The dependence of the reaction rate on temperature. The temperature coefficient of the reaction and its features for biochemical processes. Arrhenius equation. Chemical kinetics. Temperature and reaction rate
Temperature and reaction rate
At a fixed temperature, a reaction is possible if the interacting molecules have a certain amount of energy. Arrhenius called this excess energy activation energy , and the molecules themselves activated.
According to Arrhenius, the rate constant k and activation energy E a are related by a relation called the Arrhenius equation:
Here A is the pre-exponential factor, R is the universal gas constant, T is the absolute temperature.
Thus, at a constant temperature, the reaction rate determines E a. The more E a, the smaller the number of active molecules and the slower the reaction proceeds. When decreasing E a speed increases and E a= 0 the reaction proceeds instantaneously.
Value E a characterizes the nature of the reacting substances and is determined experimentally from the dependence k = f(T). Writing equation (5.3) in logarithmic form and solving it for constants at two temperatures, we find E a:
γ is the temperature coefficient of the chemical reaction rate. The van't Hoff rule has limited application, since the value of γ depends on temperature, and outside the region E a= 50–100 kJ ∙ mol–1 this rule is not fulfilled at all.
On fig. 5.4 it can be seen that the energy spent on the transfer of the initial products to the active state (A * - activated complex) is then fully or partially re-emitted during the transition to the final products. The difference between the energies of the initial and final products determines Δ H reaction that does not depend on the activation energy.
Thus, on the way from the initial state to the final state, the system must overcome the energy barrier. Only active molecules possessing at the moment of collision the necessary energy excess equal to E a, can overcome this barrier and enter into a chemical interaction. As the temperature rises, the proportion of active molecules in the reaction medium increases.
Preexponential multiplierA characterizes total number collisions. For reactions with simple molecules A close to theoretical collision magnitude Z, i.e. A = Z calculated from the kinetic theory of gases. For complex molecules A ≠ Z, so it is necessary to introduce the steric factor P:
Here Z is the number of all collisions, P is the fraction of collisions favorable in spatial relation(takes values from 0 to ), is the fraction of active, i.e., energetically favorable collisions.
The dimension of the rate constant is obtained from the relation
Analyzing expression (5.3), we come to the conclusion that there are two fundamental possibilities for accelerating the reaction:
a) an increase in temperature,
b) decrease in activation energy.
Tasks and tests on the topic "Chemical kinetics. Temperature and reaction rate"
- The rate of a chemical reaction. Catalysts - Classification of chemical reactions and patterns of their course Grade 8–9
Lessons: 5 Assignments: 8 Quizzes: 1
The rate of most chemical reactions increases with increasing temperature. Since the concentration of reactants is practically independent of temperature, in accordance with the kinetic equation of the reaction, the main effect of temperature on the reaction rate is through a change in the reaction rate constant. As the temperature increases, the energy of the colliding particles increases and the probability that a chemical transformation occurs during the collision increases.
The dependence of the reaction rate on temperature can be characterized by the value of the temperature coefficient.
Experimental data on the effect of temperature on the rate of many chemical reactions at ordinary temperatures (273–373 K), in a small temperature range, showed that an increase in temperature by 10 degrees increases the reaction rate by 2–4 times (van't Hoff rule).
According to van't Hoff temperature coefficient of rate constant(Van't Hoff coefficient)is the increase in the rate of a reaction with an increase in temperature by 10degrees.
(4.63)
where and are the rate constants at temperatures and ; is the temperature coefficient of the reaction rate.
When the temperature rises to n tens of degrees, the ratio of the rate constants will be equal to
where n can be either an integer or a fractional number.
Van't Hoff's rule is an approximate rule. It is applicable in a narrow temperature range, since the temperature coefficient changes with temperature.
A more accurate dependence of the reaction rate constant on temperature is expressed by the semi-empirical Arrhenius equation
where A is a pre-exponential factor which does not depend on temperature, but is determined only by the type of reaction; E - the activation energy of a chemical reaction. The activation energy can be represented as a certain threshold energy that characterizes the height of the energy barrier on the reaction path. The activation energy also does not depend on temperature.
This dependency is set to late XIX in. Dutch scientist Arrhenius for elementary chemical reactions.
Direct activation energy ( E 1) and reverse ( E 2) the reaction is related to the thermal effect of the reaction D H ratio (see Fig. 1):
E 1 – E 2=D N.
If the reaction is endothermic and D H> 0, then E 1 > E 2 and the activation energy of the forward reaction is greater than the reverse. If the reaction is exothermic, then E 1 < Е 2 .
The Arrhenius equation (101) in differential form can be written:
It follows from the equation that the greater the activation energy E, the faster the reaction rate increases with temperature.
Separating variables k and T and considering E constant value, after integrating equation (4.66) we get:
Rice. 5. Graph ln k–1/T.
, (4.67)
where A is a pre-exponential factor having the dimension of the rate constant. If this equation is valid, then on the graph in coordinates, the experimental points are located on a straight line at an angle a to the x-axis and slope() is equal to , which makes it possible to calculate the activation energy of a chemical reaction from the dependence of the rate constant on temperature according to the equation .
The activation energy of a chemical reaction can be calculated from the values of the rate constants at two various temperatures according to the equation
. (4.68)
The theoretical derivation of the Arrhenius equation is made for elementary reactions. But experience shows that the vast majority of complex reactions also obey this equation. However, for complex reactions, the activation energy and the pre-exponential factor in the Arrhenius equation do not have a definite physical meaning.
The Arrhenius equation (4.67) makes it possible to give a satisfactory description of a wide range of reactions in a narrow temperature range.
To describe the dependence of the reaction rate on temperature, the modified Arrhenius equation is also used
,
(4.69)
which already includes three parameters : BUT, E and n.
Equation (4.69) is widely used for reactions occurring in solutions. For some reactions, the dependence of the reaction rate constant on temperature differs from the dependences given above. For example, in third-order reactions, the rate constant decreases with increasing temperature. In chain exothermic reactions, the reaction rate constant increases sharply at a temperature above a certain limit (thermal explosion).
4.5.1. Examples of problem solving
Example 1 The rate constant of some reaction with increasing temperature changed as follows: t 1 = 20°C;
k 1 \u003d 2.76 10 -4 min. -one ; t 2 \u003d 50 0 C; k 2 = 137.4 10 -4 min. -1 Determine the temperature coefficient of the rate constant of a chemical reaction.
Decision. The van't Hoff rule makes it possible to calculate the temperature coefficient of the rate constant from the relation
g n= =2 ¸ 4, where n = = =3;
g 3 \u003d \u003d 49.78 g \u003d 3.68
Example 2 Using the van't Hoff rule, calculate at what temperature the reaction will end in 15 minutes, if it took 120 minutes at a temperature of 20 0 C. Temperature coefficient reaction rate is 3.
Decision. Obviously, the shorter the reaction time ( t), the greater the rate constant of the reaction:
3n = 8, n ln3 = ln8, n== .
The temperature at which the reaction will end in 15 minutes is:
20 + 1.9 × 10 \u003d 39 0 C.
Example 3 The rate constant of the reaction of saponification of acetic-ethyl ester with an alkali solution at a temperature of 282.4 K is equal to 2.37 l 2 / mol 2 min. , and at a temperature of 287.40 K it is equal to 3.2 l 2 / mol 2 min. Find the temperature at which the rate constant of this reaction is 4?
Decision.
1. Knowing the values of the rate constants at two temperatures, we can find the activation energy of the reaction:
= 
= 40.8 kJ/mol.
2. Knowing the value of the activation energy, from the Arrhenius equation
Questions and tasks for self-control.
1. What quantities are called "Arrhenius" parameters?
2. What is the minimum amount of experimental data needed to calculate the activation energy of a chemical reaction?
3. Show that the temperature coefficient of the rate constant depends on temperature.
4. Are there deviations from the Arrhenius equation? How can the dependence of the rate constant on temperature be described in this case?
Kinetics of complex reactions
Reactions, as a rule, do not proceed through the direct interaction of all initial particles with their direct transition into reaction products, but consist of several elementary stages. This primarily applies to reactions in which, according to their stoichiometric equation, more than three particles take part. However, even reactions of two or one particle often do not proceed by a simple bi- or monomolecular mechanism, but by a more complex path, that is, through a number of elementary stages.
Reactions are called complex if the consumption of starting materials and the formation of reaction products occur through a series of elementary stages that can occur simultaneously or sequentially. At the same time, some stages take place with the participation of substances that are neither starting substances nor reaction products (intermediate substances).
As an example complex reaction we can consider the reaction of chlorination of ethylene with the formation of dichloroethane. Direct interaction must go through a four-membered activated complex, which is associated with overcoming a high energy barrier. The speed of such a process is low. If atoms are formed in the system in one way or another (for example, under the action of light), then the process can proceed according to a chain mechanism. The atom easily joins at the double bond to form a free radical - . This free radical can easily tear off an atom from a molecule to form the final product - , as a result of which the free atom is regenerated.
As a result of these two stages, one molecule and one molecule are converted into a product molecule - , and the regenerated atom interacts with the next ethylene molecule. Both stages have low activation energies, and this way provides a fast reaction. Taking into account the possibility of recombination of free atoms and free radicals full scheme process can be written as:
With all the variety, complex reactions can be reduced to a combination of several types of complex reactions, namely parallel, sequential and series-parallel reactions.
The two stages are called successive if the particle formed in one stage is the initial particle in another stage. For example, in the above scheme, the first and second stages are sequential:
.
The two stages are called parallel, if the same particles take part as initial in both. For example, in the reaction scheme, the fourth and fifth stages are parallel:
The two stages are called series-parallel, if they are parallel with respect to one and sequential with respect to the other of the particles participating in these stages.
An example of series-parallel steps are the second and fourth steps of this reaction scheme.
To characteristics the fact that the reaction proceeds according to a complex mechanism, are the following signs:
Mismatch of reaction order and stoichiometric coefficients;
Changing the composition of products depending on temperature, initial concentrations and other conditions;
Acceleration or slowdown of the process when small amounts of substances are added to the reaction mixture;
Influence of the material and dimensions of the vessel on the reaction rate, etc.
In the kinetic analysis of complex reactions, the principle of independence is applied: “If several simple reactions occur simultaneously in the system, then the basic postulate of chemical kinetics applies to each of them, as if this reaction were the only one.” This principle can also be formulated as follows: "The value of the rate constant of an elementary reaction does not depend on whether other elementary reactions proceed simultaneously in a given system."
The principle of independence is valid for most reactions that proceed according to a complex mechanism, but is not universal, since there are reactions in which some simple reactions affect the course of others (for example, conjugated reactions.)
Important in the study of complex chemical reactions is the principle microreversibility or detailed balance:
if in complex process chemical equilibrium is established, then the rates of the forward and reverse reactions must be equal for each of the elementary stages.
The most common case of a complex reaction occurring will be the case when the reaction proceeds through several simple steps proceeding with different speeds. The difference in rates leads to the fact that the kinetics of obtaining the reaction product can be determined by the laws of only one reaction. For example, for parallel reactions, the rate of the entire process is determined by the rate of the fastest stage, and for sequential reactions, the slowest one. Therefore, when analyzing the kinetics of parallel reactions with a significant difference in the constants, the rate of the slow stage can be neglected, and when analyzing sequential reactions, it is not necessary to determine the rate of the fast reaction.
In sequential reactions, the slowest reaction is called limiting. The limiting stage has the smallest rate constant.
If the values of the rate constants of the individual stages of a complex reaction are close, then it is necessary complete analysis the entire kinetic scheme.
The introduction of the concept of a rate-determining stage in many cases simplifies the mathematical side of considering such systems and explains the fact that sometimes the kinetics of complex, multi-stage reactions is well described by simple equations, for example, of the first order.
As the temperature rises, the rate of a chemical process usually increases. In 1879, the Dutch scientist J. Van't Hoff formulated an empirical rule: with an increase in temperature by 10 K, the rate of most chemical reactions increases by 2-4 times.
Mathematical notation of the rule I. van't Hoff:
γ 10 \u003d (k t + 10) / k t, where k t is the rate constant of the reaction at temperature T; k t+10 - reaction rate constant at temperature T+10; γ 10 - Van't Hoff temperature coefficient. Its value ranges from 2 to 4. For biochemical processesγ 10 varies from 7 to 10.
All biological processes proceed in a certain temperature range: 45-50°C. Optimum temperature is 36-40°C. In the body of warm-blooded animals, this temperature is maintained constant due to the thermoregulation of the corresponding biosystem. When studying biosystems, temperature coefficients γ 2 , γ 3 , γ 5 are used. For comparison, they are brought to γ 10 .
The dependence of the reaction rate on temperature, in accordance with the van't Hoff rule, can be represented by the equation:
V 2 /V 1 \u003d γ ((T 2 -T 1) / 10)
Activation energy. A significant increase in the reaction rate with increasing temperature cannot be explained only by an increase in the number of collisions between particles of reacting substances, since, in accordance with the kinetic theory of gases, the number of collisions increases slightly with increasing temperature. The increase in the reaction rate with increasing temperature is explained by the fact that a chemical reaction does not occur with any collision of particles of reacting substances, but only with a meeting of active particles that have the necessary excess energy at the moment of collision.
The energy required to turn inactive particles into active particles is called activation energy (Ea). Activation energy - excess, compared with the average value, the energy required for the entry of reacting substances into a reaction when they collide. The activation energy is measured in kilojoules per mole (kJ/mol). Usually E is from 40 to 200 kJ/mol.
The energy diagram of the exothermic and endothermic reactions is shown in fig. 2.3. For any chemical process, it is possible to distinguish the initial, intermediate and final states. At the top of the energy barrier, the reactants are in an intermediate state called the activated complex, or transition state. The difference between the energy of the activated complex and the initial energy of the reagents is Ea, and the difference between the energy of the reaction products and starting materials (reagents) is ΔH, thermal effect reactions. The activation energy, in contrast to ΔH, is always a positive value. For exothermic reaction(Fig. 2.3, a) products are located at a lower energy level than reagents (Ea< ΔН).
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Ea is the main factor determining the reaction rate: if Ea > 120 kJ/mol (higher energy barrier, fewer active particles in the system), the reaction is slow; and vice versa, if Ea< 40 кДж/моль, реакция осуществляется с большой скоростью.
For reactions involving complex biomolecules, one should take into account the fact that in an activated complex formed during the collision of particles, the molecules must be oriented in space in a certain way, since only the reacting region of the molecule undergoes transformation, which is small in relation to its size.
If the rate constants k 1 and k 2 are known at temperatures T 1 and T 2 , the value of Ea can be calculated.
In biochemical processes, the activation energy is 2-3 times less than in inorganic ones. At the same time, the Ea of reactions involving foreign substances, xenobiotics, significantly exceeds the Ea of conventional biochemical processes. This fact is the natural bioprotection of the system from the influence of foreign substances, i.e. reactions natural for the body occur under favorable conditions with low Ea, and for foreign reactions, Ea is high. This is a gene barrier that characterizes one of the main features of the course of biochemical processes.
Task # 1. Interaction with free oxygen leads to the formation of highly toxic nitrogen dioxide / /, although this reaction proceeds slowly under physiological conditions and at low concentrations does not play a significant role in toxic cell damage, but, however, pathogenic effects increase sharply with its hyperproduction. Determine how many times the rate of interaction of nitric oxide (II) with oxygen increases when the pressure in the mixture of initial gases doubles, if the reaction rate 
is described by the equation 
?
Decision.
1. Doubling the pressure is equivalent to doubling the concentration ( with) and . Therefore, the interaction rates corresponding to and will take, in accordance with the law of mass action, the expressions: 
and
Answer. The reaction rate will increase by 8 times.
Task # 2. It is believed that the concentration of chlorine (a greenish gas with a pungent odor) in the air above 25 ppm is dangerous to life and health, but there is evidence that if the patient has recovered from acute severe poisoning with this gas, then no residual effects are observed. Determine how the reaction rate will change: , proceeding in the gas phase, if increased by a factor of 3: concentration , concentration , 3) pressure / /?
Decision.
1. If we denote the concentrations and respectively through and , then the expression for the reaction rate will take the form: .
2. After increasing the concentrations by a factor of 3, they will be equal for and for . Therefore, the expression for the reaction rate will take the form: 1) 
2)
3. An increase in pressure increases the concentration of gaseous reactants by the same amount, therefore
4. The increase in the reaction rate in relation to the initial one is determined by the ratio, respectively: 1) 
, 2) 
, 3) 
.
Answer. The reaction rate will increase: 1) , 2) , 3) times.
Task #3. How does the rate of interaction of the starting substances change with a change in temperature from to if the temperature coefficient of the reaction is 2.5?
Decision.
1. The temperature coefficient shows how the reaction rate changes with a change in temperature for every (van't Hoff rule):.
2. If the temperature change is: , then taking into account the fact that , we get: 
. Hence, .
3. According to the table of antilogarithms, we find: .
Answer. With a change in temperature (i.e. with an increase), the speed will increase by 67.7 times.
Task #4. Calculate the temperature coefficient of the reaction rate, knowing that as the temperature rises, the rate increases by a factor of 128.
Decision.
1. The dependence of the rate of a chemical reaction on temperature is expressed by the van't Hoff rule of thumb:
.Solving the equation for , we find: , . Therefore, =2
Answer. =2.
Task number 5. For one of the reactions, two rate constants were determined: at 0.00670 and at 0.06857. Determine the rate constant of the same reaction at .
Decision.
1. Based on two values of the reaction rate constants, using the Arrhenius equation, we determine the activation energy of the reaction: . For this case: Hence: J/mol.
2. Calculate the reaction rate constant at , using the rate constant at and the Arrhenius equation in the calculations: 
. For this case: and given that: 
, we get: . Hence,
Answer.
Calculation of the chemical equilibrium constant and determination of the direction of equilibrium shift according to the Le Chatelier principle .
Task number 6. Carbon dioxide / / unlike carbon monoxide / / does not disturb physiological functions and the anatomical integrity of a living organism and their suffocating effect is due only to the presence in a high concentration and a decrease in the percentage of oxygen in the inhaled air. What is equal to reaction equilibrium constant / /: 
at temperature expressed in terms of: a) partial pressures of the reactants; b) their molar concentrations , knowing that the composition of the equilibrium mixture is expressed in volume fractions: , and , and the total pressure in the system is Pa?
Decision.
1. Partial pressure gas is equal to the total pressure times the volume fraction of the gas in the mixture, so:
2. Substituting these values into the expression for the equilibrium constant, we get:
3. The relationship between and is established on the basis of the Mendeleev Clapeyron equation for ideal gases and is expressed by the equality: 
, where is the difference between the number of moles of gaseous reaction products and gaseous initial substances. For this reaction: Then: 
.
Answer. Pa. .
Task number 7. In which direction will the equilibrium shift in the following reactions:
3. 
;
a) with an increase in temperature, b) with a decrease in pressure, c) with an increase in the concentration of hydrogen?
Decision.
1. The chemical equilibrium in the system is established with the constancy of external parameters (etc.). If these parameters change, then the system leaves the state of equilibrium and the direct (to the right) or reverse reaction (to the left) begins to prevail. Influence various factors on the shift of equilibrium is reflected in Le Chatelier's principle.
2. Consider the effect on the above reactions of all 3 factors affecting the chemical equilibrium.
a) With an increase in temperature, the equilibrium shifts towards an endothermic reaction, i.e. reaction that takes place with the absorption of heat. The 1st and 3rd reactions are exothermic / /, therefore, with an increase in temperature, the equilibrium will shift towards the reverse reaction, and in the 2nd reaction / / - towards the direct reaction.
b) When the pressure decreases, the equilibrium shifts towards an increase in the number of moles of gases, i.e. towards higher pressure. In the 1st and 3rd reactions, the left and right sides of the equation will have the same number of moles of gases (2-2 and 1-1, respectively). So the change in pressure won't cause equilibrium shifts in the system. In the 2nd reaction, there are 4 moles of gases on the left side, and 2 moles on the right, therefore, as the pressure decreases, the equilibrium will shift towards the reverse reaction.
in) With an increase in the concentration of reaction components, the equilibrium shifts towards their consumption. In the 1st reaction, hydrogen is in the products, and increasing its concentration will enhance the reverse reaction, during which it is consumed. In the 2nd and 3rd reactions, hydrogen is among the initial substances, therefore, an increase in its concentration shifts the equilibrium towards the reaction proceeding with the consumption of hydrogen.
Answer.
a) With an increase in temperature in reactions 1 and 3, the equilibrium will be shifted to the left, and in reaction 2 - to the right.
b) Reactions 1 and 3 will not be affected by a decrease in pressure, and in reaction 2, the equilibrium will be shifted to the left.
c) An increase in temperature in reactions 2 and 3 will entail a shift of equilibrium to the right, and in reaction 1 to the left.
1.2. Situational tasks №№ from 7 to 21 to consolidate the material (perform in the protocol notebook).
Task number 8. How will the rate of glucose oxidation in the body change with a decrease in temperature from to if the temperature coefficient of the reaction rate is 4?
Task number 9.Using the approximate van't Hoff rule, calculate how much the temperature needs to be raised so that the reaction rate increases by 80 times? Take the temperature coefficient of speed equal to 3.
Task number 10. To practically stop the reaction, rapid cooling of the reaction mixture (“freezing the reaction”) is used. Determine how many times the reaction rate will change when the reaction mixture is cooled from 40 to , if the temperature coefficient of the reaction is 2.7.
Task number 11. An isotope used to treat certain tumors has a half-life of 8.1 days. After what time will the content of radioactive iodine in the patient's body decrease by 5 times?
Task number 12. Hydrolysis of some synthetic hormone (pharmaceutical) is a first order reaction with a rate constant of 0.25 (). How will the concentration of this hormone change after 2 months?
Task number 13. The half-life of radioactive is 5600 years. In a living organism, a constant amount is maintained due to metabolism. In the remains of a mammoth, the content was from the original. When did the mammoth live?
Task number 14. The half-life of the insecticide (a pesticide used to control insects) is 6 months. A certain amount of it got into the reservoir, where the concentration mol / l was established. How long does it take for the insecticide concentration to drop to the mol/L level?
Task number 15. Fats and carbohydrates are oxidized at a noticeable rate at a temperature of 450 - 500 °, and in living organisms - at a temperature of 36 - 40 °. What is the reason for the sharp decrease in the temperature required for oxidation?
Task number 16. Hydrogen peroxide decomposes into aqueous solutions to oxygen and water. The reaction is accelerated by both an inorganic catalyst (ion) and a bioorganic one (catalase enzyme). The activation energy of the reaction in the absence of a catalyst is 75.4 kJ/mol. The ion reduces it to 42 kJ/mol, and the enzyme catalase reduces it to 2 kJ/mol. Calculate the ratio of the reaction rates in the absence of a catalyst in the cases of the presence of and catalase. What conclusion can be drawn about the activity of the enzyme? The reaction proceeds at a temperature of 27 °C.
Task number 17 Disintegration rate constant of penicillin on walkie-talkie 
J/mol.
1.3. test questions
1. Explain what the terms mean: reaction rate, rate constant?
2. How is the average and true rate of chemical reactions expressed?
3. Why does it make sense to talk about the rate of chemical reactions only for this moment time?
4. Formulate the definition of reversible and irreversible reactions.
5. Define the law of mass action. Do the equations expressing this law reflect the dependence of the reaction rate on the nature of the reactants?
6. How does the reaction rate depend on temperature? What is the activation energy? What are active molecules?
7. What factors determine the rate of a homogeneous and heterogeneous reaction? Give examples.
8. What is the order and molecularity of chemical reactions? In what cases do they not match?
9. What substances are called catalysts? What is the mechanism of accelerating action of a catalyst?
10. What is the concept of "catalyst poisoning"? What substances are called inhibitors?
11. What is called chemical equilibrium? Why is it called dynamic? What concentrations of reactants are called equilibrium?
12. What is called the chemical equilibrium constant? Does it depend on the nature of the reacting substances, their concentration, temperature, pressure? What are the features of the mathematical notation for the equilibrium constant in heterogeneous systems?
13. What is the pharmacokinetics of drugs?
14. Processes occurring with drug in the body are quantitatively characterized by a number of pharmacokinetic parameters. Give the main ones.