Temperature coefficient of reaction rate. Van't Hoff's rule

The rate of chemical reactions increases with increasing temperature. The increase in the reaction rate with temperature can be estimated using the van't Hoff rule. According to the rule, an increase in temperature by 10 degrees increases the rate constant of the reaction by 2-4 times:

This rule is not fulfilled at high temperatures, when the rate constant hardly changes with temperature.

Van't Hoff's rule allows you to quickly determine the expiration date of a drug. An increase in temperature increases the rate of decomposition of the drug. This shortens the time to determine the expiration date of the drug.

The method consists in the fact that the drug is kept at elevated temperature T for a certain time tT, the amount of decomposed drug m is found and recalculated to a standard storage temperature of 298K. Considering the process of decomposition of the drug as a first-order reaction, the rate is expressed at the selected temperature T and T = 298K:

Considering the mass of the decomposed drug to be the same for standard and real storage conditions, the decomposition rates can be expressed by the equations:

Assuming T=298+10n, where n = 1,2,3…,

Get the final expression for the shelf life of the drug under standard conditions 298K:

Theory of active collisions. Activation energy. Arrhenius equation. Relationship between reaction rate and activation energy.

The theory of active collisions was formulated by S. Arrhenius in 1889. This theory is based on the idea that for a chemical reaction to occur, a collision between the molecules of the initial substances is necessary, and the number of collisions is determined by the intensity of the thermal motion of the molecules, i.e. temperature dependent. But not every collision of molecules leads to a chemical transformation: only active collision leads to it.

Active collisions are collisions that occur, for example, between molecules A and B with a large amount of energy. The minimum amount of energy that the molecules of the starting substances must have in order for their collision to be active is called the energy barrier of the reaction.

Activation energy is the excess energy that can be communicated or transferred to one mole of a substance.

The activation energy significantly affects the value of the reaction rate constant and its dependence on temperature: the larger Ea, the lower the rate constant and the more significantly the change in temperature affects it.

The reaction rate constant is related to the activation energy by a complex relationship described by the Arrhenius equation:

k=Ae–Ea/RT, where A is the pre-exponential factor; Ea is the activation energy, R is the universal gas constant equal to 8.31 j/mol; T is the absolute temperature;

e is the base of natural logarithms.

However, the observed reaction rate constants are generally much smaller than those calculated using the Arrhenius equation. Therefore, the equation for the reaction rate constant is modified as follows:

(minus before whole fraction)

The multiplier causes the temperature dependence of the rate constant to differ from the Arrhenius equation. Since the Arrhenius activation energy is calculated as the tangent of the slope of the logarithmic dependence of the reaction rate on the reciprocal temperature, then doing the same with the equation , we get:

Features of heterogeneous reactions. The rate of heterogeneous reactions and factors determining it. Kinetic and diffusion regions of heterogeneous processes. Examples of heterogeneous reactions of interest to pharmacy.

HETEROGENEOUS REACTIONS, chem. reactions involving substances in decomp. phases and constituting together a heterogeneous system. Typical heterogeneous reactions: thermal. decomposition of salts to form gaseous and solid products (e.g. CaCO3 -> CaO + CO2), reduction of metal oxides with hydrogen or carbon (e.g. PbO + C -> Pb + CO), dissolution of metals in acids (e.g. Zn + + H2SO4 -> ZnSO4 + H2), interaction. solid reagents (A12O3 + NiO -> NiAl2O4). In a special class, heterogeneous catalytic reactions occurring on the catalyst surface are distinguished; in this case, the reactants and products may not be in different phases. Direction, in the reaction N2 + + 3H2 -> 2NH3 occurring on the surface of an iron catalyst, the reactants and the reaction product are in the gas phase and form a homogeneous system.

The features of heterogeneous reactions are due to the participation of condensed phases in them. This makes it difficult to mix and transport reactants and products; activation of reagent molecules on the interface is possible. The kinetics of any heterogeneous reaction is defined as the rate of the chemical itself. transformations, and transfer processes (diffusion) necessary to replenish the consumption of reactants and remove reaction products from the reaction zone. In the absence of diffusion hindrances, the rate of a heterogeneous reaction is proportional to the size of the reaction zone; this is the name of the specific reaction rate calculated per unit surface (or volume) of the reaction. zones, does not change in time; for simple (single-step) reactions, it can be determined on the basis of the acting masses of the law. This law is not satisfied if the diffusion of substances proceeds more slowly than chemical. district; in this case, the observed rate of the heterogeneous reaction is described by the equations of diffusion kinetics.

The rate of a heterogeneous reaction is the amount of a substance that enters into a reaction or is formed during a reaction per unit time per unit area of the phase surface.

Factors affecting the rate of a chemical reaction:

The nature of the reactants

The concentration of reagents,

Temperature,

The presence of a catalyst.

Vheterog = Δp(S Δt), where Vheterog is the reaction rate in a heterogeneous system; n is the number of moles of any of the substances resulting from the reaction; V is the volume of the system; t - time; S is the surface area of the phase on which the reaction proceeds; Δ - increment sign (Δp = p2 - p1; Δt = t2 - t1).

Problem 336.
At 150°C, some reaction is complete in 16 minutes. Taking the temperature coefficient of the reaction rate equal to 2.5, calculate how long this reaction will end if it is carried out: a) at 20 0 °С; b) at 80°C.
Decision:
According to the van't Hoff rule, the dependence of velocity on temperature is expressed by the equation:

v t and k t - the rate and rate constant of the reaction at a temperature of t°C; v (t + 10) and k (t + 10) the same values at temperature (t + 10 0 C); - the temperature coefficient of the reaction rate, the value of which for most reactions lies in the range of 2 - 4.

a) Given that the rate of a chemical reaction at a given temperature is inversely proportional to the duration of its course, we substitute the data given in the condition of the problem into a formula that quantitatively expresses the van't Hoff rule, we get:

b) Since this reaction proceeds with a decrease in temperature, then at a given temperature the rate of this reaction is directly proportional to the duration of its course, we substitute the data given in the condition of the problem into a formula that quantitatively expresses the van't Hoff rule, we get:

Answer: a) at 200 0 С t2 = 9.8 s; b) at 80 0 С t3 = 162 h 1 min 16 s.

Problem 337.
Will the value of the reaction rate constant change: a) when replacing one catalyst with another; b) when the concentrations of reactants change?
Decision:
The reaction rate constant is a value that depends on the nature of the reactants, on temperature and on the presence of catalysts, and does not depend on the concentration of the reactants. It can be equal to the reaction rate in the case when the concentrations of the reactants are equal to unity (1 mol/l).

a) When one catalyst is replaced by another, the rate of a given chemical reaction will change, or it will increase. If a catalyst is used, the rate of a chemical reaction will increase, then, accordingly, the value of the reaction rate constant will also increase. A change in the value of the reaction rate constant will also occur when one catalyst is replaced by another, which will increase or decrease the rate of this reaction relative to the original catalyst.

b) When the concentration of the reactants changes, the values of the reaction rate will change, and the value of the reaction rate constant will not change.

Problem 338.
Does the thermal effect of a reaction depend on its activation energy? Justify the answer.
Decision:
The thermal effect of the reaction depends only on the initial and final state of the system and does not depend on the intermediate stages of the process. Activation energy is the excess energy that molecules of substances must have in order for their collision to lead to the formation of a new substance. The activation energy can be changed by raising or lowering the temperature, respectively lowering or increasing it. Catalysts lower the activation energy, while inhibitors lower it.

Thus, a change in the activation energy leads to a change in the reaction rate, but not to a change in the heat of the reaction. The thermal effect of a reaction is a constant value and does not depend on a change in the activation energy for a given reaction. For example, the reaction for the formation of ammonia from nitrogen and hydrogen is:

This reaction is exothermic, > 0). The reaction proceeds with a decrease in the number of moles of reacting particles and the number of moles of gaseous substances, which brings the system from a less stable state to a more stable one, the entropy decreases,< 0. Данная реакция в обычных условиях не протекает (она возможна только при достаточно низких температурах). В присутствии катализатора энергия активации уменьшается, и скорость реакции возрастает. Но, как до применения катализатора, так и в присутствии его тепловой эффект реакции не изменяется, реакция имеет вид:

Problem 339.
For which reaction, direct or reverse, is the activation energy greater if the direct reaction proceeds with the release of heat?
Decision:
The difference between the activation energies of the direct and reverse reactions is equal to the thermal effect: H \u003d E a (pr.) - E a (arr.) . This reaction proceeds with the release of heat, i.e. is exothermic,< 0 Исходя из этого, энергия активации прямой реакции имеет меньшее значение, чем энергия активации обратной реакции:
E a(ex.)< Е а(обр.) .

Answer: E a(ex.)< Е а(обр.) .

Problem 340.
How many times will the rate of a reaction proceeding at 298 K increase if its activation energy is reduced by 4 kJ/mol?
Decision:
Let us denote the decrease in the activation energy by Ea, and the rate constants of the reaction before and after the decrease in the activation energy, respectively, by k and k. Using the Arrhenius equation, we obtain:

E a is the activation energy, k and k" are the reaction rate constants, T is the temperature in K (298).
Substituting the data of the problem into the last equation and, expressing the activation energy in joules, we calculate the increase in the reaction rate:

Answer: 5 times.

Answer: a) at 200 0 С t2 = 9.8 s; b) at 80 0 С t3 = 162 h 1 min 16 s.

b) When the concentration of the reactants changes, the values of the reaction rate will change, and the value of the reaction rate constant will not change.

Answer: E a(ex.)< Е а(обр.) .

Answer: 5 times.

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: From here: 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 taking into account 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 violate the physiological functions and anatomical integrity of a living organism and their suffocating effect is due only to the presence in 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. The partial pressure of a 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. The influence of 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 in aqueous solutions into 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 a given moment in time?

4. Formulate the definition of reversible and irreversible reactions.

5. Define the law of mass action. Does the equation 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. The processes occurring with the drug in the body are quantitatively characterized by a number of pharmacokinetic parameters. Give the main ones.