - breaking bonds in the molecules of reacting substances, restructuring the structure of the crystal lattice, etc. If the energy barrier is high, then the theoretically possible reaction proceeds so slowly that no changes are observed within a practically limited period of time (the reaction “does not occur”).

Thus, in addition to the thermodynamic approach, another aspect of the study of chemical reactions acquires enormous importance - the study of them from the point of view of rates. The study of the patterns of processes over time is the subject of chemical kinetics.

We can distinguish two main tasks of chemical kinetics, which determine its practical and theoretical significance: 1) experimental study of the reaction rate and its dependence on the conditions (concentration of reactants, temperature, presence of other substances, etc.) and 2) establishment of the reaction mechanism, those. the number of elementary stages and the composition of the resulting intermediate products.

A rigorous theoretical consideration of kinetic parameters is currently possible only for the simplest reactions in the gas phase. The empirical macroscopic approach provides very valuable information about the course of reactions. The quantitative description of the reaction rate depending on the concentration of the reactants is based on the basic postulate of chemical kinetics and is the subject of formal kinetics.

20.2. Basic concepts and definitions

Reaction speed call the number of molecules of a substance reacting per unit time. Comparison of the rates of different reactions is possible only in the case when the volumes of the reacting systems are the same, so the rate v referred to a unit of volume:

Where V– volume of the system, dN– the number of molecules of a substance that reacted in time dt. The plus sign refers to the case when the rate is determined by the substance formed in the reaction, the minus sign - when the rate is determined by the starting substance. Since in a chemical reaction substances react in strictly defined proportions, the rate can be calculated for any substance participating in the reaction.

If the volume of the system remains unchanged, then instead of the number of particles we can use the concentration ( c = N/N A V, where N A is Avogadro’s number) and then the reaction rate is equal to the change in concentration per unit time:

Since the concentrations of substances change during a reaction, the rate is a function of time. You can introduce the concept of the average reaction rate in a given time interval from t 1 to t 2:

, (20.3)

Where N 1 and N 2 – number of molecules of a substance at moments of time t 1 and t 2 .

When the time interval decreases, when ( t 2 – t 1) ® 0, we arrive at expression (20.1, 20.2) for the true speed.

In general, the reaction rate depends on many factors: the nature of the reacting substances, the nature of the solvent for reactions in solutions, concentration, temperature, the presence of other substances (catalysts, inhibitors), etc. For a given reaction, under constant conditions, the rate at each moment depends on the concentration. This dependence is expressed basic postulate of chemical kinetics:

At each moment of time, the rate of a chemical reaction is proportional to the product of the concentrations of the reacting substances raised to certain powers.

So, for some reaction between substances A, B, D,...

a A+ b B+ d D+... ® products

speed

... (20.4)

Exponents n 1 , n 2 , n 3 ,... are called order of reaction by substance A, B, D,… and their total value n = n 1 + n 2 + n 3 + ... is called general reaction order.

Proportionality factor k in the kinetic equation (20.3) is called rate constant, or specific speed reactions. Magnitude k numerically equal to the reaction rate when the concentrations of all reacting substances are equal to unity: c A= c B= c D = 1. Rate constants are different for different reactions and depend on temperature.

In many cases, the order does not coincide with the stoichiometric coefficients in the reaction equation (i.e. n 1¹ a, n 2¹ b etc.).

So, for example, for two similar reactions with the same stoichiometric equations, completely different kinetic equations are obtained:

for the reaction H 2 + I 2 = 2HI

, (20.5)

and for the reaction H 2 + Br 2 = 2HBr

. (20.6)

This is due to differences in the reaction mechanisms. Most reactions occur in several stages at different rates, so the stoichiometric equation is the total result of all elementary stages, and the overall rate of the reaction is determined by the rate of the slowest step(limiting reaction).

In this regard, for elementary reactions the concept is introduced molecularity– the number of molecules taking part in an elementary act of chemical interaction. If one molecule participates in an elementary act (for example, a molecule disintegrates), the reaction is monomolecular. If two molecules interact in an elementary act, the reaction is called bimolecular, for example, the above reactions of hydrogen with bromine or iodine. Trimolecular reactions involve three particles, such as the recombination of hydrogen atoms into a molecule:

N + N + M = N 2 + M,

where M is a hydrogen molecule or any other particle.

Unlike molecularity, the order of a reaction can be zero, integer, or fractional. Only for elementary reactions do the numerical values ​​of molecularity and kinetic order coincide. Mono-, bi- and trimolecular reactions are at the same time reactions of the first, second and third order, but the reverse conclusion may be erroneous. For example, the decomposition reaction of dichloroethane vapor

CH 2 Cl–CH 2 Cl CHCl=CH 2 + HCl

is a first order reaction, its rate is proportional to the concentration of dichloroethane:

.

But this reaction cannot be called monomolecular, since the study of its mechanism has shown that the reaction proceeds through several elementary stages, mono- and bimolecular. In this case, one cannot speak at all about the molecular nature of the reaction as a whole; one can only point to the experimentally established first order.

In some cases, the concentrations of one or more of the reactants change very little during the reaction and can be considered constant. Then the concentrations of these substances can be included in the rate constant of equation (20.4) and apparent the reaction order decreases, the reaction becomes pseudo n-th order, where n– the sum of exponents at varying concentrations.

So, for the cane sugar inversion reaction, which is catalyzed by hydrogen ions

C 12 H 22 O 11 + H 2 O 2C 6 H 12 O 6,

the kinetic equation can be written as:

,

those. This is a third order reaction. But the concentration of hydrogen ions does not change during the reaction, and the concentration of water, if it is taken in large excess, also practically does not change. Thus, only the sugar concentration changes, and then the kinetic equation can be written as

,

those. This is a pseudo-first order reaction.

20.3. Simple irreversible reactions

In a system, reactions can occur simultaneously and independently at different rates, but in opposite directions. Some time after the start, the rates of the forward and reverse reactions become equal, and the system reaches a state of equilibrium. Such reactions are called kinetically reversible. This concept should be distinguished from the reversibility of a process in the thermodynamic sense. A thermodynamically reversible process is characterized by the fact that in it the rates of the forward and reverse processes differ by an infinitesimal amount, and at any moment of time the state of the system differs infinitely little from the equilibrium one. Thus, the concepts of kinetic and thermodynamic reversibility coincide only close to the state of chemical equilibrium, therefore kinetically reversible reactions should more accurately be called bilateral.

In principle, all chemical reactions are two-way, but in reality, some of them, under certain conditions, proceed only in one direction until the initial substances almost completely disappear, i.e. the equilibrium in such cases is very strongly shifted towards the formation of products. Such reactions are called kinetically irreversible, or one-sided.

20.3.1. One-way first order reactions

First order reactions mainly include decomposition reactions, for example, the decomposition reaction of nitric oxide

N 2 O 5 2NO 2 + O 2

or diethyl ether

CH 3 OCH 3 CH 4 + H 2 + CO

In the general case, we write the first order reaction equation in the form

A® products

t= 0) the concentration of substance A was equal to a, and after some time it decreased by x, then the reaction rate at any time, according to equations (20.3) and (20.4) is equal to

. (20.7)

Let us separate the variables and integrate the resulting equation, taking into account that at the initial moment of time x = 0:

. (20.8)

As a result, we obtain the kinetic equation of the first order reaction:

From the last equation it is clear that the dimension of the rate constant corresponds to the reciprocal time ( t–1) and depending on the speed values ​​it can be expressed in c –1 , min –1 , h–1, etc. Since the concentrations of a substance enter the equation as a ratio, they can be expressed in any units, and the numerical values ​​of the rate constant do not depend on this.

By potentiating equation (20.9), we obtain the concentrations of the reactant at any time:

(20.11)

or for the concentration of the reacted substance at the time t

, (20.12)

from which follows the exponential nature of the change in the concentration of the reactant over time (Fig. 20.1).

The reciprocal of the first-order reaction rate constant has the physical meaning of the average lifespan of an individual molecule.

Fig.20.1. Dependence of the concentrations of the reacted and remaining substance on time

Another important characteristic of the reaction is half-reaction time (half-life) t 1/2 is the time during which half of the initial amount of the substance will react. Substituting into equation (20.8) the values t= t 1/2 and x = a/2, we get:

. (20.13)

As can be seen from the equation, the half-life of the reaction does not depend on the initial amount of the substance taken, but is determined only by the value of the reaction rate constant.

From the resulting equations it also follows that the substance will react completely only after an infinitely long period of time ( x ® a at t® ¥). In practice, the reaction is considered complete when it is no longer analytically possible to determine the presence of the starting substance in the system or changes in the concentration of products over time, i.e. the practical reaction time depends on the sensitivity of the analytical methods used.

20.3.2. One-way second order reactions

Examples of second-order reactions include the formation of hydrogen iodide in the gas phase (or its decomposition)

H 2 + I 2 ® 2HI,

saponification of ester with alkali

CH 3 COOC 2 H 5 + NaOH ® CH 3 COONa + C 2 H 5 OH,

decomposition of nitric oxide (IV)

2NO 2 ® 2NO + O 2

Numerous elementary bimolecular reactions occur in the second order with the participation of atoms and free radicals, which are intermediate stages of chemical reactions.

Let's consider a second-order reaction that proceeds according to the equation:

n 1 A + n 2 B ® products

If at the initial moment of time ( t= 0) the concentrations of substances A and B are equal, respectively a And b, and after some time t concentration A decreased by x, then the reaction rate

. (20.14)

After separating the variables we get:

. (20.15)

In the simplest case, when the initial concentrations of substances are equal ( a = b) And n 1 = n 2, equation (20.15) takes the form

. (20.16)

By integrating it ranging from x= 0 to x(left side) and from t= 0 to t(right side), we obtain the kinetic equation of the second-order reaction:

(20.17)

. (20.18)

From this it can be seen that the dimension of the rate constant includes quantities that are reciprocal to time and concentration, i.e. the numerical value of the constant depends on the choice of time units and concentration.

In the case under consideration, it is also possible to use the concept of half-reaction time. Substituting into equation (20.17) t = t 1/2 and x = a/2, we get for the half-reaction time

Thus, for a second-order reaction, the half-life of the reaction depends not only on the value of the rate constant, but also on the initial concentration of the substances.

To solve equation (20.15) in the general case, when a ¹ b, n 1 ¹ n 2 , imagine the left side of the relation as a sum of two fractions with coefficients WITH 1 and WITH 2:

. (20.20)

It's obvious that

. (20.21)

This equality is valid for any values x. If we substitute the values ​​one by one x = a And x = b in (20.21), we get

And . (20.22)

Using the values ​​obtained from here WITH 1 and WITH 2, we integrate equation (20.15):

. (20.23)

Hence the second-order reaction rate constant is:

. (20.24)

In very common cases, when n 1 = n 2, we get

. (20.25)

20.3.3. Third order reactions

Examples of third-order reactions include the oxidation reaction of nitrogen (II) oxide occurring in the gas phase.

2NO + O 2 ® 2NO

or reduction reaction of iron (III) chloride in solution

2FeCl 3 + SnCl 2 ® 2FeCl 2 + SnCl 4 .

These also include processes of recombination of atoms and simple radicals with the participation of a third particle that carries away excess energy:

N + N + M ® N 2 + M

CH + CH + M ® C 2 H 2 + M

The third order reaction equation can be written as

A + B + C ® products

In the simplest case, when the concentrations of all substances are the same, i.e. c A= c B= c C= a, the reaction rate is

, (20.26)

and after integration we get:

. (20.27)

In general, when substances have different concentrations a, b, c, speed reaction

. (20.28)

Integrating this equation in the same way as in the case of a second-order reaction, we obtain the kinetic equation:

20.3.4. Nth order reactions

For an arbitrary reaction n-th order (except n= 1) at identical concentrations of all reacting substances, equal a, speed

, (20.30)

which after separation of variables and integration gives

. (20.31)

In this form, the formula is not suitable for describing the kinetics of first-order reactions, since n= 1 uncertainty arises; the disclosure of uncertainty leads to equation (20.10).

Substituting into equation (20.30) t = t 1/2 and x = a/2, we arrive at the expression for the half-reaction period:

. (20.32)

20.4. Methods for determining reaction order

When determining the order of a reaction, first find the order for each of the reactants. To do this, the concentrations of all substances, except for the one under consideration, are taken in large excess, so that they can be considered constant and introduced into the rate constant. Using any analytical methods, the concentrations of the test substance are determined at various time intervals. To ensure that the concentration of a substance does not change during sampling and analysis, the reaction is inhibited (“frozen”) - the reaction mixture is cooled, special reagents are introduced, etc. There are many different ways to determine order, the most common of which we will look at.

1. Graphic selection method. As follows from equation (20.10), for a first-order reaction, a linear relationship is satisfied in the coordinates logarithm of concentration - time. For second-order reactions, such a dependence is observed in coordinates 1/( a–x) – t(equation (20.17)), and for reactions n the th order straight line is obtained in coordinates 1/( a – x) – time (equation (20.30)). Thus, using the concentration values ​​obtained in the experiment at different points in time, plot graphs in certain coordinates until a linear dependence is obtained.

2. Method of analytical selection of equation consists in calculating the rate constant by substituting experimental data into various kinetic equations. If the equation is chosen correctly, the rate constant should remain constant within experimental errors regardless of time; the systematic variation of the rate constant indicates that the equation was chosen incorrectly.

3. Determination of order by half-life. Taking the logarithm of equation (20.31) for the half-reaction period, we obtain:

. (20.33)

This is a linear relationship in lg coordinates t 1/2 – lg a. By constructing a graph in these coordinates (Fig. 20.3) using the tangent of the angle of inclination of the straight line, we determine the order of the reaction. The segment cut off by the straight line on the ordinate is equal to , from which the reaction rate constant can be calculated k.

4. Graphical method for determining order. Speed ​​reaction n of the th order for a given substance is equal to

v = kcn or

lg v= log k + n lg c, (20.34)

Where c– current concentration of the reactant.

To determine the order, first construct a graph of the concentration-time relationship. Drawing tangents to the curve at points corresponding to different times t 1 , t 2 , ..., are found from the tangent of the tangent angle of the reaction rate v 1 , v 2 , ... at these points in time (Fig. 20.5a). The logarithms of the rates are then plotted as functions of the logarithms of the corresponding concentrations c 1 , c 2,.... According to equation (20.25), a straight line should be obtained, the tangent of the angle of inclination of which is equal to the order of the reaction, and the segment cut off on the ordinate axis is the logarithm of the rate constant (Fig. 20.5b).

There are also other methods for determining the order of reactions. To reliably determine the location of this quantity, it is usually necessary to use several methods.

20.5. Complex reactions

Complex reactions include processes in which several reactions occur simultaneously (reversible, parallel, sequential, conjugate, etc.)

To describe the kinetics of complex reactions, use principle of independence, Whereby when several reactions occur in a system, each of them proceeds independently of the others and obeys the basic law of kinetics. It should be noted that this principle is not absolutely strict and does not hold, for example, for conjugate reactions.

20.5.1. Reversible first order reactions

Reversible (two-way) first-order reactions include isomerization reactions, for example, the isomerization of ammonium cyanide to urea in an aqueous solution

NH 4 CNO L (NH 2) 2 CO

or glucose mutarotation

a-glucose L b-glucose.

The equation for such reactions in general can be represented in the form

Where k 1 and k 2 – rate constants of forward and reverse reactions.

Since the reaction under consideration proceeds in opposite directions, its overall rate is equal to the difference in the rates of the forward and reverse reactions:

, (20.35)

Where a And b– initial amounts of substances A and B, x– the amount of substance A that has reacted at the moment of time t.

Let us transform equation (20.35) to the form:

By the time equilibrium is established, it will react x¥ moles of substance A, and the reaction rate at equilibrium is zero. From these conditions it follows that

, (20.37)

and equation (20.36) takes the form:

. (20.38)

Separating variables and integrating from 0 to t and from 0 to x, we get:

. (20.39)

Using this formula, you can only determine the sum of the rate constants k 1 and k 2. To separately find these constants, we use the equilibrium condition:

. (20.40)

, (20.41)

Where Kc– equilibrium constant.

The joint solution of equations (20.29) and (20.30) allows one to calculate the rate constants of the forward and reverse reactions k 1 and k 2 .

In the case of more complex reversible reactions (second, third orders), the same approach can be used, but the complexity of mathematical processing naturally increases.

20.5.2. Parallel reactions

In the case of parallel reactions, the same substances react simultaneously in several directions, forming different products. For example, during the nitration of phenol, ortho-, meta-, and para-nitrophenols are simultaneously formed.

Let's consider the simplest case of two parallel irreversible first-order reactions:

Using the principle of independence, we write the expression for the reaction rate of the conversion of substance A into B and C:

After integrating it we get

(20.43)

. (20.44)

These equations coincide with equations (20.10) and (20.11) for an irreversible first-order reaction with the difference that instead of one rate constant k we get the sum of constants k 1 and k 2. To find individual values k 1 and k 2, we write down the equations for the rates of formation of substances B and C ( c B and c C – current concentrations of these substances):

And . (20.45)

Let's substitute the value here ( a – x) from equation (20.44). Then

. (20.46)

Integrating this equation from 0 to c B and 0 to t, we get

. (20.47)

Similarly for substance C:

. (20.48)

From the last two equations it follows that

c B/ c C= k 1 /k 2 , (20.49)

those. at any moment of the reaction, the ratio of product concentrations is a constant value equal to the ratio of the rate constants of parallel reactions. The joint solution of equations (20.31) and (20.33) allows us to calculate these constants k 1 and k 2 .

20.5.3. Sequential reactions

As mentioned above, most chemical reactions have a complex mechanism and they go through a number of successive stages, and the final products are formed from unstable intermediate products - molecules, atoms, free radicals. In this regard, the study of such sequential (consecutive) reactions represents a very important task of chemical kinetics.

The simplest case to consider is the case of two successive irreversible first-order reactions:

At the initial moment of time t= 0 the concentration of substance A is a, substances B and C are absent. At some point in time t the concentrations of substances are equal, respectively: c A= a – x; c B= x – y; c C= y.

The rate of transformation of substance A into B is equal to

, (20.50)

and the rate of formation of substance C from B

. (20.51)

The solution to the first equation was discussed earlier (see section 20.3.1):

. (20.52)

Substituting this value into the second equation, we get:

. (20.53)

Let us temporarily equate the first term on the right side of this equation to zero:

Abo. (20.54)

After integration we get

, (20.55)

Where Z– conditional integration constant. Then

In fact Z is not constant, but depends on time. Therefore, we differentiate equation (20.56), considering Z function of time:

. (20.57)

Given the value y from equation (20.55), we see that

. (20.58)

Comparing the last equation with equation (20.53), we find that

. (20.59)

After integration we find

. (20.60)

Where I– integration constant.

Received value Z substitute into equation (20.56):

. (20.61)

We find the integration constant from the condition that at the initial moment of time at t= 0 concentration of substance C y = 0:

and, finally, we obtain the dependence of the concentration of the final product on time:

. (20.63)

We will find the dependence of the concentration of the intermediate product on time using the quantities x And y:

. (20.64)

From equation (20.63) it follows that the concentration of the final product in the limit tends to the initial concentration of substance A (at t®¥ y® a), i.e. the starting substance is completely converted into product C.

The concentration of the intermediate product passes through a maximum, since according to equation (20.64) at t = 0 (x – y) = 0 and at t®¥ ( x – y)® 0, and at any other time the concentration ( x – y) >0.

Time to reach maximum t max can be determined from the extremum condition:

. (20.65)

Let's differentiate equation (20.64):

. (20.66)

In accordance with condition (20.65)

After taking logarithms and solving this equation for t we get

(20.68)

those. the time to reach the maximum depends not only on the ratio of the rate constants k 2 and k 1, but also on their absolute values.

The nature of changes in concentrations of substances over time is shown schematically in Figure 20.5.

Maximum intermediate concentration

. (20.69)

If you enter the designation k 2 /k 1 = q, That

. (20.70)

It follows that the maximum concentration of the intermediate product depends only on the ratio of the rate constants k 2 and k 1 .

If the intermediate product is relatively stable, i.e. k 1 >> k 2, magnitude q very small ( q << 1) и ею можно пренебречь по сравнению с единицей. В этих условиях

those. almost all of the starting material accumulates as an intermediate product. This is quite natural, since the intermediate substance B transforms into the final substance C at a very low rate, and in the limit at k 2 ® 0 the second reaction does not occur.

If the intermediate product is very unstable, k 2 >> k 1 , q>> 1, in equation (20.70) one can be neglected compared to q, Then

. (20.72)

Since the value q is large, then the concentration of the intermediate product is very low.

Curve y = f(t), showing the change in the concentration of the final product C during the reaction, has S-shaped character. In the initial period, the rate of formation of the final product is low and its amount is so insignificant that it is not analytically detected. This initial reaction period is called induction. After the induction period, the concentration of the final product increases slowly at first, then faster and faster, but after some time the rate of formation decreases again, i.e. there is an inflection point on the curve. To find the moment of time corresponding to the inflection point, we equate the second derivative of equation (20.62) to zero, from where we find this point:

, (20.73)

those. the inflection point coincides with the time at which the maximum concentration of the intermediate product is reached.

20.6. Stationary concentration method

In the simplest case of two consecutive first-order reactions considered above, equations were obtained for the concentration of the intermediate and final products, which cannot be strictly solved with respect to the rate constants, i.e. it is impossible to calculate the latter directly from experimental data on the dependence of concentration on time. In more complex cases of several sequential reactions of different orders, a strict mathematical description of the kinetics is often impossible.

To describe the kinetics of multistage reactions, one can use the approximate steady-state concentration method Bodenstein. The method is based on the proposition that After some short time after the start of the reaction, the rate of formation of the intermediate product becomes approximately equal to the rate of its decay, and the total rate of change in the concentration of the unstable intermediate product can be considered approximately equal to zero for a sufficiently long time, i.e. during this time a stationary concentration of an unstable product is established.

Consider, for example, some reaction

which proceeds with the formation of two intermediate products M 1 and M 2 according to the scheme:

1) A ® 2M 1 k 1

2) M 1 + B ® C + M 2 k 2

3) M 2 + A ® C + M 1 k 3

4) M 1 + M 1 ® A k 4

Let us denote by c oA and c oB initial concentrations of substances A and B, through c i– current concentrations of all reaction participants. Using the proposed reaction scheme, we write expressions for decreasing the concentrations of A and B and increasing the concentration of C over time:

, (20.74)

, (20.75)

. (20.76)

The rates of change in the concentration of intermediate products M 1 and M 2 are respectively equal to:

. (20.78)

Assuming that the concentrations of intermediate products during the reaction are low and taking into account the stoichiometric equation, we can write:

, (20.79)

. (20.80)

Then, after differentiation with respect to time, we get:

, (20.81)

. (20.82)

Let us substitute the values ​​of velocities (20.74) and (20.77) into equation (20.81):

The last expression coincides with equation (20.77) for the rate of formation of the intermediate product M 1, which implies that

Similarly, substituting the speed values ​​(20.74) and (20.75) into equation (20.82) and comparing with (20.77), we obtain

Equations (20.85) and (20.86) are expressions of the stationarity principle.

In conclusion, we note that the method of stationary concentrations is not completely strict; its application is limited to the fulfillment of conditions like (20.78), (20.79), i.e. the formation of very unstable intermediate products, the concentration of which during the reaction turns out to be small. However, in practice, such cases occur very often (the formation of atoms and free radicals as intermediate products), therefore the method of stationary concentrations has become widespread in the study of the kinetics and mechanism of various reactions.

20.7. The influence of temperature on the rate of chemical reactions

In most cases, an increase in temperature leads to an increase in the rate constant of a chemical reaction. According to van't Hoff's rule temperature coefficient of speed g, i.e. ratio of reaction rate constants at temperatures T And T+ 10, varies from 2 to 4:

. (20.87)

In general, temperature changes from T before T + 10n, Where n– positive or negative, integer or fractional number, for the temperature coefficient you can write:

Van't Hoff's rule was obtained empirically and is approximate. The temperature coefficient values ​​do not remain constant as the temperature changes and tend to unity at high temperatures. Therefore, the rule can be used for semi-quantitative estimates in the region of relatively low temperatures.

More precisely, the dependence of the rate constant on temperature is conveyed by the Arrhenius equation:

, (20.89)

Where IN And WITH– constants, characteristic of a given reaction and independent of temperature.

The Arrhenius equation was also obtained first empirically and then justified theoretically.

When deriving the equation, Arrhenius assumed that not all molecules can react, but only some of them that are in a special active state. These molecules are formed from ordinary ones in an endothermic process with the absorption of heat E A. So, for example, in the reaction

active A* molecules are formed from normal A molecules according to the following scheme:

A L A* + E A

According to Arrhenius, this process is reversible and fast, so that the system always maintains thermodynamic equilibrium between A and A*, which can be characterized by the equilibrium constant Kc:

Or = Kc[A]. (20.90)

It is assumed that the concentration of the active form is low, and the equilibrium concentration [A] of the initial molecules A is almost equal to the current concentration c A » [A]. The change in the equilibrium constant with temperature is described by the Van't Hoff isochore equation

. (20.91)

Arrhenius's final assumption is that the conversion of active molecules into the final product occurs at a rate independent of temperature and relatively slowly:

Thus, the rate of formation of substance B is equal to

Where k'– rate constant independent of temperature.

On the other hand, according to the basic postulate of chemical kinetics, the rate of reaction A ® B is equal to

Where k is an experimentally determined rate constant that depends on temperature.

Comparing equations (20.92) and (20.93) and taking into account all previously made assumptions, we obtain:

It follows that the experimental rate constant

k = k"c or ln k= log k"+ln Kc. (20.95)

Because k' does not depend on temperature, then differentiating by T, we get

. (20.96)

Using the Van't Hoff equation (20.91), we arrive at the Arrhenius equation in differential form:

Magnitude E A called activation energy, or experienced activation energy. In the framework of the presented ideas, this is the amount of heat that is necessary to convert one mole of molecules in a normal state into a special active, reactive form.

Integrating equation (20.96) under the assumption that the activation energy is independent of temperature, we obtain:

, (20.98)

Where WITH– integration constant.

The resulting equation coincides with the empirical Arrhenius equation (20.89), in which the constant IN corresponds to the value E A/R or E A = BR. By potentiating equation (20.98), we can represent it in exponential form, setting e C=A:

. (20.99)

As can be seen from equation (20.97), the logarithm of the rate constant is a linear function of the inverse temperature. Therefore, for experimental determination E A find reaction rate constants at several temperatures and plot the dependence in ln coordinates k – 1/T(Fig. 20.6). The segment cut off by the straight line on the ordinate axis is equal to the constant WITH, and the activation energy is calculated from the tangent of the straight line.

If the reaction rate constants are known at only two temperatures T 1 and T 2, the activation energy can be calculated from the relation that is obtained by integrating equation (20.97) within these temperatures:

, (20.100)

Where k 1 and k 2 – rate constants at temperatures T 1 and T 2 respectively.

In some cases, the plot of ln k – 1/T has a different appearance - it consists of two intersecting straight lines with different slopes, which indicates the complex nature of the reaction. For example, hydrogen can react with both liquid and gaseous sulfur. If hydrogen, liquid sulfur and its vapors are simultaneously present in the vessel, then at low temperatures the reaction of hydrogen with liquid sulfur occurs with a lower activation energy (segment 1 in Fig. 20.7), and at higher temperatures the reaction of hydrogen with sulfur vapors occurs with higher energy activation (segment 2).

Experimental studies show that the activation energies of reactions with valence-saturated molecules range from several tens to hundreds (50 ¸ 500) kJ/mol. At the same time, no simple patterns were found that connect the activation energy with any other characteristics of the reaction, for example, with the thermal effect. In reactions that proceed through elementary stages with the participation of free atoms and radicals, the activation energy is much lower (10 ¸ 50 kJ/mol).

In some cases, increasing the temperature causes the reaction rate to decrease. An example would be the reaction

2NO + O 2 ® 2NO 2 ,

which is one of the stages in the production of nitric acid. The anomalous course of the temperature dependence of the rate constant of this reaction can be explained by assuming that it occurs in two stages:

I. 2NO L N 2 O 2 (fast, reversible, exothermic)

II. N 2 O 2 + O 2 ® 2NO 2 (slow)

The overall rate of the reaction is determined by the rate of the second, slower stage:

.

The concentration of the N 2 O 2 dimer depends on the equilibrium constant established at the first stage:

Or .

.

This equation corresponds to the experimentally established third order of the reaction. Since the first stage is exothermic, the equilibrium constant is Kc decreases with increasing temperature. If this decrease overlaps a possible increase k, then this will lead to a general decrease in the reaction rate.

20.8 Heterogeneous chemical reactions

Chemical interaction in heterogeneous systems occurs at the phase interface: solid - gas, solid - liquid (solution) or liquid - liquid in the case of immiscible liquids. The rate of a heterogeneous process is defined as the amount of substance reacting per unit time per unit surface area:

Where S– surface area on which the reaction takes place. Finding the true value of the surface area is a difficult task due to the roughness of the surface, the presence of pores, and capillaries.

In a heterogeneous process, three main stages can be distinguished: supply of the reactant to the interface, interaction on the surface (which can consist of several stages), and removal of reaction products into the bulk phase. The speed of the entire process is generally determined by the speed of the slowest stage, which can be any of the named stages.

The supply of reagents to the surface and removal of products is carried out by molecular or convective diffusion. Diffusion is described by Fick's law:

, (20.102)

Where dm– the amount of substance diffused over time dt through the surface S, dc/dx– concentration gradient.

If the concentration of a substance at the interface is equal to c s, and at some distance d – c x, then the concentration gradient

AND . (20.103)

Dividing the last equation by the volume V and moving on to concentrations, we get:

. (20.104)

The diffusion rate is

. (20.105)

The resulting equation corresponds to the kinetic equation of the first order reaction. Thus, if the rate-limiting step is diffusion, then the reaction kinetics will be described by equation (20.70), although it does not reflect the true rate and order of the chemical reaction on the surface. In this case, the process is said to proceed in diffusion region.

If the rate of a chemical reaction is significantly less than the rate of diffusion, the process occurs in kinetic region and is described by the equation of the reaction that occurs on the surface.

At comparable rates of diffusion and reaction, the process occurs in the transition region. The rate constant as a function of temperature can be expressed by the equation:

, (20.106)

Rice. 20.8. Temperature dependence of the rate constant of a heterogeneous chemical reaction

Where E A– activation energy of a chemical reaction, E D– diffusion activation energy.

Magnitude E D small (5 ¸ 10 kJ/mol), i.e. E D << E A, therefore the experimentally determined activation energy is approximately two times less than the true activation energy of a chemical reaction.

Since the activation energy of diffusion is small, when the temperature changes by 10°, the diffusion rate changes by 1.1 - 1.2 times, while the rate of the chemical reaction changes by 2 - 4 times. Therefore, when determining the reaction rate over a wide temperature range, a complex nature of the ln dependence is observed k from 1/ T(Fig. 20.8).

At low temperatures, the reaction usually occurs in the kinetic region (section CD) and the speed is highly dependent on temperature. At high temperatures, the rate of diffusion is usually significantly less than the rate of the chemical reaction; the process occurs in the diffusion region with a slightly varying rate (section AB). Plot B.C. corresponds to the transition region.

The rate of removal of reaction products can play a significant role in the kinetics of heterogeneous reactions. If, for example, sparingly soluble substances are formed in the reaction, then, deposited on the surface, they block it, and the reaction practically stops.

In the 19th century As a result of the development of the fundamentals of chemical thermodynamics, chemists learned to calculate the composition of an equilibrium mixture for reversible chemical reactions. In addition, based on simple calculations, it was possible, without conducting experiments, to draw a conclusion about the fundamental possibility or impossibility of a specific reaction occurring under given conditions. However, the “principal possibility” of a reaction does not mean that it will take place. For example, the reaction C + O 2 → CO 2 is very favorable from the point of view of thermodynamics, in any case, at temperatures below 1000 ° C (at higher temperatures, CO 2 molecules already decompose), i.e. carbon and oxygen should (with almost 100% yield) turn into carbon dioxide. However, experience shows that a piece of coal can lie in the air for years, with free access to oxygen, without undergoing any changes. The same can be said about many other known reactions. For example, mixtures of hydrogen with chlorine or with oxygen can persist for a very long time without any signs of chemical reactions, although in both cases the reactions are thermodynamically favorable. This means that after reaching equilibrium, only hydrogen chloride should remain in the stoichiometric mixture of H 2 + Cl 2, and only water in the mixture 2H 2 + O 2. Another example: acetylene gas is quite stable, although the reaction C 2 H 2 → 2C + H 2 is not only thermodynamically allowed, but is also accompanied by a significant release of energy. Indeed, at high pressures, acetylene explodes, but under normal conditions it is quite stable.

Thermodynamically allowed reactions like those considered can only occur under certain conditions. For example, after ignition, coal or sulfur spontaneously combines with oxygen; hydrogen reacts easily with chlorine when the temperature rises or when exposed to ultraviolet light; a mixture of hydrogen and oxygen (explosive gas) explodes when ignited or when a catalyst is added. Why do all these reactions require special influences - heating, irradiation, the action of catalysts? Chemical thermodynamics does not answer this question - the concept of time is absent in it. At the same time, for practical purposes it is very important to know whether a given reaction will take place in a second, in a year, or over many millennia.

Experience shows that the speed of different reactions can differ greatly. Many reactions occur almost instantly in aqueous solutions. Thus, when an excess of acid is added to an alkaline solution of crimson-colored phenolphthalein, the solution instantly becomes discolored, which means that the neutralization reaction, as well as the reaction of converting the colored form of the indicator into a colorless one, proceed very quickly. The oxidation reaction of an aqueous solution of potassium iodide with atmospheric oxygen proceeds much more slowly: the yellow color of the reaction product, iodine, appears only after a long time. Corrosion processes of iron and especially copper alloys, as well as many other processes, occur slowly.

Predicting the rate of a chemical reaction, as well as elucidating the dependence of this rate on the reaction conditions is one of the important tasks of chemical kinetics - a science that studies the patterns of reactions over time. No less important is the second task facing chemical kinetics - the study of the mechanism of chemical reactions, that is, the detailed path of transformation of starting substances into reaction products.

Speed ​​reaction.

The easiest way to determine the rate is for a reaction occurring between gaseous or liquid reagents in a homogeneous (homogeneous) mixture in a vessel of constant volume. In this case, the reaction rate is defined as the change in the concentration of any of the substances participating in the reaction (it can be the starting substance or the reaction product) per unit time. This definition can be written as a derivative: v=d c/d t, Where v- speed reaction; t– time, c– concentration. This speed is easy to determine if there is experimental data on the dependence of the concentration of the substance on time. Using this data, you can construct a graph called a kinetic curve. The rate of reaction at a given point on the kinetic curve is determined by the slope of the tangent at that point. Determining the slope of a tangent always involves some error. The initial reaction rate is most accurately determined, since at first the kinetic curve is usually close to a straight line; this makes it easier to draw a tangent at the starting point of the curve.

If time is measured in seconds and concentration in moles per liter, then the reaction rate is measured in units of mol/(l s). Thus, the reaction rate does not depend on the volume of the reaction mixture: under the same conditions, it will be the same in a small test tube and in a large-scale reactor.

Value d t is always positive, whereas the sign of d c depends on how the concentration changes over time - it decreases (for starting substances) or increases (for reaction products). To ensure that the reaction rate always remains a positive value, in the case of starting substances a minus sign is placed in front of the derivative: v= –d c/d t. If the reaction occurs in the gas phase, pressure is often used instead of the concentration of substances in the rate equation. If the gas is close to ideal, then the pressure R is related to concentration with a simple equation: p = cRT.

During a reaction, different substances can be consumed and formed at different rates, according to the coefficients in the stoichiometric equation ( cm. STOICHIOMETRY), therefore, when determining the rate of a particular reaction, these coefficients should be taken into account. For example, in the ammonia synthesis reaction 3H 2 + N 2 → 2NH 3, hydrogen is consumed 3 times faster than nitrogen, and ammonia accumulates 2 times faster than nitrogen is consumed. Therefore, the rate equation for this reaction is written as follows: v= –1/3 d p(H2)/d t= –d p(N 2)/d t= +1/2d p(NH 3)/d t. In general, if the reaction is stoichiometric, i.e. proceeds exactly in accordance with the written equation: aA + bB → cC + dD, its speed is determined as v= –(1/a)d[A]/d t= –(1/b)d[B]/d t= (1/c)d[C]/d t= (1/d)d[D]/d t(square brackets are used to indicate the molar concentration of substances). Thus, the rates for each substance are strictly related to each other and, having determined experimentally the rate for any participant in the reaction, it is easy to calculate it for any other substance.

Most reactions used in industry are heterogeneous-catalytic. They occur at the interface between the solid catalyst and the gas or liquid phase. At the interface between two phases, reactions such as roasting of sulfides, dissolution of metals, oxides and carbonates in acids, and a number of other processes also occur. For such reactions, the rate also depends on the size of the interface, therefore the rate of a heterogeneous reaction is related not to a unit volume, but to a unit surface area. Measuring the surface area on which a reaction occurs is not always easy.

If a reaction occurs in a closed volume, then its speed in most cases is maximum at the initial moment of time (when the concentration of the starting substances is maximum), and then, as the starting reagents are converted into products and, accordingly, their concentration decreases, the reaction rate decreases. There are also reactions in which the rate increases with time. For example, if a copper plate is immersed in a solution of pure nitric acid, the reaction rate will increase over time, which is easy to observe visually. The processes of dissolution of aluminum in alkali solutions, oxidation of many organic compounds with oxygen, and a number of other processes also accelerate over time. The reasons for this acceleration may be different. For example, this may be due to the removal of a protective oxide film from the metal surface, or to the gradual heating of the reaction mixture, or to the accumulation of substances that accelerate the reaction (such reactions are called autocatalytic).

In industry, reactions are usually carried out by continuously feeding starting materials into the reactor and removing products. Under such conditions, it is possible to achieve a constant rate of chemical reaction. Photochemical reactions also proceed at a constant rate, provided that the incident light is completely absorbed ( cm. PHOTOCHEMICAL REACTIONS).

Limiting stage of the reaction.

If a reaction is carried out through sequential stages (not necessarily all of them are chemical) and one of these stages requires much more time than the others, that is, it proceeds much more slowly, then this stage is called limiting. It is this slowest stage that determines the speed of the entire process. Let us consider as an example the catalytic reaction of ammonia oxidation. There are two possible limiting cases here.

1. The flow of reagent molecules - ammonia and oxygen - to the surface of the catalyst (physical process) occurs much more slowly than the catalytic reaction itself on the surface. Then, to increase the rate of formation of the target product - nitrogen oxide, it is completely useless to increase the efficiency of the catalyst, but care must be taken to accelerate the access of the reagents to the surface.

2. The supply of reagents to the surface occurs much faster than the chemical reaction itself. This is where it makes sense to improve the catalyst, to select optimal conditions for the catalytic reaction, since the limiting stage in this case is the catalytic reaction on the surface.

Collision theory.

Historically, the first theory on the basis of which the rates of chemical reactions could be calculated was the collision theory. Obviously, in order for molecules to react, they must first collide. It follows that the reaction should proceed faster, the more often the molecules of the starting substances collide with each other. Therefore, every factor that affects the frequency of collisions between molecules will also affect the rate of reaction. Some important laws concerning collisions between molecules were obtained on the basis of the molecular kinetic theory of gases.

In the gas phase, molecules move at high speeds (hundreds of meters per second) and very often collide with each other. The frequency of collisions is determined primarily by the number of particles per unit volume, that is, concentration (pressure). The frequency of collisions also depends on temperature (as it increases, molecules move faster) and on the size of molecules (large molecules collide with each other more often than small ones). However, concentration has a much stronger effect on collision frequency. At room temperature and atmospheric pressure, each medium-sized molecule experiences several billion collisions per second.

Based on these data, you can calculate the rate of the reaction A + B → C between two gaseous compounds A and B, assuming that a chemical reaction occurs with each collision of reactant molecules. Let there be a mixture of reagents A and B at equal concentrations in a liter flask at atmospheric pressure. In total, there will be 6 10 23 / 22.4 = 2.7 10 22 molecules in the flask, of which 1.35 10 22 molecules of substance A and the same number of molecules of substance B. Let each molecule A experience 10 9 collisions in 1 s with other molecules, half of which (5 10 8) occur in collisions with molecules B (collisions A + A do not lead to a reaction). Then, in total, 1.35 10 22 5 10 8 ~ 7 10 30 collisions of molecules A and B occur in the flask in 1 s. Obviously, if each of them led to a reaction, it would take place instantly. However, many reactions proceed quite slowly. From this we can conclude that only a tiny fraction of collisions between reactant molecules leads to interaction between them.

To create a theory that would allow one to calculate the reaction rate based on the molecular kinetic theory of gases, it was necessary to be able to calculate the total number of collisions of molecules and the proportion of “active” collisions leading to reactions. It was also necessary to explain why the rate of most chemical reactions increases greatly with increasing temperature - the speed of molecules and the frequency of collisions between them increase with temperature slightly - in proportion to , that is, only 1.3 times with an increase in temperature from 293 K (20 ° C) to 373 K (100° C), while the reaction rate can increase thousands of times.

These problems were solved based on collision theory as follows. During collisions, molecules continuously exchange velocities and energies. Thus, as a result of a “successful” collision, a given molecule can noticeably increase its speed, while in an “unsuccessful” collision it can almost stop (a similar situation can be observed in the example of billiard balls). At normal atmospheric pressure, collisions, and therefore changes in speed, occur with each molecule billions of times per second. In this case, the velocities and energies of the molecules are largely averaged. If at a given moment in time we “recount” molecules with certain speeds in a given volume of gas, it turns out that a significant part of them have a speed close to the average. At the same time, many molecules have a speed less than the average, and some move at speeds greater than the average. As speed increases, the fraction of molecules having a given speed quickly decreases. According to collision theory, only those molecules that, when colliding, have a sufficiently high speed (and, therefore, a large supply of kinetic energy) react. This suggestion was made in 1889 by the Swedish chemist Svante Arrhenius.

Activation energy.

Arrhenius introduced into use by chemists the very important concept of activation energy ( E a) is the minimum energy that a molecule (or a pair of reacting molecules) must have in order to enter into a chemical reaction. Activation energy is usually measured in joules and is referred not to one molecule (this is a very small value), but to a mole of a substance and is expressed in units of J/mol or kJ/mol. If the energy of the colliding molecules is less than the activation energy, then the reaction will not take place, but if it is equal to or greater, then the molecules will react.

Activation energies for different reactions are determined experimentally (from the dependence of the reaction rate on temperature). The activation energy can vary over a fairly wide range – from a few to several hundred kJ/mol. For example, for the reaction 2NO 2 → N 2 O 4 the activation energy is close to zero, for the reaction 2H 2 O 2 → 2H 2 O + O 2 in aqueous solutions E a = 73 kJ/mol, for thermal decomposition of ethane into ethylene and hydrogen E a = 306 kJ/mol.

The activation energy of most chemical reactions significantly exceeds the average kinetic energy of molecules, which at room temperature is only about 4 kJ/mol and even at a temperature of 1000 ° C does not exceed 16 kJ/mol. Thus, in order to react, molecules usually must have a speed much greater than average. For example, in case E a = 200 kJ/mol colliding molecules of small molecular weight should have a speed of the order of 2.5 km/s (the activation energy is 25 times greater than the average energy of molecules at 20 ° C). And this is a general rule: for most chemical reactions, the activation energy significantly exceeds the average kinetic energy of the molecules.

The probability for a molecule to accumulate large energy as a result of a series of collisions is very small: such a process requires for it a colossal number of successive “successful” collisions, as a result of which the molecule only gains energy without losing it. Therefore, for many reactions, only a tiny fraction of molecules have sufficient energy to overcome the barrier. This share, in accordance with the Arrhenius theory, is determined by the formula: a = e – E a/ RT = 10 –E a/2.3 RT ~ 10 –E a/19 T, Where R= 8.31 J/(mol . TO). From the formula it follows that the proportion of molecules with energy E a, like the fraction of active collisions a, depends very strongly on both the activation energy and temperature. For example, for a reaction with E a = 200 kJ/mol at room temperature ( T~ 300 K) the fraction of active collisions is negligible: a = 10 –200000/(19 , 300) ~ 10 –35 . And if every second in a vessel there are 7·10 30 collisions of molecules A and B, then it is clear that the reaction will not take place.

If you double the absolute temperature, i.e. heat the mixture to 600 K (327 ° C); in this case, the proportion of active collisions will increase sharply: a = 10 –200000/(19 , 600) ~ 4·10 –18 . Thus, a 2-fold increase in temperature increased the proportion of active collisions by 4·10 17 times. Now every second out of a total number of approximately 7·10 30 collisions will result in a reaction of 7·10 30 ·4·10 –18 ~ 3·10 13 . Such a reaction, in which 3·10 13 molecules disappear every second (out of approximately 10 22), although very slowly, still occurs. Finally, at a temperature of 1000 K (727° C) a ~ 3·10 –11 (out of every 30 billion collisions of a given reactant molecule, one results in a reaction). This is already a lot, since in 1 s 7 10 30 3 10 –11 = 2 10 20 molecules will enter into the reaction, and such a reaction will take place in several minutes (taking into account the decrease in the frequency of collisions with a decrease in the concentration of reagents).

Now it is clear why increasing the temperature can increase the rate of a reaction so much. The average speed (and energy) of molecules increases slightly with increasing temperature, but the proportion of “fast” (or “active”) molecules that have a sufficient speed of movement or sufficient vibrational energy for a reaction to occur increases sharply.

Calculation of the reaction rate, taking into account the total number of collisions and the fraction of active molecules (i.e., activation energy), often gives satisfactory agreement with experimental data. However, for many reactions the experimentally observed rate turns out to be less than that calculated by collision theory. This is explained by the fact that for a reaction to occur, the collision must be successful not only energetically, but also “geometrically,” that is, the molecules must be oriented in a certain way relative to each other at the moment of the collision. Thus, when calculating reaction rates using collision theory, in addition to the energy factor, the steric (spatial) factor for a given reaction is also taken into account.

Arrhenius equation.

The dependence of the reaction rate on temperature is usually described by the Arrhenius equation, which in its simplest form can be written as v = v 0 a = v 0 e – E a/ RT, Where v 0 is the speed that the reaction would have at zero activation energy (in fact, this is the frequency of collisions per unit volume). Because the v 0 weakly depends on temperature, everything is determined by the second factor - exponential: with increasing temperature this factor increases rapidly, and the faster the higher the activation energy E A. This dependence of the reaction rate on temperature is called the Arrhenius equation; it is one of the most important in chemical kinetics. To approximate the effect of temperature on the reaction rate, the so-called “van’t Hoff rule” is sometimes used ( cm. Van't Hoff's Rule).

If a reaction obeys the Arrhenius equation, the logarithm of its rate (measured, for example, at the initial moment) should linearly depend on the absolute temperature, that is, the plot of ln v from 1/ T must be straightforward. The slope of this line is equal to the activation energy of the reaction. Using such a graph, you can predict what the reaction rate will be at a given temperature, or at what temperature the reaction will proceed at a given speed.

Several practical examples of using the Arrhenius equation.

1. The packaging of a frozen product says that it can be stored on a refrigerator shelf (5°C) for 24 hours, in a freezer marked with one star (–6°C) for a week, with two stars (–12°C) for a month. , and in a freezer with a *** symbol (which means the temperature in it is –18° C) – 3 months. Assuming that the rate of product spoilage is inversely proportional to the guaranteed shelf life t xp, in ln coordinates t xp, 1/ T we obtain, in accordance with the Arrhenius equation, a straight line. From it you can calculate the activation energy of biochemical reactions leading to spoilage of a given product (about 115 kJ/mol). From the same graph you can find out to what temperature the product must be cooled so that it can be stored, for example, 3 years; it turns out to be –29° C.

2. Mountaineers know that in the mountains it is difficult to boil an egg, or in general any food that requires more or less long boiling. Qualitatively, the reason for this is clear: with a decrease in atmospheric pressure, the boiling point of water decreases. Using the Arrhenius equation, you can calculate how long it will take, for example, to hard boil an egg in Mexico City, located at an altitude of 2265 m, where the normal pressure is 580 mm Hg, and water at such a reduced pressure boils at 93 ° C The activation energy for the protein folding (denaturation) reaction was measured and turned out to be very large compared to many other chemical reactions - about 400 kJ/mol (it may differ slightly for different proteins). In this case, lowering the temperature from 100 to 93 ° C (that is, from 373 to 366 K) will slow down the reaction by 10 (400000/19)(1/366 – 1/373) = 11.8 times. This is why residents of the highlands prefer frying food to cooking: the temperature of a frying pan, unlike the temperature of a pan of boiling water, does not depend on atmospheric pressure.

3. In a pressure cooker, food is cooked at increased pressure and, therefore, at an increased boiling point of water. It is known that in a regular saucepan, beef is cooked for 2–3 hours, and apple compote for 10–15 minutes. Considering that both processes have similar activation energies (about 120 kJ/mol), we can use the Arrhenius equation to calculate that in a pressure cooker at 118°C, meat will cook for 25–30 minutes, and compote for only 2 minutes.

The Arrhenius equation is very important for the chemical industry. When an exothermic reaction occurs, the released thermal energy heats not only the environment, but also the reactants themselves. this may result in an undesirable rapid acceleration of the reaction. Calculating the change in reaction rate and heat release rate with increasing temperature allows us to avoid a thermal explosion ( cm. EXPLOSIVES).

Dependence of the reaction rate on the concentration of reagents.

The rate of most reactions gradually decreases over time. This result is in good agreement with the collision theory: as the reaction proceeds, the concentrations of the starting substances fall, and the frequency of collisions between them decreases; Accordingly, the frequency of collisions of active molecules decreases. This leads to a decrease in the reaction rate. This is the essence of one of the basic laws of chemical kinetics: the rate of a chemical reaction is proportional to the concentration of reacting molecules. Mathematically, this can be written as the formula v = k[A][B], where k– a constant called the reaction rate constant. The equation given is called the chemical reaction rate equation or kinetic equation. The rate constant for this reaction does not depend on the concentration of the reactants and on time, but it depends on temperature in accordance with the Arrhenius equation: k = k 0 e – E a/ RT .

The simplest speed equation v = k[A][B] is always true in the case when molecules (or other particles, for example, ions) A, colliding with molecules B, can directly transform into reaction products. Such reactions, occurring in one step (as chemists say, in one stage), are called elementary reactions. There are few such reactions. Most reactions (even seemingly simple ones like H 2 + I 2 ® 2HI) are not elementary, therefore, based on the stoichiometric equation of such a reaction, its kinetic equation cannot be written.

The kinetic equation can be obtained in two ways: experimentally - by measuring the dependence of the reaction rate on the concentration of each reagent separately, and theoretically - if the detailed reaction mechanism is known. Most often (but not always) the kinetic equation has the form v = k[A] x[B] y, Where x And y are called reaction orders for reactants A and B. These orders, in the general case, can be integer and fractional, positive and even negative. For example, the kinetic equation for the reaction of thermal decomposition of acetaldehyde CH 3 CHO ® CH 4 + CO has the form v = k 1.5, i.e. the reaction is one and a half order. Sometimes a random coincidence of stoichiometric coefficients and reaction orders is possible. Thus, the experiment shows that the reaction H 2 + I 2 ® 2HI is first order in both hydrogen and iodine, that is, its kinetic equation has the form v = k(This is why this reaction was considered elementary for many decades, until its more complex mechanism was proven in 1967).

If the kinetic equation is known, i.e. It is known how the reaction rate depends on the concentrations of the reactants at each moment of time, and the rate constant is known, then it is possible to calculate the time dependence of the concentrations of the reactants and reaction products, i.e. theoretically obtain all kinetic curves. For such calculations, methods of higher mathematics or computer calculations are used, and they do not present any fundamental difficulties.

On the other hand, the experimentally obtained kinetic equation helps to judge the reaction mechanism, i.e. about a set of simple (elementary) reactions. Elucidation of reaction mechanisms is the most important task of chemical kinetics. This is a very difficult task, since the mechanism of even a seemingly simple reaction can include many elementary stages.

The use of kinetic methods to determine the reaction mechanism can be illustrated using the example of alkaline hydrolysis of alkyl halides to form alcohols: RX + OH – → ROH + X – . It was experimentally discovered that for R = CH 3, C 2 H 5, etc. and X = Cl, the reaction rate is directly proportional to the concentrations of the reactants, i.e. has the first order with respect to the halide RX and the first order with respect to alkali, and the kinetic equation has the form v = k 1 . In the case of tertiary alkyl iodides (R = (CH 3) 3 C, X = I), the order in RX is first, and in alkali it is zero: v = k 2. In intermediate cases, for example, for isopropyl bromide (R = (CH 3) 2 CH, X = Br), the reaction is described by a more complex kinetic equation: v = k 1 + k 2. Based on these kinetic data, the following conclusion was made about the mechanisms of such reactions.

In the first case, the reaction occurs in one step, through direct collision of alcohol molecules with OH – ions (the so-called SN 2 mechanism). In the second case, the reaction occurs in two stages. The first stage is the slow dissociation of the alkyl iodide into two ions: RI → R + + I – . The second is a very fast reaction between ions: R + + OH – → ROH. The rate of the total reaction depends only on the slow (limiting) stage, so it does not depend on the alkali concentration; hence the zero order in alkali (SN 1 mechanism). In the case of secondary alkyl bromides, both mechanisms occur simultaneously, so the kinetic equation is more complex.

Ilya Leenson

Literature:

History of the doctrine of the chemical process. M., Nauka, 1981
Leenson I.A. Chemical reactions. M., AST – Astrel, 2002



Chemical kinetics is a branch of physical chemistry that studies the influence of various factors on the rates and mechanisms of chemical reactions.

Under mechanism A chemical reaction refers to those intermediate reactions that occur during the transformation of starting substances into reaction products.

The basic concept of chemical kinetics is the concept chemical reaction rate. Depending on the system in which the reaction occurs, the definition of “reaction rate” is somewhat different.

Homogeneous chemical reactions are reactions in which the reactants are in the same phase. These can be reactions between gaseous substances or reactions in aqueous solutions. For such reactions, the average rate (equal to the change in the concentration of any of the reactants per unit time)

.

The instantaneous or true rate of a chemical reaction is

.

Minus sign in right parts indicates a decrease in the concentration of the starting substance. Means, The rate of a homogeneous chemical reaction is the derivative of the concentration of the starting substance with respect to time.

Heterogeneous reaction is a reaction in which the reactants are in different phases. Heterogeneous reactions include reactions between substances in different states of aggregation.

The rate of a heterogeneous chemical reaction is equal to the change in the amount of any starting substance per unit time per unit interface area:

.

Kinetic equation chemical reaction is a mathematical formula that relates the rate of reaction to the concentrations of substances. This equation can only be established experimentally.

Depending on the mechanism, all chemical reactions are classified into simple (elementary) and complex. Simple are reactions that occur in one stage due to the simultaneous collision of molecules written on the left side of the equation. A simple reaction may involve one, two, or, which is extremely rare, three molecules. Therefore, simple reactions are classified into monomolecular, bimolecular and trimolecular reactions. Since, from the point of view of probability theory, the simultaneous collision of four or more molecules is unlikely, reactions of higher molecularity than three do not occur. For simple reactions, the kinetic equations are relatively simple. For example, for the reaction H 2 + I 2 = 2 HI, the kinetic equation has the form

= k ∙ C(I 2) ∙ C(H 2).

Complex reactions occur in several stages, and all stages are interconnected. Therefore, the kinetic equations of complex reactions are more cumbersome than simple reactions. For example, for the complex reaction H 2 + Br 2 = 2 HBr it is known

= .

The complexity of the kinetic equation is directly related to the complexity of the reaction mechanism.

The basic law of chemical kinetics is a postulate that follows from a large number of experimental data and expresses the dependence of the reaction rate on concentration. This law is called the law of mass action. It states that the rate of a chemical reaction at any given time is proportional to the concentrations of the reactants raised to certain powers.

If the equation of a chemical reaction has the form

a A + b B + d D → products,

then the formula for the law of mass action can be represented as

= k ∙ .

In this equation, k is the rate constant of a chemical reaction - the most important characteristic of the reaction, which does not depend on concentrations, but depends on temperature. The rate constant of a chemical reaction is equal to the reaction rate if the concentrations of all substances are 1 mol/l. The exponents n 1, n 2, n 3 are called private orders chemical reaction for substances A, B and D. For simple reactions, partial orders are small integers from zero to three. For complex reactions, partial orders can be either fractional or negative numbers. The sum of particular orders is called in order chemical reaction n = n 1 + n 2 + n 3. Thus , The order of a chemical reaction is the sum of the exponents of the powers of concentration in the kinetic equation.

Kinetic classification of simple homogeneous chemical reactions

From the point of view of chemical kinetics, simple chemical reactions are classified into reactions zero, first, second and third orders. Zero order reactions are extremely rare. In order for a reaction to proceed in zero order, specific conditions are required for its implementation. For example, the decomposition reaction of nitric oxide (5+) N 2 O 5 → N 2 O 4 + ½ O 2 proceeds as a zero-order reaction only in the case of solid nitric oxide (5+).

If a gaseous oxide is taken, then the reaction proceeds as a first-order reaction.

At the same time, it should be said that there are a large number of reactions in which the partial order for any substance is equal to zero. Usually these are reactions in which a given substance is taken in large excess compared to other reagents. For example, in the hydrolysis reaction of sucrose

C 12 H 22 O 11 + H 2 O → C 6 H 12 O 6 + C 6 H 12 O

Sucrose Glucose Fructose

the partial order of the reaction in water is zero.

The most common reactions are first and second order. There are few third-order reactions.

Let us consider, for example, a mathematical description of the kinetics of a first-order chemical reaction. Let us solve the kinetic equation of such a reaction

= kC.

Let us divide the variables dC = – kdt. After integration

= -∫kdt.

lnС = – kt + const.

Let's find the integration constant, taking into account the initial condition: at time t = 0, the concentration is equal to the initial C = C 0. Hence const = lnC 0 and

ln С = ln С 0 – kt,

ln С – ln С 0 = – kt,

= – kt,

C = C 0 ∙ e - kt .

This is the integral kinetic equation of the first order reaction.

An important kinetic characteristic of a reaction of any order is half-transformation time τ ½. The half-life is the time during which half the initial amount of a substance reacts. Let us find an expression for the half-conversion time of the first-order reaction. For t = τ ½ C = C 0 /2. That's why

= ln = – kt,

k τ ½ = ln 2.

= .

We present the results of solving differential kinetic equations for reactions of all orders in the form of a table (Table 2). The data in this table applies to the case when all reacting substances have the same initial concentrations.

Table - Kinetic characteristics of simple homogeneous reactions

Kinetic characteristic	Order of chemical reaction
	n=0	n=1	n=2	n=3
1Differential kinetic equation	= k.	= kC.	= kC 2 .	= kC 3 .
2 Integral kinetic equation	C 0 - C = kt	C = C 0 ∙e -kt	() = kt	() = 2kt
3 Reaction rate constant, its dimension	k = [(mol/l)∙s -1 ]	k = [s - 1 ]	k = [(mol/l) -1 ∙s -1 ]	k = [(mol/l) -2 ∙s -1 ]
4 Half-life	τ ½ =	τ ½ =	τ ½ =	τ ½ =
5 Function linear with time	C	ln C

Methods for determining reaction order

To determine the orders of chemical reactions, differential and integral methods are used. Differential methods use differential kinetic equations. The reaction order using these methods is calculated and represented as a number. Moreover, since the method is based on a kinetic experiment, the calculation result contains some error.