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   chemical reactions understand those intermediate reactions that occur during the conversion of the starting materials into reaction products.

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

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

.

The instantaneous or true rate of a chemical reaction is

.

Minus sign in right   part indicates a decrease in the concentration of the starting material. Means the speed of a homogeneous chemical reaction is called the time derivative of the concentration of the starting material.

Heterogeneous reaction  called a reaction in which reacting substances are in different phases. Heterogeneous are 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 material per unit time per unit surface area of \u200b\u200bthe interface:

.

Kinetic equation   chemical reaction is called a mathematical formula that relates the reaction rate 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   reactions that occur in one stage due to the simultaneous collision of molecules recorded on the left side of the equation are called. 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 higher than three do not occur. For simple reactions, kinetic equations are relatively simple. For example, for the reaction H 2 + I 2 \u003d 2, the HI kinetic equation has the form

   \u003d k ∙ C (I 2) ∙ C (H 2).

Difficult   reactions proceed in several stages, and all stages are interconnected. Therefore, the kinetic equations of complex reactions are more cumbersome than simple reactions. For example, for a complex reaction, H 2 + Br 2 \u003d 2 HBr 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 the postulate arising from a large number of experimental data and expressing 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 concentration of reacting substances raised to some extent.

If the chemical reaction equation has the form

a A + b B + d D → products,

then the formula of the law of the acting masses can be represented as

   \u003d k ∙.

In this equation, k is the chemical reaction rate constant, which is the most important characteristic of the reaction, which does not depend on concentrations, but depends on temperature. The chemical reaction rate constant 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 reactions for substances A, B and D. For simple reactions, particular orders are small integers from zero to three. For complex reactions, partial orders can be both fractional and negative numbers. The sum of private orders is called order   chemical reaction n \u003d n 1 + n 2 + n 3. Thus ,   the order of the chemical reaction is the sum of the indicators of the degrees 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 the reaction to proceed in the zeroth order, specific conditions for its implementation are necessary. 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 gaseous oxide is taken, 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 particular order for any substance is zero. Usually these are reactions in which this substance is taken in large excess in comparison with other reagents. For example, in the reaction of hydrolysis of sucrose

С 12 Н 22 О 11 + Н 2 О → С 6 Н 12 О 6 + С 6 Н 12 О

Sucrose Glucose Fructose

the partial reaction order in water is zero.

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

Consider, for example, a mathematical description of the kinetics of a first-order chemical reaction. We solve the kinetic equation of such a reaction

  \u003d kC.

Separate the variables dC \u003d - kdt. After integration

   \u003d -∫kdt.

lnС \u003d - kt + const.

We find the integration constant, taking into account the initial condition: at time t \u003d 0, the concentration is equal to the initial C \u003d C 0. Hence, const \u003d lnC 0 and

ln C \u003d ln C 0 - kt,

ln С - ln С 0 \u003d - kt,

  \u003d - kt,

C \u003d C 0 ∙ e - kt.

This is an 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-transformation time is the time during which half of the initial amount of substance reacts. Let us find an expression for the half-time of a first-order reaction. For t \u003d τ ½ C \u003d C 0/2. therefore

   \u003d ln \u003d - kt,

k τ ½ \u003d ln 2.

= .

The results of solving differential kinetic equations for reactions of all orders are presented in the form of a table (Table 2). The data in this table apply to the case when all reactants have the same initial concentration.

Table - Kinetic characteristics of simple homogeneous reactions

Kinetic characteristic	Chemical reaction order
	n \u003d 0	n \u003d 1	n \u003d 2	n \u003d 3
1 Differential kinetic equation	\u003d k.	\u003d kC.	\u003d kC 2.	\u003d kC 3.
2 Integral kinetic equation	C 0 - C \u003d kt	C \u003d C 0 ∙ e -kt	() \u003d kt	() \u003d 2kt
3 Reaction rate constant, its dimension	k \u003d [(mol / l) ∙ s -1]	k \u003d [s - 1]	k \u003d [(mol / L) -1 ∙ s -1]	k \u003d [(mol / L) -2 ∙ s -1]
4 Half-time	τ ½ =	τ ½ =	τ ½ =	τ ½ =
5 Time-linear function	C	ln C

Methods for determining the reaction order

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

Chemical kinetics -this is a branch of chemistry that studies the rates of reactions and the influence of various factors on them.

In a homogeneous (single-phase) process, the reaction proceeds in the entire volume of the system and its speed is characterized by a change in the concentration of any reagent, or any product per unit time. Distinguish average speed v  cf \u003d ± ΔС / Δt, where ΔC is the change in molar concentration over a time period Δt, and the true velocity at time t, which is a derivative of the concentration with respect to time: v  \u003d ± dС / dt.

The rate of each particular reaction in the absence of a catalyst depends on the concentration of the reactants and on the temperature . The rate of heterogeneous reactions occurring on the interphase interface also depends on the size of this surface.

The influence of the concentrations of the reagents on the reaction rate is established by the law of the active masses: at a fixed temperature, the reaction rate is proportional to the production of reagent concentrations in degrees equal to stoichiometric coefficients.

For the reaction aA + bB \u003d cC + dD, the mathematical expression of the law of acting masses, called kinetic reaction equation, is recorded: v  \u003d kС А а С B b, where k - coefficient of proportionality, called the rate constant,C A and C BAre the molar concentrations of the reactants, and a and b are their stoichiometric coefficients. The sum of the exponents in the kinetic equation is called the order of reaction.   In multi-stage reactions, the reaction order can be fractional, but no more than 3.

The kinetic equations of reactions concentration of substances in a condensed state  in view of their invariability are not indicated. These constant concentrations as constituents are included in the rate constant.

Reaction mechanism  called the set of stages of a chemical reaction, as a result of which the starting materials are converted to final. Reactions can be single-stage and multi-stage. The reaction rate is determined by the speed of its slowest stage (limiting stage).

Distinguish homogeneousand   heterogeneouschemical reactions. Reactions proceeding in a single-phase (homogeneous) system, for example, liquid or gaseous, are called homogeneous. Such reactions occur throughout the system. Reactions occurring in multiphase systems (consisting of two or more phases, for example, gaseous and solid phases) are called heterogeneous. Such reactions proceed only at the interface. The heterogeneous reaction rate is determined by the change in the concentration of reacting substances per unit surface per unit time.

Reaction molecular  called the number of particles involved in an elementary act of chemical interaction. In real reactions, the molecularity can be 1, 2, 3. In simple reactions proceeding in one stage, the order coincides with the molecularity. The law of masses is valid for simple reactions. In the case of complex reactions proceeding in several stages, the law applies to any single reaction, but not to their sum.

The dependence of the reaction rate on temperature is explained by the fact that, as already noted, the reaction rate depends on the number of collisions of particles (atoms, molecules, ions) participating in the reaction. But not all collisions lead to chemical interactions. In order for the reaction to occur, the particles must have some excess energy (compared with the average value), called activation energy  (E A). The higher the temperature, the more particles have an energy greater than or equal to E A. Therefore, the reaction rate increases with increasing temperature. The chemical reaction rate constant is determined by the number of effective collisions, i.e. the number of active molecules capable of entering into a chemical reaction. The dependence of the reaction rate constant on temperature and activation energy is expressed arrhenius equation :

where kis the reaction rate constant, Z is a constant called the steric factor and depending on the number of collisions leading to the reaction; e is the base of the natural logarithm (e \u003d 2.7183 ...); - activation energy, J / mol; R is the gas constant (R \u003d 8.314 J / K · mol), T  - temperature, K.

Chemical equilibrium is established in reversible reactions -in reactions that can occur in both forward and reverse directions. If the reaction aA + bB ↔ cC + dD) is reversible, this means that reagents A and B are able to turn into products C and D (direct reaction), and products C and D, in turn, can react with each other and again form the starting materials A and B (reverse reaction).

The thermodynamic condition for chemical equilibrium is the invariability of the Gibbs energy of the reaction, i.e. r G \u003d 0, and the kinetic condition for equilibrium is the equality of the rates of the direct (v 1) and reverse (v 2) reactions: v 1 \u003d v 2.

Since both direct and reverse reactions proceed at the same rate in a state of chemical equilibrium, the concentrations of reactants and products do not change over time. These concentrations that do not change in time are called equilibrium. Equilibrium concentrations, in contrast to nonequilibrium ones, changing during the reaction, are usually denoted in a special way, namely, by the formula of the substance enclosed in square brackets. For example, the entries [H 2], mean that we are talking about the equilibrium concentrations of hydrogen and ammonia.

At a given temperature, the ratio of equilibrium concentrations of reactants and products is a constant and characteristic value for each reaction. This ratio is quantitatively characterized by the value of the chemical equilibrium constant Kc equal to the ratio of the product of the equilibrium concentrations of the products to the product of the equilibrium concentrations of the reagents raised to degrees equal to their stoichiometric coefficients.

For the reversible reaction aА + bВ ↔ cС + dD, the expression Kc has the form:

Ks = .   As in the kinetic equations of reactions, in the expressions of the equilibrium constants, the concentrations of substances in the condensed state, due to their constancy, are not recorded.

For reactions involving gases, the chemical equilibrium constant can be expressed not only through equilibrium concentrations, but also through equilibrium partial pressures of gases. In this case, the symbol of the equilibrium constant "K" is indexed not by the symbol of concentration "c", but by the pressure symbol "p".

In the equilibrium state, characterized by the equality of the rates of the forward and reverse reactions, the system can remain arbitrarily long if the conditions do not change. When conditions change, the equality of speeds v 1= v 2  disrupted, one of the two reactions begins to proceed at a faster rate. This is expressed by saying that a shift (shift) of chemical equilibrium occurs in the system.

If, as a result of changing conditions in the system, a direct reaction begins to proceed at a higher rate, i.e. v 1> v 2 , the equilibrium shifts to the side of the direct reaction — to the right and, conversely, if the rate of the reverse reaction becomes greater than the rate of the direct reaction, the condition is satisfiedv 2 > v 1 , there is a shift of equilibrium towards the reverse reaction - to the left.

A shift in chemical equilibrium can be achieved by changing the concentrations of the reactants or products and changing the temperature, and for reactions involving gases, also by changing the pressure. The direction of the equilibrium shift under such changes in conditions is determined by the Le Chatelier principle (counteraction principle): if the conditions are changed in the equilibrium system, the equilibrium will shift in the direction of the reaction that counteracts the change.

Task 1  For a given chemical reaction, write the kinetic equation and determine the theoretical order of the reaction. Calculate how the reaction rate changes under the indicated changes in the reaction conditions: Fe 2 O 3 (tv) + 3CO (g) → 2Fe (tv) + 3CO 2 (g)

How many times will the reaction rate change (increase or decrease) if:

a) increase the pressure by 2 times;

b) increase the volume of the reaction mixture by 2 times

c) increase the temperature by 40 ° C (γ \u003d 2)

d) lower the temperature by 20? C (γ \u003d 2)

  Fe 2 O 3 (tv) + 3CO (g) → 2Fe (tv) + 3CO 2 (g) is a heterogeneous reaction (substances in different phase states are involved).

Kinetic equation: υ 1 \u003d k · s 3 (CO),

k is the rate constant. The kinetic equation of heterogeneous reactions includes only concentrations of gases or substances dissolved in a solvent.

Theoretical reaction order: 3 (the sum of the indicators of the degrees of concentration in the kinetic equation is called the theoretical reaction order).

The calculation of the change in reaction rate:

a)   with a 2-fold increase in pressure:the reaction rate to an increase in pressure is described by the kinetic equation:

υ 1 \u003d k · s 3 (CO), where c 3 (CO) is the initial (initial) concentration of carbon monoxide (II).

With increasing pressure, an increase in concentration occurs, i.e. if the pressure is increased by 2 times, then the concentration will increase by 2 times, therefore, the kinetic equation of the reaction after changing the pressure has the following form:

υ 2 \u003d k · (2с) 3 (CO), where (2с) 3 (CO) is the concentration of carbon monoxide (II) after increasing the pressure in the system by 2 times.

  \u003d \u003d \u003d 2 3 \u003d 8 - the reaction rate will increase by 8 times.

b)   with an increase in the volume of the reaction mixture by 2 times:

a 2-fold increase in the volume of the reaction mixture will lead to a 2-fold decrease in gas concentration: υ 1 \u003d k · s 3 (CO), where 3 (CO) is the initial (initial) concentration of carbon monoxide (II).

  υ 2 \u003d k (CO), where (CO) is the concentration of carbon monoxide (II) after increasing the volume of the reaction mixture by 2 times.

Change in reaction rate ():

  \u003d \u003d \u003d - the reaction rate will decrease by 8 times.

in) temperature increase by 40 ° C (γ \u003d 2):

When the temperature changes, the reaction rate changes according to the Vant-Hoff rule:

According to the problem conditions temperature increased by 40 ° C, Consequently

ΔT \u003d T 2 - T 1 \u003d 40,

  \u003d 2 40/10 \u003d 2 4 \u003d 16 - the reaction rate will increase by 16 times.

d) temperature decrease by 20 ° С (γ \u003d 2):

When the temperature changes, the reaction rate changes according to the Vant-Hoff rule:

  \u003d γ ΔТ / 10, where γ is the temperature coefficient of the reaction, ΔТ is the change in temperature (T 2 - T 1), υ 1 is the reaction rate at temperature T 1, υ 2 is the reaction rate at temperature T 2.

According to the problem conditions the temperature decreased by 20 ° C,

therefore, ΔT \u003d T 1 - T 2 \u003d -20,

  \u003d 2 -20/10 \u003d 2 -2 \u003d - the reaction rate will decrease by 4 times.

Task 21) For reversible reactions

CuO (tv) + CO (g) ↔ Cu (tv) + CO 2 (g) + QN 2 (g) + O 2 (g) ↔ 2NO (g) - Q, determine in which direction the reaction equilibrium will shift if :

a) increase the temperature; b) reduce the temperature

2) For reversible reactions:

C 2 H 2 (g) + 2H 2 (g) ↔ C 2 H 6 (g)

3S (tv) + H 2 O (g) ↔ 2H 2 S (g) + SO 2 (g)

C (tv) + O 2 (g) ↔ СО 2 (g), determine in which direction the reaction equilibrium will shift if:

a) increase pressure; b) reduce pressure

3) For a reversible reaction:

Fe 2 O 3 (tv) + 3H 2 (g) ↔ 2Fe (tv) + 3H 2 O (g), determine in which direction the reaction equilibrium will shift if:

a) increase the concentration of H 2;

b) reduce the concentration of H 2;

c) increase the concentration of H 2 O

g) reduce the concentration of H 2 O

The direction in which the chemical equilibrium shifts is determined by the Le Chatelier principle: if an external influence is exerted on the equilibrium system, then the equilibrium shifts in the direction that counteracts this effect.

1) An increase in temperature shifts the equilibrium toward the endothermic reaction (-Q), a decrease in temperature shifts the equilibrium toward the exothermic reaction (+ Q).

CuO (tv) + CO (g) ↔ Cu (tv) + CO 2 (g) + Q

In this case:

- direct reaction CuO (tv) + CO (g) → Cu (tv) + CO 2 (g) + Q - exothermic ,

- reverse reaction Cu (tv) + CO 2 (g) → CuO (tv) + CO (g) - Q - endothermic ,

consequently:

a) with increasing temperature  the equilibrium will shift towards the reverse reaction (towards the formation of reagents, to the left (←)),

b) with decreasing temperature  the equilibrium will shift towards a direct reaction (towards the formation of products, to the right (→)).

N 2 (g) + O 2 (g) ↔ 2NO (g) - Q

In this case:

direct reaction N 2 (g) + O 2 (g) → 2NO (g) - Q - endothermic,

reverse reaction 2NO (g) → N 2 (g) + O 2 (g) + Q - exothermic,

consequently:

a) with increasing temperature the equilibrium will shift towards a direct reaction (towards the formation of products, to the right (→))

b) with decreasing temperature  the equilibrium will shift towards the reverse reaction (towards the formation of reagents, to the left (←)).

2)  The increase in pressure shifts the equilibrium towards the reaction in which the number of gas molecules decreases. The decrease in pressure shifts the equilibrium towards that reaction in which the number of gas molecules increases.

In the system C 2 H 2 (g) + 2H 2 (g) ↔ C 2 H 6 (g)the direct reaction (C 2 H 2 (g) + 2H 2 (g) → C 2 H 6 (g)) proceeds with a decrease in the number of gas molecules (one molecule of the final product is formed from three molecules of the source gases), and the reverse reaction

(C 2 H 6 (g) → C 2 H 2 (g) + 2H 2 (g)) - proceeds with an increase in the number of molecules (three new ones are formed from one C 2 H 6 molecule (one C 2 H 2 molecule and two molecules H 2).

Consequently:

a) pressure increase  shifts the equilibrium towards a direct reaction (towards the formation of products, to the right (→));

b) pressure reduction  shifts the equilibrium towards the reverse reaction (towards the formation of reagents, to the left (←)).

In the system 3S (tv) + H 2 O (g) ↔ 2H 2 S (g) + SO 2 (g)the direct reaction (3S (tv) + H 2 O (g) → 2H 2 S (g) + SO 2 (g)) proceeds with an increase in the number of gas molecules, and the reverse (2H 2 S (g) + SO 2 (g) → 3S (tv) + H 2 O (g)) - proceeds with a decrease in gas molecules (S (sulfur) is a solid, the number of molecules of solids are not taken into account).

  Consequently:

a) pressure increase  shifts the equilibrium toward the reverse reaction (towards the formation of reagents, to the left (←));

b) pressure reduction  shifts the equilibrium towards a direct reaction (towards the formation of products, to the right (→)).

In system C (tv) + O 2 (g) ↔ СО 2 (g) the number of gas molecules among the reagents and among the products are equal (one O 2 molecule and one CO 2 molecule (g)), hence the pressure change (increase or decrease) will not affect  to a shift in chemical equilibrium in a given system.

a) pressure increase  balance does not bias;

b) pressure reduction  balance does not bias.

3) a) an increase in the concentration of reagents shifts the equilibrium towards the formation of products, therefore:

for this reaction, Fe 2 O 3 (tv) + 3H 2 (g) ↔ 2Fe (tv) + 3H 2 O (g) an increase in the concentration of H 2 reagent will shift the equilibrium towards the direct reaction (towards the formation of products, to the right (→ )).

b) a decrease in the concentration of reagents shifts the equilibrium towards the formation of reagents, therefore:

for this reaction, Fe 2 O 3 (tv) + 3H 2 (g) ↔ 2Fe (tv) + 3H 2 O (g) an increase in the concentration of reagent Н 2 will lead to a shift in equilibrium towards the reverse reaction (towards the formation of reagents, to the left (← ));

in) an increase in the concentration of products shifts the equilibrium towards the formation of reagents, therefore:

for this reaction, Fe 2 O 3 (tv) + 3H 2 (g) ↔ 2Fe (tv) + 3H 2 O (g) an increase in the concentration of the product H 2 O will lead to a shift in equilibrium towards the reverse reaction (towards the formation of reagents, to the left ( ←));

d) a decrease in the concentration of products shifts the equilibrium towards the formation of products, therefore:

for this reaction, Fe 2 O 3 (tv) + 3H 2 (g) ↔ 2Fe (tv) + 3H 2 O (g) a decrease in the concentration of the product H 2 O will lead to a shift in equilibrium towards the direct reaction (towards the formation of products, to the right ( →)).

Task 3.1) For the reversible reaction Fe 2 O 3 (tv) + 3CO (g) ↔ 2Fe (tv) + 3CO 2 (g), calculate the equilibrium constant if the initial concentration of CO is 3 mol / l, 75% of the reaction has occurred by the time of equilibrium .

2) For the reversible reaction S (tv) + H 2 (g) ↔ H 2 S (g), calculate the equilibrium concentrations of the substances if the initial concentration of H 2 is 3 mol / L and the equilibrium constant is Cr \u003d 15.

C) For the reversible reaction 2NH 3 (g) ↔ 3H 2 (g) + N 2 (g), calculate the initial concentration of NH 3 and the equilibrium constant of this reaction if the equilibrium concentrations of the substances are \u003d 0.4 mol / L, \u003d 1.2 mol / L, [H 2] \u003d 3.6 mol / L.

To solve these problems, it is convenient to use a table of the following form:

1) The equilibrium constant in heterogeneous reactions depends only on the concentration of gases; therefore, the amounts of solids (Fe 2 O 3 (tv) and Fe (tv)) are not taken into account .

In the line of initial concentrations, we enter the initial concentration of CO - 3 mol / L. The initial concentration of CO 2 is zero (this is the reaction product, which had not yet formed at the start of the reaction).

By condition, at the time of equilibrium, 75% of CO reacted,those. 3 mol 0.75 \u003d 2.25 mol.

The reaction formed 2.25 mol of CO 2, because according to the reaction equation  the amount of CO 2 is equal to the amount of CO.

After the reaction, the following amount of CO will remain:

From the beginning - With proreag \u003d 3 mol - 2.25 mol \u003d 0.75 mol.

Thus, the equilibrium concentrations will be equal to: \u003d 0.75 mol / L \u003d 2.25 mol / L

We calculate the chemical equilibrium constant (in accordance with the Law of the acting masses: in a state of chemical equilibrium at a certain temperature, the product of the concentrations of the reaction products in degrees, the indices of which are equal to the corresponding coefficients in the stoichiometric reaction equation, divided by the similar product of the concentrations of the reactants in the corresponding degrees, is a constant )

Cr \u003d \u003d \u003d 27

2)

In heterogeneous reactions, only gas concentrations are taken into account.

The initial concentration of H 2 is equal to 3 mol / L. The initial concentration of H 2 S is zero (this is the reaction product, which had not yet formed at the time the reaction started).

Let the H 2 mol form. In this case, the concentration of H 2 S will also be equal to chmol (since, according to the reaction equation, their ratio is 1: 1). The equilibrium concentration of H 2 is calculated:

С equal \u003d С beginning - С proreag \u003d (3 - х) mol, and the equilibrium concentration of H 2 S: С equal \u003d

\u003d C beginning + C proreag \u003d 0 + x \u003d x mol.

The expression for the equilibrium constant of this reaction has the following form:

Kp \u003d, substituting the known data, we obtain the equation:

15 \u003d, hence x \u003d 45-15x;

16x \u003d 45; x \u003d 2.8

Thus, the equilibrium concentration of H 2 S:

  \u003d x \u003d 2.8 mol / l

Equilibrium concentration of H 2:

  \u003d 3-x \u003d 3 - 2.8 \u003d 0.2 mol / l

3) We compile a table according to the reaction equation:

In the line of equilibrium concentrations, we write the data in the problem of concentration of substances. The amount of reacted NH 3 can be calculated by the amount of any of the substances obtained: for example, the ratio of NH 3 and N 2 according to the reaction equation  is 2: 1, which means that if 1.2 mol N 2 was formed after the reaction, then NH 3 reacted 2 times more: n (NH 3) \u003d 2 · 1.2 \u003d 2.4 mol.

The initial concentration of NH 3 is calculated:

With nach \u003d C proreag + C equ \u003d 2.4 + 0.4 \u003d 2.8 mol / L.

KINETICS.

Kinetics- This is the science of process speeds.

Chemical kineticsconsiders the speed and mechanism of chemical reactions. The most important parameter of kinetics is the process time.

The reaction rates depend on many factors: the nature of the reacting substances, concentration, temperature, pressure, the presence of catalysts, and in the case of phase transformations, also on a number of other conditions (state of the interface, heat and mass transfer conditions, etc.). The goal of kinetics is to elucidate the role of these factors and to establish the mechanism of reactions and phase transformations.

Chemical kinetics includes two sections:

1) a formal-mathematical description of the reaction rate without taking into account the actual mechanism of the reaction itself (formal kinetics);

2) the doctrine of the mechanism of chemical interaction.

FORMAL KINETICS.

In formal kinetics, the rate of a chemical reaction appears to depend only on the concentration of the reacting substances.

The laws of formal kinetics allow:

1) determine the kinetic parameters of the chemical reaction (rate constant, half-period, etc.);

2) to extend the obtained laws to complex multi-stage chemical reactions characteristic of technological processes;

3) classify chemical reactions.

Substances that enter the process of chemical transformation are called starting materials.

Substances formed in the process of chemical transformation and not undergoing further chemical changes during this process are called reaction products.

Substances formed in some stages of the chemical transformation process and diverging in other stages of the same process are called intermediate substances.

The reactions of formation and consumption of intermediate substances are called intermediate reactions.

A chemical reaction that proceeds in one phase is called   homogeneous chemical reaction(reaction in solution).

A chemical reaction occurring at the phase boundary is called heterogeneous chemical reaction(reaction on the surface of the catalyst). It should be noted that in a heterogeneous process, both reacting substances can be in the same phase. So, ethylene hydrogenation

C 2 H 4 + H 2 → C 2 H 6

goes on the surface of a catalyst, for example nickel. However, both reactants are in the same phase (in the gas phase above the catalyst surface).

Complex chemical reactions in which some stages are homogeneous and others heterogeneous are called homogeneous heterogeneous.

Homophasica process is called in which all components: initial, intermediate and final substances are in the limit of one phase. (For example, the reaction of neutralizing an acid with an alkali in a solution is homogeneous homophasic process).

Heterophase is a process in which components form more than one phase (for example, hydrogenation of ethylene on a nickel catalyst is heterogeneous homophasic process- the process proceeds at the boundary of the phases of the metal and gas, and the starting materials and the reaction product are in the same gas phase).

The main quantity in chemical kinetics is speed reaction.

Chemical reaction rateIs a change in the concentration of a substance per unit time in a unit volume. In the general case, the reaction rate changes over time and therefore it is better to define it as a derivative of the concentration of the reacting substance with time (with a constant volume of the system):

where
- speed, expressed as a decrease in concentration from the reacting substance; - time. Since, over time, the concentration of reacting substances decreases, therefore, the minus sign (“-”) is placed in front of the derivative (speed is a positive value).

When two or more substances interact, the reaction rate can be expressed in terms of the derivative of the concentration of any substance.

aA + bB → cC + dD

Equality takes place subject to the stoichiometric ratio between the participants in the reaction.

The change in concentration over time is expressed by a kinetic curve (
).

Knowing the kinetic curve for any component, one can easily determine the rate of its accumulation or expenditure by graphically differentiating the kinetic curve.

The tangent of the angle of inclination of the tangent to the kinetic curve is a graphical interpretation of the rate of a chemical reaction.

The steepness of the kinetic curve characterizes the true rate of a chemical reaction at a given point in time. In addition, the order and constant of the reaction rate can be determined from kinetic curves.

In the general case, chemical kinetics studies the optimal process conditions only for thermodynamically resolved reactions.

Chemical kinetics has 2 postulates:

I . On the independence of the reaction.

If the process proceeds through a series of stages, it is assumed that the speed of each individual stage does not depend on the speed of the remaining stages.

II . The speed of a chemical reaction is directly proportional to the concentration of starting materials (HMD).

aA + bB → cC + dD

This record of the reaction rate expression is called kinetic equation.

The speed of a chemical reaction depends on the concentration of the starting materials, on temperature, time, catalyst, and the nature of the substances.

k Is the rate constant. It is numerically equal to the reaction rate at a concentration of substances equal to unity.

Speed \u200b\u200bconstant kindependent of reagent concentration and time (
) It depends on temperature, the presence of a catalyst and the nature of the substances (
catalyst, nature of matter ).

OrderIs an exponent at the concentration of a given substance in the kinetic equation.

In the case of a one-stage process, the degree indicators are equal to stoichiometric coefficients:
;
.

The sum of the reaction orders for all reactants is called reaction order(
).

The reaction rate constants of various orders have different dimensions and are different physical quantities; comparing their absolute values \u200b\u200bis devoid of any meaning.

First-order speed constant: ;

Second-order speed constant:
;

Third-order speed constant:
.

CLASSIFICATION OF CHEMICAL REACTIONS:

I. In order of reaction. N \u003d 0, 1, 2, 3, fractional;

II.By molecularity.

Reaction molecular- this is the number of molecules that take part in a single act of collisions. Molecularity can only be determined by establishing a reaction mechanism. Depending on the number of reacting molecules (particles) participating in the elementary act, one-molecular (monomolecular), two-molecular, trimolecular reactions are distinguished.

TO single moleculartype A → P reactions include molecular decomposition into simpler components and isomerization reactions. Bimolecularelementary reactions of the form are called: A + B → P and 2A → P (H 2 + J 2 \u003d 2HJ, HJ + HJ \u003d H 2 + J 2, CH 3 COOCH 3 + H 2 O \u003d CH 3 COOH + CH 3 OH and t .d.). Significantly less common three molecularreactions A + 2B → P or 3A → P. In all cases, the type and quantity of the reaction products formed does not matter, since the molecularity is determined only by the number of molecules of substances that react in an elementary act.

The reaction order is established experimentally.

The molecularity and order of the reaction may coincide, but may vary. Molecularity and reaction order coincideonly for simple reactions proceeding in only one elementary stage without the participation of extraneous molecules.

Molecularity and reaction order do not matchin three main cases:

1) for complex reactions;

2) for heterogeneous reactions;

3) for reactions with an excess of one of the reacting substances.

KINETIC EQUATIONS OF DIFFERENT ORDER REACTIONS.

The differentiation of reactions in order occurs according to a formal attribute - the sum of the exponents in the kinetic equations of chemical reactions, which limits the possibilities of formal kinetics. Nevertheless, formal kinetics makes it possible to use mathematical dependences to find kinetic parameters. All the dependencies below are valid for simple homogeneous reactions in closed systems at constant volume and temperature (V \u003d const, T \u003d const).

Zero-order reactions (n=0).

In this case, the reaction rate is constant, since the concentration of the reaction components is constant.
.

Consider the saponification reaction of the ester:

The rate of saponification of ether will be described by the following equation:

1 excess

If you take a large excess of water, then its concentration will be constant and the kinetic equation will take the form:

We can say that the reaction order in the private order of the water component will be zero.

Thus, a large excess of one of the reagents reduces the reaction order by a certain amount.

In the general case, the kinetic equation of the reaction of the zero order has the form:

–kineticthe equationzeroof order

For example, the reaction A → P and its speed is described by the equation
, if substance A is taken in large excess, then we obtain:

The rate constant of this reaction is equal to:

Separate the variables and integrate this equation:

At
the integration constant is equal to the initial concentration C 0 (const \u003d C 0), then we obtain:

;
for n \u003d 0

The reaction rate is often used as a criterion for the reaction rate. called half-life.

Half life- this is the time during which half of the taken substance will react.

→
;

– half-life for a zero order reaction

Zero order occurs in heterogeneous and photochemical reactions.

First-Order Reactions (n=1).

An example of a reaction that strictly obeys a first-order equation is the thermal decomposition of acetone (although the reaction actually proceeds by a complex mechanism):

CH 3 COCH 3 → CO + CH 3 CH 3

If we denote the concentration of acetone at each point in time through C, then at a constant temperature the reaction rate will be:

Separating the variables and integrating the equation, we get:

At
integration constantconst \u003d lnС 0, then:

(1)

(2)

Equations (1) and (2) are various forms of the kinetic equation of the first order reaction. They make it possible to calculate the concentration of the reacting substance at any time using the known value of the rate constant or, conversely, to find the reaction rate constant at a given temperature by determining the concentration at any time. Express half-life for a first order reaction:

Thus, the half-time of the first-order reaction does not depend on the initial concentration of the starting material and is inversely proportional to the reaction rate constant.

This dependence can be represented graphically in the coordinates
. Since the half-conversion time in this case will be the same, at each instant of time, the concentration of the reacting substance can be determined.

For practical purposes, it is more advantageous to express the rate of loss of matter. Let V \u003d const, at the beginning of the reaction
, the number of moles of the reactant is a. Through seconds reacted x moles of substance A. Then at this point in time the concentration of substance A will be
or
where
. After separation of variables and integration, the equation will look like:

At
, x \u003d 0

, so

A → P (V \u003d const)

The initial number of moles ( =0)

The subject of chemical kinetics is the study of all factors affecting the speed of both the total process and all intermediate stages

Encyclopedic YouTube

1 / 5

✪ Physical chemistry. Lecture 3. Chemical kinetics and catalysis

✪ Korobov M.V. - Physical chemistry II - Chemical reaction rate. Formal kinetics

✪ Chemistry. Kinetics of chemical reactions. The speed of a chemical reaction. Foxford Online Learning Center

✪ Introduction to kinetics

✪ Chemical kinetics

Subtitles

Basic concepts

Homogeneous reaction - a reaction in which reacting substances are in one phase

A heterogeneous reaction is a reaction that occurs at the phase boundary - between a gaseous substance and a solution, between a solution and a solid, between solid and gaseous substances

The reaction is called simple if the product is formed as a result of direct interaction of the molecules (particles) of the reagents

A reaction is called complex if the final product is obtained as a result of two or more simple reactions (elementary acts) with the formation of intermediate products

Chemical reaction rate

An important concept of chemical kinetics is chemical reaction rate. This value determines how the concentration of reaction components changes over time. The speed of a chemical reaction is always a positive value, so if it is determined by the starting material (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:

   A + B → C + D, (\\ displaystyle A + B \\ to C + D,)    v \u003d ∂ C ∂ t \u003d - ∂ A ∂ t. (\\ displaystyle v \u003d (\\ frac (\\ partial C) (\\ partial t)) \u003d - (\\ frac (\\ partial A) (\\ partial t)).)

Chemical reaction order

The reaction order for a given substance is an exponent at the concentration of this substance in the kinetic equation of the reaction.

Zero order reaction

The kinetic equation has the following form:

   V 0 \u003d k 0 (\\ displaystyle V_ (0) \u003d k_ (0))

The reaction rate of the zero order is constant in time and does not depend on the concentrations of the reacting substances. Zero order is characteristic, for example, for heterogeneous reactions if the diffusion rate of the reactants to the interface is less than the rate of their chemical transformation.

First order reaction

The kinetic equation of the first order reaction:

   V 1 \u003d k 1 ⋅ C \u003d - d C d τ (\\ displaystyle V_ (1) \u003d k_ (1) \\ cdot C \u003d - (\\ frac (dC) (d \\ tau)))

Reducing the equation to a linear form gives the equation:

   ln \u2061 C \u003d ln \u2061 C 0 - k 1 ⋅ τ (\\ displaystyle \\ ln C \u003d \\ ln C_ (0) -k_ (1) \\ cdot \\ tau)

The reaction rate constant is calculated as the slope of the straight line to the time axis:

   k 1 \u003d - t g α (\\ displaystyle k_ (1) \u003d - \\ mathrm (tg) \\ alpha)

Half-life:

   τ 1 2 \u003d ln \u2061 2 k 1 (\\ displaystyle \\ tau _ (\\ frac (1) (2)) \u003d (\\ frac (\\ ln 2) (k_ (1))))

Second order reaction

For second-order reactions, the kinetic equation has the following form:

   V \u003d k 2 C A 2 (\\ displaystyle V \u003d k_ (2) (C_ (A)) ^ (2))    V \u003d k 2 C A ⋅ C B (\\ displaystyle V \u003d k_ (2) C_ (A) \\ cdot C_ (B))

In the first case, the reaction rate is determined by the equation

   V \u003d k 2 C A 2 \u003d - d C d τ (\\ displaystyle V \u003d k_ (2) (C_ (A)) ^ (2) \u003d - (\\ frac (dC) (d \\ tau)))

The linear form of the equation:

   1 C \u003d k 2 ⋅ τ + 1 C 0 (\\ displaystyle (\\ frac (1) (C)) \u003d k_ (2) \\ cdot \\ tau + (\\ frac (1) (C_ (0))))

The reaction rate constant is equal to the slope of the straight line to the time axis:

   k 2 \u003d - t g α (\\ displaystyle k_ (2) \u003d - \\ mathrm (tg) \\ alpha)    k 2 \u003d 1 τ (1 C - 1 C 0) (\\ displaystyle k_ (2) \u003d (\\ frac (1) (\\ tau)) \\ left ((\\ frac (1) (C)) - (\\ frac ( 1) (C_ (0))) \\ right))

In the second case, the expression for the reaction rate constant will look like this:

   k 2 \u003d 1 τ (C 0, A - C 0, B) ln \u2061 C 0, B ⋅ CAC 0, A ⋅ CB (\\ displaystyle k_ (2) \u003d (\\ frac (1) (\\ tau (C_ (0 , A) -C_ (0, B)))) \\ ln (\\ frac (C_ (0, B) \\ cdot C_ (A)) (C_ (0, A) \\ cdot C_ (B))))

Half-life (for the case of equal initial concentrations!):

   τ 1 2 \u003d 1 k 2 ⋅ 1 C 0 (\\ displaystyle \\ tau _ (\\ frac (1) (2)) \u003d (\\ frac (1) (k_ (2))) \\ cdot (\\ frac (1) ( C_ (0))))

Reaction molecular

The molecularity of an elementary reaction is the number of particles that, according to the experimentally established reaction mechanism, participate in an elementary act of chemical interaction.

Monomolecular reactions  - reactions in which the chemical transformation of one molecule occurs (isomerization, dissociation, etc.):

   H 2 S → H 2 + S (\\ displaystyle (\\ mathsf (H_ (2) S \\ rightarrow H_ (2) + S)))

Bimolecular reactions  - reactions whose elementary act occurs when two particles collide (identical or different):

   C H 3 B r + K O H → C H 3 O H + K B r (\\ displaystyle (\\ mathsf (CH_ (3) Br + KOH \\ rightarrow CH_ (3) OH + KBr)))

Trimolecular reactions  - reactions whose elementary act occurs when three particles collide:

   N O + N O + O 2 → 2 N O 2 (\\ displaystyle (\\ mathsf (NO + NO + O_ (2) \\ rightarrow 2NO_ (2))))

Reactions with a molecular weight of more than three are unknown.

For elementary reactions carried out at close concentrations of the starting materials, the molecular values \u200b\u200band the order of the reaction coincide. There is no clearly defined relationship between the concepts of molecularity and the order of the reaction, since the order of the reaction characterizes the kinetic equation of the reaction, and molecularity is the reaction mechanism.

Catalysis

  . An example of a negative is a decrease in the corrosion rate when introduced into the liquid in which the metal is operated, sodium nitrite, chromate and potassium dichromate.

Many important chemical industries, 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.

Catalysis in biochemistry

Enzymatic catalysis is inextricably linked with the vital activity of organisms of the plant and animal world. Many vital chemical reactions that take place in the 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 has chosen for this one single building material - amino acids and combined them into polypeptide chains of different lengths and in different sequences

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

For some enzymes, the complete amino acid composition and the sequence of their arrangement 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 are enzymes so selective and accelerate the chemical transformations of molecules of only a very definite structure (which we also know); 2) how the enzyme lowers the energy barrier, that is, chooses an energetically more favorable path, so that reactions can proceed at ordinary temperature.

Strict selectivity and high speed are two main features of enzymatic catalysis that distinguish it from laboratory and industrial catalysis. None of the catalysts created by human hands (with the possible exception of 2-hydroxypyridine) can be compared with enzymes in terms of the strength and selectivity of their effects on organic molecules. The activity of the enzyme, like any other catalyst, also depends on temperature: with increasing temperature, the rate of the enzymatic reaction also increases. In this case, a sharp decrease in the activation energy E as compared to the non-catalytic reaction is noteworthy. 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.

Types of Enzymatic Reactions

• Type Ping Pong  - the enzyme first interacts with substrate A, taking away any chemical groups from it and turning it into the corresponding product. Substrate B, which receives these chemical groups, is then attached to the enzyme. An example is the reaction of transferring amino groups from amino acids to keto acids: transamination.
• Type of sequential reactions  - substrates A and B are sequentially attached to the enzyme, forming a “triple complex”, after which catalysis is carried out. The reaction products are also sequentially cleaved from the enzyme.
• Type of random interactions  - substrates A and B are attached to the enzyme in any order, disordered, and after catalysis are also cleaved.

General chemistry: textbook / A. V. Zholnin; under the editorship of V.A. Popkova, A.V. Zholnina. - 2012 .-- 400 p .: ill.

Chapter 2. BASES OF KINETICS OF CHEMICAL REACTIONS

Chapter 2. BASES OF KINETICS OF CHEMICAL REACTIONS

The difference between breathing and burning 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 is judged by the magnitude of the change in free energy (ΔG ≤0). However, this value does not indicate the real possibility of a reaction under these conditions.

For example, the reaction of nitrous oxide with oxygen proceeds instantly at room temperature:

At the same time, 2Н 2 (g) + О 2 (g) \u003d 2Н 2 О (ж), Δ ° g\u003d -286.8 kJ / mol - a reaction characterized by a significantly larger decrease in free energy, under normal conditions, the interaction does not proceed, but at 700 ° C or in the presence of a catalyst the process proceeds instantly. Therefore, thermodynamics does not answer the question of conditions and the rate of the process. This shows the limitations of the thermodynamic approach. To describe a chemical reaction, it is also necessary to know the laws of its course in time, which are studied by kinetics.

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

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

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

The rate of a chemical reaction is determined by the amount of substance that has reacted per unit time in a unit volume (in the case of homogeneous reactions, when the reacting substances are in the same phase) or on a unit of interface(in the case of heterogeneous reactions, when the reacting substances 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. The equation describing the dependence of the reaction rate (v) on the concentration (from)reactants called kinetic.The reaction rate is often expressed in mol / l-s, in biochemistry in mg / 100ml-s, or in mass fraction, in% / 100 ml-s. Distinguish between the average reaction rate in the time interval and the true reaction rate at a certain point in time. If in the time interval t 1and t 2the concentration of one of the starting materials or reaction products is equal to 1 and 2, respectively, then the average reaction rate (v) in the time interval t 1and t 2can express:

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

By equation (2.2) determine average speedchemical reaction. True (instantaneous) speedreactions are determined graphically. A graph is plotted of the concentration of the starting material 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 (e.g. t 1)the true reaction rate is equal to the tangent of the angle of inclination of the tangent to the kinetic curve at the point corresponding to a given moment in time. According to the schedule, the instantaneous reaction rate will be calculated by the formula:

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

Fig. 2.1.Kinetic curve

where V m- maximum reaction rate; K m - Michaelis constant equal to the concentration of the substrate at which the reaction rate is half of the maximum; S- substrate concentration.

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

2.2. MOLECULARITY AND ORDER OF REACTION. HALF-PERIOD

In kinetics, chemical reactions differ in terms of molecularity and reaction order. Reaction molecularis 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 the elementary act of the reaction. The probability of collision of a larger number of particles is very small. On this basis, monomolecular, bimolecular and trimolecular reactions are distinguished. Experimentally, the molecularity of the reaction can be determined only for elementary (simple) reactions proceeding in one stage in accordance with the stoichiometric equation. Most of these reactions require a large activation energy (150-450 kJ / mol).

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

tion.Therefore, to characterize the kinetics of the reaction, the concept of reaction orderwhich is determined by the stoichiometric equation.

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

Monomolecular reactions include decomposition and isomerization reactions.

Reactions whose velocity equation includes the concentration of one reacting substance in the first degree are called first-order reactions.

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

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

In heterogeneous systems, the collision of particles occurs at the phase boundary, therefore, the mass of the solid phase does not affect the reaction rate and therefore is not taken into account in the expression for the reaction rate.

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

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

Trimolecular reactions are rare, and four-molecular reactions are not known.

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

Reactions whose rate does not depend on the concentration of the starting materials are called zero order reactions (v \u003d 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 process is judged by one substance. Moreover, a quantitative characteristic of the course of reactions in time is half-life (time)reagent - the time during which the amount or concentration of the starting material is halved (by 50%) or half of the reaction products is formed. In this way, they characterize, in particular, the decay of radionuclides, since their half-life is independent of the initial amount.

By analyzing the dependence of the half-reaction period of the reaction on the initial concentration, it is possible to determine the reaction order (Ostwald-Noyes method). The constancy of the half-transformation period (at a given temperature) is characterized by many decomposition reactions and, in general, first-order reactions. With an increase in the reagent concentration, the half-transformation period decreases for second-order reactions and increases for zero-order reactions.

2.3. REACTION SPEED CONSTANT, ITS DEFINITION. LAW OF CURRENT MASSES

The speed 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 degrees equal to the stoichiometric coefficients of the corresponding substances in the reaction equation. This pattern is called the law of the masses(the law of the rate of a chemical reaction), which is

basic law of chemical kinetics. The law of the masses was established by the Norwegian scientists C. Gouldberg and P. Wage in 1867.

For example, for a reaction that proceeds in general, according to the scheme

the kinetic equation is true:

where v- the speed of the chemical reaction; with Aand with B- concentration of substances Aand IN[mol / l]; v aand v b- indicators of the order of reagents Aand B; k- chemical reaction rate constant - coefficient independent of the concentration of reacting substances.

Chemical reaction rate constant (k) represents the speed of a chemical reaction under conditions when the product of the concentrations of the reacting substances is 1 mol / L. In this case, v \u003d k.

For example, if in the reaction Н 2 (g) + I 2 (g) \u003d 2НI (g) c (H 2) and c (I 2) are equal to 1 mol / L, or if c (H2) is 2 mol / L , and c (I 2) 0.5 mol / l, then v\u003d k.

Units of measurement of the 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 in meaning quantities with 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 conduct direct observations of the course 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) \u003d 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 has a complex character and consists of 3 elementary reactions: I 2 \u003d 2I; 2I \u003d I 2; 2I + H 2 \u003d 2HI. Although the reaction can be formally classified as trimolecular, its speed is described by a kinetic equation resembling a second-order reaction equation:

In complex reactions, the molecularity and order of the reaction, as a rule, do not coincide. Unusual - fractional or negative - the order of the reaction clearly indicates its complex mechanism.

The kinetic equation for the oxidation of carbon monoxide with oxygen 2CO (g) + O 2 (g) \u003d CO 2 (g) has a negative (minus first) order in CO:

with increasing concentration of carbon monoxide, the reaction rate decreases.

The reaction mechanism can be divided into several types.

Sequential reactionscomplex reactions are called, 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 the third, etc., until the final product is formed:

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

The stages of successive reactions proceed at different rates. The stage, the rate constant of which is minimal, is called the limiting one.It determines the kinetic regularity of the reaction as a whole. Substances formed in the intermediate stages are called intermediate productsor intermediateswhich are substrates of subsequent stages. If the intermediate is slowly formed and rapidly decomposes, then its concentration does not change for a long time. Almost all metabolic processes are sequential reactions (for example, glucose metabolism).

Parallel reactionsreactions with the same starting reagents to which different products correspond are called. FROM the rate of parallel reactions is equal to the sum of the rates of individual reactions.This rule also applies to bimolecular parallel chemical reactions.

Sequentially parallel reactionsreactions that have the same initial reagents that can react in two ways (mechanisms) or more, including with a different number of intermediate stages, are called. This case underlies the phenomenon. catalysiswhen an intermediate of one of the paths will increase the speed of the other paths.

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

Conjugated reactionscomplex reactions are called in which one reaction proceeds only in the presence of another. In conjugated reactions, the intermediate substance serves as a link between the primary and secondary processes and causes the course of both.

A living cell needs energy for its existence. Adenosine triphosphoric acid (ATP) is a universal source of energy in living organisms. This compound acts as an energy accumulator, since when it interacts with water, i.e. hydrolysis, adenosine diphosphoric (ADP) and phosphoric (F) acids are formed and energy is released. Therefore, ATP is called macro-ergic connectionand the P-O-P bond breaking during its hydrolysis is macroergic. Macroergic linkcalled a chemical bond, in the break of which as a result of the hydrolysis reaction significant energy is released:

As you know, breaking any connection (including macroergic) always requires energy. In the case of ATP hydrolysis, in addition to the process of breaking bonds between phosphate groups, for which Δ G\u003e 0, processes of hydration, isomerization and neutralization of products formed during hydrolysis occur. As a result of all these processes, the total change in Gibbs energy has a negative

value. Therefore, macroergic is not a bond break, but the energy result of its hydrolysis.

In order for endergonic reactions to occur in living systems (ΔG\u003e 0), 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 ATP hydrolysis reaction, accompanied by the formation of a common intermediate compound of glucose-1-phosphate, leads to the fact that the total process has ∑ΔG<0:

Chain reactionschemical and nuclear reactions are called in which the appearance of an active particle (free radical or atom in a chemical, 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 proceed through a chain mechanism. Theory of chain reactions was developed by academician H.H. Semenov, S.N. Hinshelwood (England) and others. The main stages of chain reactions are: nucleation (initiation), continuation (elongation), and chain termination (termination). There are two types of chain reactions: reactions with unbranched and branched chains. A feature of chain reactions is that one primary act of activation leads to the transformation of a huge number of molecules of the starting materials. Biochemical reactions of free radical oxidation are chain.

Periodic (self-oscillating) reactionscomplex multi-stage autocatalytic reactions involving several substances are called, in which there is a periodic fluctuation of the concentrations of the oxidized and reduced forms. Vibrational reactions are discovered B.P. Belousov, investigated A.M. Jabotinsky et al. The frequency and form of oscillations depend on the concentrations of the starting materials, acids

nost, temperature. An example of such reactions may be the interaction of bromomalonic acid with potassium bromate in an acidic medium, the cerium (III) salt being the catalyst. 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, Academy of Sciences of the USSR A.G. Merzhanov and I.G. Borovinskaya. The essence of the SHS method is that after local initiation of the reaction of reactants, the front of the combustion reaction spontaneously spreads throughout the system due to heat transfer from hot products to the starting materials, initiating the reaction in them. Thus, the combustion process is carried out, which is both the cause and the consequence of the reaction. The mechanism for the occurrence of SHS reactions is quite complex and includes processes reaction diffusion.The term "reaction diffusion" defines the totality of phenomena that occur during the interaction of two chemically different components that can form chemical compounds in the form of solid phases. The products of chemical interaction form a continuous layer that differs in structure from the initial components, but does not interfere with the course of further interaction.

2.5. Theory of active collisions. ENERGY ACTIVATION. DEPENDENCE OF REACTION SPEED ON THE NATURE OF REACTIVE SUBSTANCES AND TEMPERATURE

In order for an elementary act of chemical interaction to occur, the reacting particles must collide with each other. However, not every collision leads to chemical interaction. The latter occurs when particles approach a distance at which a redistribution of electron density and the appearance of new chemical bonds are possible. The interacting particles must have sufficient energy to overcome the repulsive forces arising between their electron shells.

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

is within a short (10 -15 s) time. The energy that needs to be spent to bring the system into a transition state is called activation energy.In multi-stage reactions, which 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.

The active molecules A 2 and B 2 in a collision are combined into an intermediate active complex A 2 ... B 2 with the weakening and then breaking of the bonds AA and BB and the strengthening of bonds AB.

The “activation energy" of the HI formation reaction (168 kJ / mol) is much less than the energy required for complete bond breaking in the starting H 2 and I 2 molecules (571 kJ / mol). Therefore, the reaction path through education active (activated) complexenergetically more advantageous than the path through a complete breaking of bonds in the original molecules. Through the formation of intermediate active complexes, the vast majority of reactions occur. The provisions of the theory of the active complex were developed by G. Eyring and M. Polyany in the 30s of the 20th century.

Activation energyrepresents the excess kinetic energy of particles relative to the average energy required for the chemical transformation of colliding particles. Reactions are characterized by different values \u200b\u200bof activation energy (E a). In most cases, the activation energy of chemical reactions between neutral molecules is from 80 to 240 kJ / mol. For biochemical processes, the values \u200b\u200bof Е а are often lower - up to 20 kJ / mol. This is because the vast majority of biochemical processes proceed through the stage of enzyme-substrate complexes. Energy barriers limit the progress of 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 progress is difficult to notice.

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

Fig. 2.2.Favorable (a) and unfavorable (b, c) orientation of A 2 molecules

and B 2 in a collision

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

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

Equation (2.8) was derived by Arrhenius in 1889. The preexponential 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 share of active collisions of their total number, i.e. colliding molecules must have

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 velocity (2.6), it was specifically agreed 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 proceed 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 acting masses, 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 the increase in the rate of reactions 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.

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

However, chemical transformations, the rate of which decreases with increasing temperature, are now well known. 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 abnormal.

Of particular interest to doctors is the temperature dependence of the rate of enzymatic reactions, i.e. reactions involving enzymes. Almost all reactions that occur in the body belong to this class. For example, during the decomposition of hydrogen peroxide in the presence of a catalase enzyme, the decomposition rate depends on temperature. In the range 273–320 ° K, the temperature dependence is normal. With an increase in temperature, the velocity increases, with a decrease, it decreases. When the temperature rises

320 ° K there is a sharp abnormal drop in the rate of decomposition of peroxide. A similar picture holds for other enzymatic reactions (Fig. 2.3, c).

From the Arrhenius equation for kit can be seen that since Tincluded in the exponent, the rate of a chemical reaction is very sensitive to temperature changes. The temperature dependence of the rate of a homogeneous reaction can be expressed by the Van Goff rule, according to which with an increase in temperature for every 10 °, the reaction rate increases 2-4 times;a number showing how many times the rate of a given reaction increases with a temperature increase of 10 ° is called temperature coefficient of reaction rate- γ.

where k- speed constant at temperature t° C. Knowing the value of γ, we can calculate the change in the reaction rate with a change in temperature from T 1before T 2according to the formula:

With increasing temperature in an arithmetic progression, the speed increases exponentially.

For example, if γ \u003d 2.9, then with a temperature increase of 100 °, the reaction rate increases 2.9 × 10 times, i.e. 40 thousand times. Deviations from this rule are biochemical reactions, the rate of which increases tens of times with a slight increase in temperature. This rule is valid only in a rough approximation. Reactions in which large molecules (protein) are involved are characterized by a large temperature coefficient. The rate of protein (egg albumin) denaturation increases 50 times with a temperature increase of 10 ° C. After reaching a maximum (50-60 ° C), the reaction rate decreases sharply as a result of protein thermal denaturation.

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

Pre-exhibitor And withindependent of temperature, but concentration dependent. The unit of measurement is mol / l s.

Theoretical dependence allows you to pre-calculate the speed at any temperature, if the activation energy and pre-exponent are known. Thus, the effect of temperature on the speed of the chemical transformation is predicted.

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

A chemical reaction does not always “reach the end”, in other words, the starting materials are not always completely converted into reaction products. This is because, as the reaction products accumulate, conditions can be created for the reaction to proceed in the opposite direction. Indeed, if, for example, mixed iodine vapors with hydrogen at a temperature of ~ 200 ° C, then the reaction will occur: H 2 + I 2 \u003d 2HI. However, it is known that, even when heated to 180 ° C, iodine begins to decompose into iodine and hydrogen: 2HI \u003d H 2 + I 2.

Chemical reactions, which under the same conditions can go in opposite directions, are called reversible.When writing the equations of reversible reactions, instead of the equal sign put two oppositely directed arrows. The reaction proceeding from left to right is called straight(direct reaction rate constant k 1)from right to left - reverse(feedback 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 materials. Conversely, the reverse reaction at the initial moment has a minimum rate, which increases as the concentration of reaction products increases. Finally, there comes a moment when the rates of direct and reverse reactions become equal. The state in which the rate of the reverse reaction becomes equal to the rate of the direct reaction is called chemical equilibrium.

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

where K is equilibrium constantrepresenting the ratio of the rate constants of direct 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 at chemical equilibrium. It should be especially noted that, in contrast to the law of the acting masses, for the reaction rate in this equation, the exponents a, b, d, f andetc. always equal to stoichiometric coefficients in the equilibrium reaction.

The numerical value of the equilibrium constant of a given reaction determines its yield. Reaction outputthey call the ratio of the amount of the product actually obtained to the amount that would have been obtained if the reaction progressed to the end (usually expressed as a percentage). So, at K \u003e\u003e 1, the reaction yield is large and, conversely, at K<<1 выход реакции очень мал.

Equilibrium constant is related to standard Gibbs energyreactions as follows:

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

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

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

At ΔG \u003d 0 - the reaction reached equilibrium (thermodynamic condition);

  when ΔG\u003e 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 converse is true: in equilibrium, the concentrations themselves take such values \u200b\u200bthat the ratio of their products in degrees of stoichiometric coefficients

it turns out to be a constant value at a given temperature. This statement complies with the law of the current masses and can even be used as one of its formulations.

As mentioned above, reversible reactions do not proceed to the end. However, if one of the products of the reversible reaction leaves the reaction sphere, then the essentially reversible process proceeds almost to the end. If electrolytes are involved in the 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 the end. Irreversible reactionsthey call such reactions, the products of which do not interact with each other with the formation of starting materials. Irreversible reactions, as a rule, “reach the end”, i.e. until the complete use of at least one of the starting materials.

2.7. PRINCIPLE OF LATER

The state of chemical equilibrium under constant external conditions can theoretically persist for an infinitely long time. In reality, when the temperature, pressure or concentration of the reactants changes, the equilibrium can “shift” to one side or another of the process.

Changes that occur in the system as a result of external influences are determined by the principle of mobile equilibrium - le Chatelier principle.

External action on a system in equilibrium leads to a shift of this equilibrium in the direction in which the effect of the effect is weakened.

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

With an increase in the concentration of one of the reacting substances, the equilibrium shifts toward the consumption of this substance; with a decrease in the concentration, the equilibrium shifts toward the formation of this substance.

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

With increasing pressure, the equilibrium shifts towards a decrease in the quantities of gaseous substances, i.e. downward pressure; with decreasing pressure, the equilibrium shifts upward

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

With a change in temperature, both the direct and reverse reactions change, but to a different extent. Therefore, to determine the effect of temperature on chemical equilibrium, it is necessary to know the sign of the thermal effect of the reaction.

With increasing temperature, the equilibrium shifts toward the endothermic reaction, and with decreasing temperature, toward the exothermic reaction.

As applied to biosystems, the Le Chatelier principle states that in every biosystem, a reaction is formed in response to the same strength and character that balances biological regulatory processes and reactions and forms a conjugate level of their disequilibrium.

In pathological processes, the existing isolation of the regulatory circuit is violated. Depending on the level of disequilibrium, the quality of intersystem and interorgan relationships changes; they become more and more non-linear. The structure and specificity of these relationships is confirmed by an analysis of the relationship between 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 OBJECTIVES FOR SELF-TESTING PREPAREDNESS FOR LESSONS AND EXAMS

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

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

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

4. The speed of a 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 rate (in a sufficiently large time interval) coincide?

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

7. The half-period of some first-order reaction is 30 minutes. What part of the initial amount of substance will remain in an hour?

8. Give the concept of a general reaction order and a reaction order for a substance.

9. Methods for determining the reaction rate.

10. The basic law of chemical kinetics.

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

12. Simple and complex reactions.

13. Conjugated reactions. What factors determines the rate constant of chemical reactions?

14. Is the reaction rate really proportional to the product of the concentrations of the reacting substances in the degree 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 a 0.02 mol / L solution of H 2 O 2 and 0.05 mol / L of an HI solution are mixed. The rate constant is 0.05 l / mol s.

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

18. Prove that the speed 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 the Vant Hoff rule, when the temperature rises by 10 °, the speed of many reactions:

a) reduced by 2-4 times;

b) decreases by 5-10 times;

c) increases by 2-4 times;

g) increases by 5-10 times.

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

a) reaction order;

b) reaction rate;

c) the molecularity of the reaction;

d) half-period.

3. What factors affect the increase in reaction rate?

a) the nature of the reacting substances;

b) temperature, concentration, catalyst;

c) only the catalyst;

d) only concentration;

e) only temperature.

4. How many times will the reaction rate increase 2A (g) + B (g)→ And 2 B (g) with a 2-fold increase in the concentration of substance A?

a) the speed does not change;

b) increase by 18 times;

c) increase by 8 times;

g) will increase 4 times;

d) increase by 2 times.

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

a) k [A] [B] 2;

b) k [A] [B];

c) to [B];

d) to [B] 2;

e) to [A].

6. How to change the pressure in the system to increase the reaction rate A (tv) + 2V (g)→  AB 2 (g) 9 times?

a) increase the pressure by 9 times;

b) reduce the pressure by 9 times;

c) increase pressure by 3 times;

d) reduce pressure by 3 times.

7. What is the temperature coefficient of reaction?γ 10 , if during cooling of the reaction mixture by 30 ° the reaction rate decreased by 8 times?

a) 16;

b) 8;

at 6;

d) 4;

d 2.

8. Which reaction is faster?

a) E act\u003d 40 kJ / mol;

b)   E act \u003d 80 kJ / mol;

in)   E act \u003d 160 kJ / mol;

d)   E act \u003d 200 kJ / mol.