where g - ttemperature coefficient, taking values from 2 to 4.
The explanation of the dependence of the reaction rate on temperature was given by S. Arrhenius. Not every collision of reactant molecules leads to a reaction, but only the strongest collisions. Only molecules with an excess of kinetic energy are capable of a chemical reaction.
S. Arrhenius calculated the proportion of active (i.e. leading to a reaction) collisions of reacting particles a, depending on temperature: - a = exp(-E/RT). and brought Arrhenius equation for the reaction rate constant:
k = koe-E/RT
where ko and E d depend on the nature of the reagents. E is the energy that must be given to molecules in order for them to interact, called activation energy.
Van't Hoff's rule- an empirical rule that allows, as a first approximation, to estimate the effect of temperature on the rate of a chemical reaction in a small temperature range (usually from 0 ° C to 100 ° C). J. H. van't Hoff, on the basis of many experiments, formulated the following rule:
Activation energy in chemistry and biology, the minimum amount of energy required to impart to a system (in chemistry expressed in joules per mole) for a reaction to occur. The term was introduced by Svante August Arrhenius in. Typical reaction energy notation Ea.
The activation entropy is considered as the difference between the entropy of the transition state and the ground state of the reactants. It is determined mainly by the loss of the translational and rotational degrees of freedom of the particles during the formation of the activated complex. Significant changes (vibrational degrees of freedom) can also occur if the activated complex is somewhat more densely packed than the reactants.
The activation entropy of such a transition is positive.
The entropy of activation depends on many factors. When, in a bimolecular reaction, two initial particles join together to form a transition state, the translational and rotational entropy of the two particles is reduced to values corresponding to a single particle; a slight increase in vibrational entropy is not enough to compensate for this effect.
Activation entropies, in fact, vary more with structure than enthalpies. The activation entropies are in good agreement in most cases with the Price and Hammett rule. This series also has the particular significance that the increase and entropy of the silap can probably be accurately calculated from the known absolute entropies of the corresponding hydrocarbons.
The dependence of the rate of a chemical reaction on temperature.
The rate of heterogeneous reactions.
In heterogeneous systems, reactions proceed at the interface. In this case, the concentration of the solid phase remains practically constant and does not affect the reaction rate. The rate of a heterogeneous reaction will depend only on the concentration of the substance in the liquid or gaseous phase. Therefore, in the kinetic equation, the concentrations of solids are not indicated, their values are included in the values of the constants. For example, for a heterogeneous reaction
the kinetic equation can be written
EXAMPLE 4. The kinetic order of the reaction of the interaction of chromium with aluminum is 1. Write the chemical and kinetic equations of the reaction.
The reaction of interaction of aluminum with chlorine is heterogeneous, the kinetic equation can be written
EXAMPLE 5 Kinetic Reaction Equation
has the form
Determine the dimension of the rate constant and calculate the rate of dissolution of silver at a partial pressure of oxygen Pa and a concentration of potassium cyanide of 0.055 mol/l.
The dimension of the constant is determined from the kinetic equation given in the condition of the problem:
Substituting these problems into the kinetic equation, we find the rate of silver dissolution:
EXAMPLE 6 Kinetic Reaction Equation
has the form
How will the reaction rate change if the concentration of mercury chloride (P) is halved, and the concentration of oxalate – ions to double?
After changing the concentration of the starting substances, the reaction rate is expressed by the kinetic equation
Comparing and, we find that the reaction rate increased in 2 times.
As the temperature rises, the rate of a chemical reaction increases markedly.
The quantitative dependence of the reaction rate on temperature is determined by the van't Hoff rule.
To characterize the dependence of the rate of a chemical reaction (rate constant) on temperature, the temperature coefficient of the rate, reaction (), also called the Van't Hoff coefficient, is used. The temperature coefficient of the reaction rate shows how many times the reaction rate will increase with an increase in the temperature of the reactants by 10 degrees.
Mathematically, the dependence of the reaction rate on temperature is expressed by the relation
Where – temperature coefficient of speed;
– T;
T;
–– reaction rate constant at temperature T+ 10;
–– reaction rate at temperature T+ 10.
For calculations, it is more convenient to use the equations
as well as the logarithmic forms of these equations
The increase in the reaction rate with increasing temperature explains activation theory. According to this theory, the particles of the reacting substances in the collision must overcome the repulsive forces, weaken or break old chemical bonds and form new ones. For this, they must spend a certain amount of energy, i.e. overcome some energy barrier. A particle with excess energy sufficient to overcome the energy barrier is called active particles.
Under normal conditions, there are few active particles in the system, and the reaction proceeds at a slower rate. But inactive particles can become active if you give them additional energy. One way to activate the particles is by increasing the temperature. As the temperature rises, the number of active particles in the system sharply increases and the reaction rate increases.
The dependence of the reaction rate on temperature is approximately determined by the van't Hoff rule of thumb: for every 10 degrees change in temperature, the rate of most reactions changes by a factor of 2-4.
Mathematically, Van't Hoff's rule is expressed as follows:
where v(T2) and v(T1) are the reaction rates, respectively, at temperatures T2 and T1 (T2> T1);
γ is the temperature coefficient of the reaction rate.
The value of γ for an endothermic reaction is higher than for an exothermic one. For many reactions, γ is in the range 2-4.
The physical meaning of the value of γ is that it shows how many times the reaction rate changes with a change in temperature for every 10 degrees.
Since the reaction rate and the rate constant of a chemical reaction are directly proportional, expression (3.6) is often written in the following form:
(3.7)
where k(T2), k(T1) are reaction rate constants, respectively
at temperatures T2 and T1;
γ is the temperature coefficient of the reaction rate.
Example 8 By how many degrees should the temperature be raised to increase the rate of the reaction by 27 times? The temperature coefficient of the reaction is 3.
Solution. We use expression (3.6):
We get: 27 = , = 3, DT = 30.
Answer: 30 degrees.
The reaction rate and the time it takes are inversely related: the larger v, the
less than t. Mathematically, this is expressed by the relation
Example 9 At a temperature of 293 K, the reaction proceeds in 2 minutes. How long will this reaction take at a temperature of 273 K if γ = 2.
Solution. Equation (3.8) implies:
.
We use equation (3.6) because 
We get:
min.
Answer: 8 min.
Van't Hoff's rule is applicable to a limited number of chemical reactions. The effect of temperature on the rate of processes is often determined by the Arrhenius equation.
Arrhenius equation . In 1889, the Swedish scientist S. Arreius, on the basis of experiments, derived an equation that is named after him
where k is the reaction rate constant;
k0 - pre-exponential factor;
e is the base of the natural logarithm;
Ea is a constant, called the activation energy, determined by the nature of the reactants:
R is the universal gas constant, equal to 8.314 J/mol×K.
The values of Ea for chemical reactions are in the range of 4 - 400 kJ/mol.
Many reactions are characterized by a certain energy barrier. To overcome it, activation energy is needed - some excess energy (compared to the harmful energy of molecules at a given temperature), which molecules must have in order for their collision to be effective, i.e., would lead to the formation of a new substance. As the temperature rises, the number of active molecules increases rapidly, which leads to a sharp increase in the reaction rate.
In the general case, if the reaction temperature changes from T1 to T2, equation (3.9) after taking the logarithm will take the form:
. (3.10)
This equation allows you to calculate the activation energy of the reaction when the temperature changes from T1 to T2.
The rate of chemical reactions increases in the presence of a catalyst. The action of a catalyst lies in the fact that it forms unstable intermediate compounds (activated complexes) with the reagents, the decomposition of which leads to the formation of reaction products. At the same time, the activation energy decreases, and molecules become active, the energy of which was insufficient to carry out the reaction in the absence of a catalyst. As a result, the total number of active £ molecules increases and the reaction rate increases.
The change in the reaction rate in the presence of a catalyst is expressed by the following equation:
, (3.11)
where vcat, and Ea(cat) - the rate and activation energy of a chemical reaction in the presence of a catalyst;
v and Ea are the rate and activation energy of a chemical reaction without a catalyst.
Example 10. The activation energy of a certain reaction in the absence of a catalyst is 75.24 kJ/mol, with a catalyst - 50.14 kJ/mol. How many times does the reaction rate increase in the presence of a catalyst if the reaction proceeds at a temperature of 298 K? Solution. We use equation (3.11). Substituting data into the equation
An increase in temperature speeds up all chemical reactions. Initially, van't Hoff experimentally found that when increase in temperature for every 10 degrees, the speed increases by 2 ¸ 4 times ( Van't Hoff's rule ). This corresponds to the power-law dependence of velocity on temperature:
where T > T 0, g - van't Hoff temperature coefficient.
However, this equation is not theoretically justified. ; experimental data are better described by an exponential function (Arrhenius equation):
,
where A is a pre-exponential factor independent of T, E a is the activation energy of a chemical reaction (kJ/mol), R is the universal gas constant.
The Arrhenius equation is usually written for the rate constant:
.
This equation is theoretically substantiated by the methods of statistical physics. Qualitatively, this justification is as follows: since reactions proceed as a result of random collisions of molecules, these collisions are characterized by an almost continuous set of energies from the smallest to the very largest. Obviously, a reaction will only occur when the molecules collide with enough energy to break (or significantly stretch) some chemical bonds. For each system, there is an energy threshold E a, starting from which the energy is sufficient for the reaction to proceed - this mechanism corresponds to curve 1 in Figure 5.1. Since collisions occur with a frequency that depends on temperature according to an exponential law, formulas 5.9 and 5.10 are obtained. Then the pre-exponential factors A and k 0 represent some characteristic of the total number of collisions, and the term is the fraction of successful collisions.
The analysis of experimental data is carried out using the logarithmic form of the Arrhenius equation:
.
The graph is built in the so-called Arrhenius coordinates
(ln k - ), fig. 7.2; from the graph find k o and E a.
In the presence of experimental data for two temperatures k o and E a, it is easy to theoretically find:
; 
;
The rate of a chemical reaction largely depends on the activation energy. For the vast majority of reactions, it lies in the range from 50 to 250 kJ/mol. Reactions for which
E a > 150 kJ/mol, practically do not leak at room temperature.
Example 1 The complex irreversible reaction 2N 2 O 5 \u003d 4NO 2 + O 2 is a first-order reaction. How will its speed change when the pressure is increased by 5 times?
Solution. The kinetic equation of this reaction in general form: V = k · a . Since the reaction is complex, it is possible that a ¹ 2. By condition, the order of the reaction
a = 1. For gas reactions, pressure plays the role of concentration. That's why
V = kP, and if Р 1 = 5Р, then V 1 /V = 5, i.e. speed increases five times.
Find the rate constant, the orders of the reactants and write down the kinetic equation.
Solution. The general kinetic equation for the rate of this reaction is:
V = k a b .
The data in the table make it possible to find the reaction orders for NO (a) and H 2 (b) by lowering the reaction order, i.e. analyzing experiments in which one of the reagents has a constant concentration. So, = 0.01 in the first and second columns, while changing.
. (private order in H 2).
For the second and third columns, on the contrary, it is the same, but - are different, therefore:
(private order for NO).
Since a and b coincide with stoichiometric coefficients, the reaction can be simple. The rate constant can be found from each column's data:
Thus, the kinetic equation is: V = 2.5. 10 3 2 .
The total (general) order of this reaction (a + b) is 3.
Example 3 The reaction rate A + 3B = AB 3 is determined by the kinetic equation V = k[A]·[B]. Determine the general order of the reaction. Is this reaction simple or complex? How many times will the reaction rate increase when the concentration is increased by 3 times?
Solution. The reaction order is determined by the sum of the exponents of the reactants in the kinetic equation. For this reaction, the overall order is two (1 + 1).
If this reaction were simple, then according to the law of mass action
V = k[A] 1 . [B] 3 and the total order would be (1+ 3) = 4, i.e. the exponents in the kinetic equation do not coincide with the stoichiometric coefficients, therefore, the reaction is complex and takes place in several stages.
With an increase in the concentrations of reagents by 3 times: V 1 = k·3[A]·3[B] = 3 2 V, that is, the speed will increase by 3 2 = 9 times.
Example 4 Determine the activation energy of the reaction and its temperature coefficient, if at 398 and 600 0 C the rate constants are, respectively, 2.1×10 -4 and 6.25×10 -1 .
Solution. E a for two values can be calculated using the formula 5.12 :
192633 J/mol.
The temperature coefficient is found from expression (5.8), because Vµk:
.
Catalysis
One of the most common methods in chemical practice for accelerating chemical reactions is catalysis. A catalyst is a substance that repeatedly participates in the intermediate stages of a reaction, but leaves it chemically unchanged.
For example, for the reaction A 2 + B 2 \u003d 2AB
the participation of catalyst K can be expressed by the equation
A 2 + K + B 2 ® A 2 .... K + B 2 ® A 2 ... K ... B 2 ® 2AB + K.
These equations can be represented by potential energy curves (Fig. 5.2.).
Rice. 5.2. Energy scheme of the reaction
with and without catalyst
Figure 5.2 shows that:
1) the catalyst reduces the activation energy by changing the reaction mechanism - it proceeds through new stages, each of which is characterized by a low activation energy;
2) the catalyst does not change the DH of the reaction (as well as DG, DU, and DS);
3) if the catalyzed reaction is reversible, the catalyst does not affect the equilibrium, does not change the equilibrium constant and the equilibrium concentrations of the system components. It speeds up both the forward and reverse reactions equally, thereby speeding up the time to reach equilibrium.
Obviously, in the presence of a catalyst, the activation energy of the reaction decreases by the value DE k. Since in the expression for the reaction rate constant (Equation 5.10) the activation energy is included in the negative exponent, even a small decrease in E a causes a very large increase in the reaction rate: 
.
The effect of the catalyst on the decrease in Еа can be shown by the example of the decomposition reaction of hydrogen iodide:
2HI \u003d H 2 + I 2.
Thus, for the reaction under consideration, the decrease in energy
activation by 63 kJ, i.e. 1.5 times, corresponds to an increase in the reaction rate at 500 K by more than 10 6 times.
It should be noted that the pre-exponential factor of the catalytic reaction k 0 1 is not equal to k 0 and is usually much less, however, the corresponding decrease in the rate does not compensate for its increase due to Еа.
Example 5 The activation energy of a certain reaction in the absence of a catalyst is 75.24 kJ / mol, and with a catalyst - 50.14 kJ / mol. How many times does the reaction rate increase in the presence of a catalyst if the reaction proceeds at 25 0 C, and the pre-exponential factor in the presence of a catalyst decreases by 10 times.
Solution. Let us denote the activation energy of the reaction without a catalyst as E a, and in the presence of a catalyst - through Ea 1 ; the corresponding reaction rate constants will be denoted by k and k 1 . Using the Arrhenius equation (5.9) (see section 5.3) and assuming k 0 1 /k 0 = 10, we find:
From here 
We finally find:
Thus, a decrease in the activation energy by the catalyst by 25.1 kJ led to an increase in the reaction rate by a factor of 2500, despite a 10-fold decrease in the pre-exponential factor.
Catalytic reactions are classified by the type of catalysts and by the type of reactions. So, for example, according to the state of aggregation of catalysts and reagents, catalysis is divided into homogeneous(catalyst and reactant form one phase) and heterogeneous(the catalyst and the reagents are in different phases, there is a phase boundary between the catalyst and the reagents).
An example of homogeneous catalysis would be the oxidation of CO to CO 2 with oxygen in the presence of NO 2 (catalyst). The mechanism of catalysis can be represented by the following reactions:
CO (g) + NO 2 (g) ® CO 2 (g) + NO (g),
2NO (g) + O 2 (g) ® 2NO 2 (g);
and the catalyst (NO 2) again participates in the first reaction.
Similarly, the oxidation of SO 2 to SO 3 can be catalyzed; a similar reaction is used in the production of sulfuric acid by the "nitrous" process.
An example of heterogeneous catalysis is the production of SO 3 from SO 2 in the presence of Pt or V 2 O 5:
SO 2 (g) + O 2 (g) ® SO 3 (g).
This reaction is also used in the production of sulfuric acid (the "contact" method).
The heterogeneous catalyst (iron) is also used in the production of ammonia from nitrogen and hydrogen and in many other processes.
The efficiency of heterogeneous catalysts is usually much greater than that of homogeneous ones. The rate of catalytic reactions in the case of a homogeneous catalyst depends on its concentration, and in the case of a heterogeneous one, on its specific surface area (that is, dispersion) - the larger it is, the greater the rate. The latter is due to the fact that the catalytic reaction takes place on the surface of the catalyst and includes the stages of adsorption (sticking) of reactant molecules on the surface; after the completion of the reaction, its products are desorbed. To increase the surface area of the catalysts, they are crushed or obtained by special methods, in which very fine powders are formed.
The examples given are also examples redox catalysis. In this case, transition metals or their compounds (Mn 3+ , Pt, Au, Ag, Fe, Ni, Fe 2 O 3, etc.) usually act as catalysts.
In acid-base catalysis the role of the catalyst is performed by H + , OH - and other similar particles - carriers of acidity and basicity. So the hydrolysis reaction
CH 3 COOCH 3 + H 2 O CH 3 COOH + CH 3 OH
accelerates by about 300 times with the addition of any of the strong acids: HCl, HBr or HNO 3 .
Catalysis is of great importance in biological systems. In this case, the catalyst is called enzyme. The efficiency of many enzymes is much greater than conventional catalysts. For example, for the reaction of nitrogen binding to ammonia
N 2 + 3H 2 \u003d 2NH 3
In industry, a heterogeneous catalyst is used in the form of sponge iron with the addition of metal oxides and sulfates.
In this case, the reaction is carried out at T » 700 K and P » 30 MPa. The same synthesis takes place in the nodules of leguminous plants under the action of enzymes at ordinary T and P.
Catalytic systems are not indifferent to impurities and additives. Some of them increase the efficiency of catalysis, such as in the above example of catalysis of the synthesis of ammonia by iron. These catalyst additives are called promoters(potassium and aluminum oxides in iron). Some impurities, on the contrary, suppress the catalytic reaction ("poison" the catalyst), this catalytic poisons. For example, the synthesis of SO 3 on a Pt catalyst is very sensitive to impurities containing sulfide sulfur; sulfur poisons the surface of the platinum catalyst. Conversely, the catalyst based on V 2 O 5 is insensitive to such impurities; the honor of developing a catalyst based on vanadium oxide belongs to the Russian scientist G.K. Boreskov.
The reaction rate constant is a function of temperature; an increase in temperature generally increases the rate constant. The first attempt to take into account the effect of temperature was made by van't Hoff, who formulated the following rule of thumb:
With an increase in temperature for every 10 degrees, the rate constant of an elementary chemical reaction increases by 2-4 times.
The value showing how many times the rate constant increases with an increase in temperature by 10 degrees is temperature coefficient of reaction rate constantγ. Mathematically, the van't Hoff rule can be written as follows:
(II.30)
However, the van't Hoff rule is applicable only in a narrow temperature range, since the temperature coefficient of the reaction rate γ is itself a function of temperature; at very high and very low temperatures, γ becomes equal to unity (i.e., the rate of a chemical reaction ceases to depend on temperature).
Arrhenius equation
Obviously, the interaction of particles is carried out during their collisions; however, the number of collisions of molecules is very large, and if each collision led to a chemical interaction of particles, all reactions would proceed almost instantly. Arrhenius postulated that collisions of molecules would be effective (i.e., they would lead to a reaction) only if the colliding molecules had a certain amount of energy, the activation energy.
The activation energy is the minimum energy that molecules must have in order for their collision to lead to a chemical interaction.
Consider the path of some elementary reaction
A + B ––> C
Since the chemical interaction of particles is associated with the breaking of old chemical bonds and the formation of new ones, it is believed that any elementary reaction passes through the formation of some unstable intermediate compound, called an activated complex:
A ––> K # ––> B
The formation of an activated complex always requires the expenditure of a certain amount of energy, which is caused, firstly, by the repulsion of electron shells and atomic nuclei when the particles approach each other and, secondly, by the need to build a certain spatial configuration of atoms in the activated complex and redistribute the electron density. Thus, on the way from the initial state to the final state, the system must overcome a kind of energy barrier. The reaction activation energy is approximately equal to the excess of the average energy of the activated complex over the average energy level of the reactants. Obviously, if the direct reaction is exothermic, then the activation energy of the reverse reaction E "A is higher than the activation energy of the direct reaction E A. The activation energies of the direct and reverse reactions are related to each other through a change in internal energy during the reaction. The above can be illustrated using the energy chemical reaction diagrams (Fig. 2.5).
Rice. 2.5. Energy diagram of a chemical reaction. E ref is the average energy of the particles of the initial substances, E prod is the average energy of the particles of the reaction products.
Since temperature is a measure of the average kinetic energy of particles, an increase in temperature leads to an increase in the proportion of particles whose energy is equal to or greater than the activation energy, which leads to an increase in the reaction rate constant (Fig. 2.6):
Rice. 2.6. Energy distribution of particles. Here nE/N is the fraction of particles with energy E; E i - average particle energy at temperature T i (T 1< T 2 < T 3).
Let us consider the thermodynamic derivation of the expression describing the dependence of the reaction rate constant on temperature and the value of the activation energy - the Arrhenius equation. According to the van't Hoff isobar equation,
Since the equilibrium constant is the ratio of the rate constants of the forward and reverse reactions, expression (II.31) can be rewritten as follows:
(II.32)
Representing the change in the enthalpy of the reaction ΔHº as the difference between two values E 1 and E 2, we obtain:
(II.33)
(II.34)
Here C is some constant. Postulating that C = 0, we obtain the Arrhenius equation, where E A is the activation energy:
After indefinite integration of expression (II.35), we obtain the Arrhenius equation in integral form:
(II.36)
(II.37)
Rice. 2.7. Dependence of the logarithm of the rate constant of a chemical reaction on the reciprocal temperature.
Here A is the constant of integration. From equation (II.37) it is easy to show the physical meaning of the pre-exponential factor A, which is equal to the rate constant of the reaction at a temperature tending to infinity. As can be seen from expression (II.36), the logarithm of the rate constant depends linearly on the reciprocal temperature (Fig. 2.7); the value of the activation energy E A and the logarithm of the pre-exponential factor A can be determined graphically (the tangent of the slope of the straight line to the abscissa axis and the segment cut off by the straight line on the y-axis).
Knowing the activation energy of the reaction and the rate constant at any temperature T 1, using the Arrhenius equation, you can calculate the value of the rate constant at any temperature T 2:
(II.39)
