First order reaction [k] = .
Second order reaction [k] = [l/mol∙t]
nth order reaction [k] = [mol 1- n ∙ l n -1 ∙ t - t ]
III. Temperature. With increasing temperature it increases kinetic energy molecules, and, consequently, the speed of their movement. An increase in speed leads to an increase in the number of collisions of molecules and, as a consequence, to an increase reaction speed. It was experimentally established that with an increase in temperature for every 10 0 the speed chemical reaction increases by 2-4 times:
V 2 = V 1 ∙γ (T 2 – T 1)/10 or V 2 /V 1 = γ (T 2 – T 1)/10
where V 1 is the reaction rate at temperature T 1, V 2 is the reaction rate at temperature T 2,
γ is the temperature coefficient of the reaction rate; its value for most inorganic reactions varies from two to four. This pattern is called the rule van't Hoff.
As the temperature increases, the reaction rate increases, but the concentrations of the reactants do not change. Consequently, the rate constant changes and increases with increasing temperature. The dependence of the rate constant of a chemical reaction on temperature is described by the Arrhenius equation:
k = k o ∙e -Ea /RT
where k o is a coefficient taking into account the number of active collisions, R is the universal gas constant, T is temperature, E a is activation energy.
Activation energy is the energy of molecules at which each collision leads to a chemical reaction.
Physical meaning activation energies can be easily understood from the figure.
prod.r-tion
The ordinate axis shows the sum of the enthalpies of the starting substances and reaction products, and the abscissa axis shows the direction of the reaction. In this case, the difference between the sum of the energies of the starting substances and the maximum of the curve gives the activation energy of the forward reaction (E a), and the difference between the sum of the energies of the reaction products and the same maximum gives the activation energy of the reverse reaction (E " a).
IV. Catalyst. Catalysts are substances that change the rate of a chemical reaction, but are not included in the stoichiometric equation of the reaction. Catalysts can either increase the rate of a chemical reaction or decrease it. Substances that reduce the rate of a reaction are called inhibitors. Catalysts are directly involved in a chemical reaction, but at the end of the reaction they can be isolated from the reaction mixture in the original amount. Catalysts are characterized by selectivity, i.e. the ability to influence the passage of a reaction in a certain direction:
4 NH 3 + 3 O 2 = 6 H 2 O +2 N 2 (without catalyst)
4 NH 3 + 5 O 2 = 4 NO + 6 H 2 O (Pt catalyst)
Co, Rh→ CH 3 CH 2 CH 2 OH + CH 3 CH OH CH 3
Biocatalysts occupy a special place - enzymes, representing proteins. They influence the rate of strictly defined reactions, i.e. have high selectivity. They are capable of increasing the rate of reactions by billions and trillions of times at room temperature. When the temperature rises, they lose their activity, because protein denaturation occurs.
The mechanisms of chemical transformations and their rates are studied by chemical kinetics. Chemical processes occur over time at different rates. Some happen quickly, almost instantly, while others take a very long time to occur.
Reaction speed- the rate at which reagents are consumed (their concentration decreases) or reaction products are formed per unit volume.
Factors that can influence the rate of a chemical reaction
The following factors can affect how quickly a chemical reaction occurs:
- concentration of substances;
- nature of reagents;
- temperature;
- presence of a catalyst;
- pressure (for reactions in a gas environment).
Thus, by changing certain conditions of a chemical process, you can influence how quickly the process will proceed.
In progress chemical interaction particles of reacting substances collide with each other. The number of such coincidences is proportional to the number of particles of substances in the volume of the reacting mixture, and therefore proportional to the molar concentrations of the reagents.
Law of mass action describes the dependence of the reaction rate on the molar concentrations of the substances that interact.
For an elementary reaction (A + B → ...) this law is expressed by the formula:
υ = k ∙С A ∙С B,
where k is the rate constant; C A and C B - molar concentrations reagents A and B.
If one of the reacting substances is in a solid state, then the interaction occurs at the interface, and therefore the concentration of the solid substance is not included in the equation kinetic law acting masses. To understand the physical meaning of the rate constant, it is necessary to take C, A and C B equal to 1. Then it becomes clear that the rate constant is equal to the reaction rate at reactant concentrations equal to unity.
Nature of the reagents
Since in the process of interaction they are destroyed chemical bonds reactants and new bonds of reaction products are formed, then the nature of the bonds involved in the reaction of the compounds and the structure of the molecules of the reacting substances will play a large role.
Surface area of contact of reagents
Such a characteristic as the surface area of contact of solid reagents affects the course of the reaction, sometimes quite significantly. Grinding a solid allows you to increase the surface area of contact of the reagents, and therefore speed up the process. The contact area of soluble substances is easily increased by dissolving the substance.
Reaction temperature
As the temperature increases, the energy of colliding particles will increase; it is obvious that with increasing temperature the chemical process itself will accelerate. A clear example How an increase in temperature affects the process of interaction of substances can be read from the data given in the table.
Table 1. Effect of temperature changes on the rate of water formation (O 2 +2H 2 →2H 2 O)
To quantitatively describe how temperature can affect the rate of interaction of substances, the Van't Hoff rule is used. Van't Hoff's rule is that when the temperature increases by 10 degrees, an acceleration occurs by 2-4 times.
The mathematical formula describing van't Hoff's rule is as follows:
Where γ is the temperature coefficient of the rate of the chemical reaction (γ = 2−4).
But the Arrhenius equation describes the temperature dependence of the rate constant much more accurately:
Where R is the universal gas constant, A is a factor determined by the type of reaction, E, A is the activation energy.
Activation energy is the energy that a molecule must acquire for a chemical transformation to occur. That is, it is a kind of energy barrier that molecules colliding in the reaction volume will need to overcome in order to redistribute bonds.
The activation energy does not depend on external factors, but depends on the nature of the substance. The activation energy value of up to 40 - 50 kJ/mol allows substances to react with each other quite actively. If the activation energy exceeds 120 kJ/mol, then the substances (at ordinary temperatures) will react very slowly. A change in temperature leads to a change in the number of active molecules, that is, molecules that have reached an energy greater than the activation energy, and therefore are capable of chemical transformations.
Catalyst action
A catalyst is a substance that can speed up a process, but is not part of its products. Catalysis (acceleration of a chemical transformation) is divided into homogeneous and heterogeneous. If the reactants and catalyst are in the same states of aggregation, then catalysis is called homogeneous, if different, then heterogeneous. The mechanisms of action of catalysts are varied and quite complex. In addition, it is worth noting that catalysts are characterized by selectivity of action. That is, the same catalyst, while accelerating one reaction, may not change the rate of another.
Pressure
If gaseous substances are involved in the transformation, then the rate of the process will be affected by changes in pressure in the system . This happens because that for gaseous reagents, a change in pressure leads to a change in concentration.
Experimental determination of the rate of a chemical reaction
The speed of a chemical transformation can be determined experimentally by obtaining data on how the concentration of substances entering the reaction or products changes per unit time. Methods for obtaining such data are divided into
- chemical,
- physico-chemical.
Chemical methods quite simple, accessible and accurate. With their help, the speed is determined by directly measuring the concentration or amount of the substance of the reactants or products. In case of a slow reaction, samples are taken to monitor how the reagent is consumed. Then the content of the reagent in the sample is determined. By taking samples at regular intervals, it is possible to obtain data on changes in the amount of a substance during the interaction process. The most commonly used types of analysis are titrimetry and gravimetry.
If the reaction proceeds quickly, then it has to be stopped in order to take a sample. This can be done using cooling, abrupt removal of the catalyst, it is also possible to dilute or transfer one of the reagents to a non-reactive state.
Methods physical and chemical analysis in modern experimental kinetics they are used more often than chemical ones. With their help, you can observe changes in the concentrations of substances in real time. In this case, there is no need to stop the reaction and take samples.
Physicochemical methods are based on measurement physical properties, depending on the quantitative content of a certain compound in the system and changing over time. For example, if gases are involved in a reaction, then pressure may be such a property. Electrical conductivity, refractive index, and absorption spectra of substances are also measured.
1. Basic concepts and postulates of chemical kinetics
Chemical kinetics - section physical chemistry, studying the rates of chemical reactions. The main tasks of chemical kinetics: 1) calculation of reaction rates and determination of kinetic curves, i.e. dependence of the concentrations of reactants on time ( direct task); 2) determination of reaction mechanisms from kinetic curves ( inverse problem).
The rate of a chemical reaction describes the change in the concentrations of reactants per unit time. For reaction
a A+ b B+... d D+ e E+...
the reaction rate is determined as follows:
where square brackets indicate the concentration of the substance (usually measured in mol/l), t- time; a, b, d, e- stoichiometric coefficients in the reaction equation.
The reaction rate depends on the nature of the reactants, their concentration, temperature and the presence of a catalyst. The dependence of the reaction rate on concentration is described by the basic postulate of chemical kinetics - law of mass action:
The rate of a chemical reaction at each moment in time is proportional to the current concentrations of the reactants, raised to certain powers:
,
Where k- rate constant (independent of concentration); x, y- some numbers that are called order of reaction by substance A and B, respectively. In general, these numbers have nothing to do with the coefficients a And b in the reaction equation. Sum of exponents x+ y called general reaction order. The order of the reaction can be positive or negative, integer or fractional.
Most chemical reactions consist of several steps called elementary reactions. An elementary reaction is usually understood as a single act of formation or rupture of a chemical bond, proceeding through the formation of a transition complex. The number of particles participating in an elementary reaction is called molecularity reactions. There are only three types of elementary reactions: monomolecular (A B + ...), bimolecular (A + B D + ...) and trimolecular (2A + B D + ...). For elementary reactions, the overall order is equal to the molecularity, and the orders by substance are equal to the coefficients in the reaction equation.
EXAMPLES
Example 1-1. The rate of NO formation in the reaction 2NOBr (g) 2NO (g) + Br 2 (g) is 1.6. 10 -4 mol/(l.s). What is the rate of reaction and the rate of NOBr consumption?
Solution. By definition, the reaction rate is:
Mol/(l.s).
From the same definition it follows that the rate of NOBr consumption is equal to the rate of NO formation with the opposite sign:
mol/(l.s).
Example 1-2. In the 2nd order reaction A + B D, the initial concentrations of substances A and B are equal to 2.0 mol/L and 3.0 mol/L, respectively. The reaction rate is 1.2. 10 -3 mol/(l.s) at [A] = 1.5 mol/l. Calculate the rate constant and reaction rate at [B] = 1.5 mol/L.
Solution. According to the law of mass action, at any moment of time the reaction rate is equal to:
.
By the time when [A] = 1.5 mol/l, 0.5 mol/l of substances A and B have reacted, so [B] = 3 – 0.5 = 2.5 mol/l. The rate constant is:
L/(mol. s).
By the time when [B] = 1.5 mol/l, 1.5 mol/l of substances A and B have reacted, therefore [A] = 2 – 1.5 = 0.5 mol/l. The reaction rate is:
Mol/(l.s).
TASKS
1-1. How is the rate of the ammonia synthesis reaction 1/2 N 2 + 3/2 H 2 = NH 3 expressed in terms of the concentrations of nitrogen and hydrogen? (answer)
1-2. How will the rate of the ammonia synthesis reaction 1/2 N 2 + 3/2 H 2 = NH 3 change if the reaction equation is written as N 2 + 3H 2 = 2NH 3? (answer)
1-3. What is the order of elementary reactions: a) Cl + H 2 = HCl + H; b) 2NO + Cl 2 = 2NOCl? (answer)
1-4. Which of the following quantities can take a) negative; b) fractional values: reaction rate, reaction order, reaction molecularity, rate constant, stoichiometric coefficient? (answer)
1-5. Does the rate of a reaction depend on the concentration of reaction products? (answer)
1-6. How many times will the rate of the gas-phase elementary reaction A = 2D increase when the pressure increases by 3 times? (answer)
1-7. Determine the order of the reaction if the rate constant has the dimension l 2 / (mol 2 . s). (answer)
1-8. The rate constant of a 2nd order gas reaction at 25 o C is equal to 10 3 l/(mol. s). What is this constant equal to if the kinetic equation is expressed in terms of pressure in atmospheres? (answer)
1-9. For gas phase reaction n th order nA B, express the rate of formation of B in terms of the total pressure. (answer)
1-10. The rate constants for the forward and reverse reactions are 2.2 and 3.8 l/(mol. s). By which of the following mechanisms can these reactions occur: a) A + B = D; b) A + B = 2D; c) A = B + D; d) 2A = B.(answer)
1-11. The decomposition reaction 2HI H 2 + I 2 has a 2nd order with a rate constant k= 5.95. 10 -6 l/(mol. s). Calculate the reaction rate at a pressure of 1 atm and a temperature of 600 K. (answer)
1-12. The rate of the 2nd order reaction A + B D is 2.7. 10 -7 mol/(l.s) at concentrations of substances A and B, respectively, 3.0. 10 -3 mol/l and 2.0 mol/l. Calculate the rate constant.(answer)
1-13. In the 2nd order reaction A + B 2D, the initial concentrations of substances A and B are equal to 1.5 mol/l. The reaction rate is 2.0. 10 -4 mol/(l.s) at [A] = 1.0 mol/l. Calculate the rate constant and reaction rate at [B] = 0.2 mol/L. (answer)
1-14. In the 2nd order reaction A + B 2D, the initial concentrations of substances A and B are equal to 0.5 and 2.5 mol/l, respectively. How many times is the reaction rate at [A] = 0.1 mol/l less? initial speed? (answer)
1-15. The rate of the gas-phase reaction is described by the equation w = k. [A] 2 . [B]. At what ratio between the concentrations of A and B will the initial reaction rate be maximum at a fixed total pressure? (answer)
2. Kinetics of simple reactions
In this section, we will compose and solve kinetic equations for irreversible reactions of a whole order based on the law of mass action.
0th order reactions. The rate of these reactions does not depend on concentration:
,
where [A] is the concentration of the starting substance. Zero order occurs in heterogeneous and photochemical reactions.
1st order reactions. In type A–B reactions, the rate is directly proportional to the concentration:
.
When solving kinetic equations, the following notation is often used: initial concentration [A] 0 = a, current concentration [A] = a - x(t), Where x(t) is the concentration of the reacted substance A. In this notation, the kinetic equation for the 1st order reaction and its solution have the form:
The solution to the kinetic equation is also written in another form, convenient for analyzing the reaction order:
.
The time during which half of substance A decays is called the half-life t 1/2. It is defined by the equation x(t 1/2) = a/2 and equal
2nd order reactions. In reactions of type A + B D + ..., the rate is directly proportional to the product of concentrations:
.
Initial concentrations of substances: [A] 0 = a, [B] 0 = b; current concentrations: [A] = a- x(t), [B] = b - x(t).
When solving this equation, two cases are distinguished.
1) identical initial concentrations of substances A and B: a = b. The kinetic equation has the form:
.
The solution to this equation is written in various forms:
The half-lives of substances A and B are the same and equal to:
2) The initial concentrations of substances A and B are different: a
b. The kinetic equation has the form: 
.
The solution to this equation can be written as follows:
The half-lives of substances A and B are different: 
.
Nth order reactions n A D + ... The kinetic equation has the form:
.
Solution of the kinetic equation:
. (2.1)
The half-life of substance A is inversely proportional to ( n-1)th degree of initial concentration:
. (2.2)
Example 2-1. The half-life of the radioactive isotope 14 C is 5730 years. During archaeological excavations, a tree was found whose 14 C content was 72% of normal. How old is the tree?
Solution. Radioactive decay is a 1st order reaction. The rate constant is:
The lifetime of a tree can be found from solving the kinetic equation, taking into account the fact that [A] = 0.72. [A] 0:
Example 2-2. It has been established that a 2nd order reaction (one reagent) is 75% complete in 92 minutes at an initial reagent concentration of 0.24 M. How long will it take for the reagent concentration to reach 0.16 M under the same conditions?
Solution. Let us write the solution of the kinetic equation for a 2nd order reaction with one reagent twice:
,
where, by condition, a= 0.24 M, t 1 = 92 min, x 1 = 0.75. 0.24 = 0.18 M, x 2 = 0.24 - 0.16 = 0.08 M. Let's divide one equation by another:
Example 2-3. For an elementary reaction n A B we denote the half-life of A by t 1/2, and the decay time of A by 75% by t 3/4. Prove that the ratio t 3/4 / t 1/2 does not depend on the initial concentration, but is determined only by the order of the reaction n.Solution. Let us write the solution of the kinetic equation for the reaction twice n-th order with one reagent:
and divide one expression by another. Constants k And a both expressions will cancel and we get:
.
This result can be generalized by proving that the ratio of the times for which the degree of conversion is a and b depends only on the order of the reaction:
.
TASKS
2-1. Using the solution to the kinetic equation, prove that for 1st order reactions the time t x, during which the degree of conversion of the starting substance reaches x, does not depend on the initial concentration. (answer)2-2. The first order reaction proceeds 30% in 7 minutes. How long will it take for the reaction to be 99% complete? (answer)
2-3. The half-life of the radioactive isotope 137 Cs, which entered the atmosphere as a result of Chernobyl accident, - 29.7 years. After what time will the amount of this isotope be less than 1% of the original? (answer)
2-4. The half-life of the radioactive isotope 90 Sr, which enters the atmosphere during nuclear tests, is 28.1 years. Let's assume that the body of a newborn child absorbed 1.00 mg of this isotope. How much strontium will remain in the body after a) 18 years, b) 70 years, if we assume that it is not excreted from the body? (answer)
2-5. The rate constant for the first order reaction SO 2 Cl 2 = SO 2 + Cl 2 is 2.2. 10 -5 s -1 at 320 o C. What percentage of SO 2 Cl 2 will decompose when kept for 2 hours at this temperature? (answer)
2-6. 1st order reaction rate constant
2N 2 O 5 (g) 4NO 2 (g) + O 2 (g)
at 25 o C is equal to 3.38. 10 -5 s -1 . Why equal to the period half-life of N 2 O 5? What will be the pressure in the system after a) 10 s, b) 10 min, if the initial pressure was 500 mm Hg? Art. (answer)
2-7. The first order reaction is carried out with varying amounts of the starting material. Will the tangents to the initial sections of the kinetic curves intersect at one point on the x-axis? Explain your answer. (answer)
2-8. The first order reaction A 2B occurs in the gas phase. The initial pressure is p 0 (B missing). Find the dependence of total pressure on time. After what time will the pressure increase by 1.5 times compared to the original? What is the progress of the reaction by this time? (answer)
2-9. The second order reaction 2A B occurs in the gas phase. The initial pressure is p 0 (B missing). Find the dependence of total pressure on time. After what time will the pressure decrease by 1.5 times compared to the original? What is the progress of the reaction by this time? (answer)
2-10. Substance A was mixed with substances B and C in equal concentrations of 1 mol/l. After 1000 s, 50% of substance A remains. How much substance A will remain after 2000 s if the reaction has: a) zero, b) first, c) second, c) third general order? (answer)
2-11. Which of the reactions - first, second or third order - will end faster if the initial concentrations of substances are 1 mol/l and all rate constants expressed in terms of mol/l and s are equal to 1? (answer)
2-12. Reaction
CH 3 CH 2 NO 2 + OH - H 2 O + CH 3 CHNO 2 -
has second order and rate constant k= 39.1 l/(mol. min) at 0 o C. A solution was prepared containing 0.004 M nitroethane and 0.005 M NaOH. How long will it take for 90% of nitroethane to react?
2-13. The rate constant for the recombination of H + and FG - (phenylglyoxynate) ions into the UFG molecule at 298 K is equal to k= 10 11.59 l/(mol. s). Calculate the time it takes for the reaction to complete 99.999% if the initial concentrations of both ions are 0.001 mol/L. (answer)
2-14. The rate of oxidation of 1-butanol by hypochlorous acid does not depend on the alcohol concentration and is proportional to 2. How long will it take for the oxidation reaction at 298 K to complete 90% if the initial solution contained 0.1 mol/L HClO and 1 mol/L alcohol? The reaction rate constant is k= 24 l/(mol min). (answer)
2-15. At a certain temperature, a 0.01 M ethyl acetate solution is saponified by a 0.002 M NaOH solution by 10% in 23 minutes. After how many minutes will it be saponified to the same degree with a 0.005 M KOH solution? Consider that this reaction is of second order, and the alkalis are completely dissociated. (answer)
2-16. The second order reaction A + B P is carried out in a solution with initial concentrations [A] 0 = 0.050 mol/L and [B] 0 = 0.080 mol/L. After 1 hour, the concentration of substance A decreased to 0.020 mol/l. Calculate the rate constant and half-lives of both substances.
Subject of chemical kinetics.
Thermodynamics takes into account only the initial and final state of the system and allows one to predict with great accuracy the fundamental possibility of a process occurring, but it does not provide any information about the mechanism of the process or its changes over time.
All these questions of physical chemistry are considered in the section of chemical kinetics.
Section of physical chemistry devoted to the laws of flow chemical processes in time is called chemical kinetics.
Problems of chemical kinetics:
1. experimental study of reaction rates and their dependence on conditions (concentration of reacting substances, temperature, presence of other substances, etc.);
2. establishing the reaction mechanism, that is, the number of elementary stages and the composition of the resulting intermediate products.
A quantitative description of the dependence of the reaction rate on the concentration of reactants is based on the basic postulate of chemical kinetics and is the subject of formal kinetics.
IN general view a chemical reaction can be written as follows:
ν 1 А 1 + ν 2 А 2 +…+ ν i А i ν 1 ´А 1 ´ + ν 2 ´А 2 ´ +…+ν n ´А n ´,
where ν i and ν n ´ are the stoichiometric coefficients of the starting substances and reaction products, respectively; A i and A n ´ are the starting materials and reaction products.
Speed of chemical reaction υ is the change in the amount of reacting substances per unit time per unit volume (measured in mol/(l∙s)).
Since the amount of reacting substances changes over time, the rate of reaction is a function of time. You can introduce the concept average speed reactions, considered in a certain period of time:
Where n 1 And n 2- concentration of one of the starting substances in the initial t 1 and final t 2 moment in time.
The rate of a reaction is determined by the decrease in the amount of one of the reacting substances (with a “-” sign) or by the increase in the amount of one of the resulting substances (with a “+” sign) per unit time in a unit volume.
When the hourly interval decreases, when, we obtain the expression for true speed at this moment in time:
If the volume of the system is constant ( V=const), then we can use the concept of concentration:
This equation is considered for reactions in solutions, when the change in volume can be neglected.
Chemical reactions usually proceed through several stages. The rate of the overall reaction is determined by the rate of the slowest stage, called limiting.
The reaction rate depends on many factors: the nature and concentration of the reacting substances, temperature, the presence of other substances (catalysts, inhibitors), etc.
In general, according to law of mass action, we can write, that the rate of a chemical reaction is directly proportional to the product of the concentrations of the reacting substances in certain powers equal to the order of the reaction for a given substance:
| , | (1) |
where is the rate of the chemical reaction;
k- rate constant of a chemical reaction;
- concentrations of reactants;
n i– the order of reaction for a given substance.
Expression (1) is called the basic postulate of chemical kinetics. At the same time ν i = n i in cases where the reaction proceeds in one stage, as well as for all reactions that occur under equilibrium conditions (regardless of the fact that under conditions far from equilibrium they can proceed through a number of intermediate stages). In most cases, the reaction order is not equal to the stoichiometric coefficient (for multi-stage reactions) and is determined experimentally.
The proportionality coefficient in the basic postulate of chemical kinetics is called reaction rate constant k . Physical meaning of the coefficient k can be established if we take the concentrations of the reactants equal to 1, then the rate constant of the chemical reaction will be equal to the value of the reaction rate. Rate constant k depends on the nature of the reacting substances, temperature, but does not depend on the concentration of the starting substances.
What factors does it depend on? The reaction rate constant (specific reaction rate) is a coefficient of proportionality in the kinetic equation. The physical meaning of the reaction rate constant k follows from the equation of the law of mass action: k is numerically equal to the reaction rate at the concentration of each of the reactants equal to 1 mol/l .The reaction rate constant depends on temperature, on the nature of the reactants, on the catalyst, but does not depend on their concentration. For a reaction of the type 2A+2B->3C+D, the rate of formation of reaction products and the rate of consumption of reagents can be represented as: d[A]/(2*dt)=d[B]/(2*dt)=d[C] /(3*dt)=d[D]/dt Thus, in order to avoid using several forms of recording speed for the same reaction, use a chemical variable that determines the degree of reaction and does not depend on the stoichiometric coefficients: ξ=(Δn) /ν where ν is the stoichiometric coefficient. Then the reaction rate: v=(1/V)*dξ/dt where V is the volume of the system.
57. How does the rate of a chemical reaction depend on temperature? Van't Hoff's rule, Arrhenius equation.
The dependence of the reaction rate on temperature is approximately determined by the empirical Van't Hoff rule: With every 10 degree change in temperature, the rate of most reactions changes by 2-4 times.
Mathematically, van't Hoff's rule is expressed as follows:
where v(T2) and v(T1) are reaction rates, respectively, at temperatures T2 and T1 (T2> T1);
γ -temperature coefficient reaction speed.
The value of γ for an endothermic reaction is higher than for an exothermic one. For many reactions, γ lies in the range of 2-4.
The physical meaning of the value 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:
where k(T2), k(T1) are reaction rate constants, respectively
at temperatures T2 and T1;
γ is the temperature coefficient of the reaction rate.
Arrhenius equation. In 1889, the Swedish scientist S. Arre-1ius, based on experiments, derived an equation that is named after him
where k is the reaction rate constant;
k0 - pre-exponential factor;
e - base natural logarithm;
Ea is a constant called activation energy, determined by the nature of the reagents:
R is the universal gas constant equal to 8.314 J/mol×K.
Ea values for chemical reactions range from 4 to 400 kJ/mol.
Many reactions are characterized by a certain energy barrier. To overcome it, activation energy is necessary - 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, that is, to 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 general, if the reaction temperature changes from T1 to T2, equation (3.9) after logarithm takes the form:
.
This equation allows you to calculate the activation energy of a reaction as the temperature changes from T1 to T2.
The rate of chemical reactions increases in the presence of a catalyst. The effect of a catalyst is that it forms unstable intermediate compounds with reagents ( activated complexes), the decay of which leads to the formation of reaction products. In this case, the activation energy decreases, and molecules whose energy was insufficient to carry out the reaction in the absence of a catalyst become active. As a result, it increases total number active £ molecules and the reaction rate increases.
