The reaction rate is 2a c. Theme. The rate of chemical reactions. Questions for self-control

Example 1... The reaction between substances A and B proceeds according to the equation 2A + B \u003d C, the concentrations of substances (mol / l) are [A] \u003d 6, [B] \u003d 5. The reaction rate constant is 0.5 l 2 × mol -2 × s -1 . Calculate the rate of the chemical reaction at the initial moment and at the moment when 45% of substance B remains in the reaction mixture.

Decision.According to the law of mass action, the rate of a chemical reaction is directly proportional to the product of the concentrations of the reactants in powers equal to the stoichiometric coefficients in the reaction equation. Therefore, for the reaction 2A + B C

V = k C A 2 C B.

The rate of the chemical reaction at the initial moment is equal to:

V 1 \u003d0.5 · 6 2 · 5 \u003d 90 mol · s -1 · l -1.

If the concentration of at least one of the reactants has changed, then the concentration of all other substances will also change:

After some time, 45% of substance B remains in the reaction mixture, i.e. [B] \u003d 5 * 0.45 \u003d 2.25 mol / l. This means that the concentration of substance B decreased by 5.0 - 2.25 \u003d 2.75 mol / l. Since substances A and B interact with each other in a ratio of 2: 1, the concentration of substance A decreased by 5.5 mol (2.752) and became equal to 0.5 mol / l (6.0 - 5.5). Hence,

V 2 \u003d 0.5 ∙ (0.5) 2 2.25 \u003d 0.28 mol s -1 l -1.

Example 2... Determine how the forward reaction rate will change

2CO (g) + O 2 (g) \u003d 2CO 2 (g), if the total pressure in the system is increased by 4 times.

Decision.An increase in pressure in the system by 4 times will cause a decrease in the volume of the system by 4 times, and the concentration of reactants will increase by 4 times. According to the law of mass action, the initial reaction rate is

After increasing pressure

Consequently, after increasing the pressure by 4 times, the reaction rate increased by 64 times.

Note... The law of action of masses in its classical form (expressed through concentration) is valid for non-electrolytes and dilute solutions of weak electrolytes (i.e., for gases and solutions). Solids are not included in the expression for the reaction rate, since the concept of concentration is unacceptable for them; the rate of reactions in the solid phase depends on the surface area of \u200b\u200bthe solid, i.e. the degree of its grinding.

So, for the reaction C (t) + CO 2 (g) \u003d 2CO (g), the rate of the forward reaction is reverse.

A change in pressure shifts the equilibrium if the number of moles of the initial and formed gaseous substances is not the same. For the reaction 2CO + O 2 \u003d 2CO 2, the rate of the forward reaction is reverse.

Example 3... In the system A (g) + 2B (g) \u003d C (g), the equilibrium concentrations are: [A] \u003d 0.06 mol / l; [B] \u003d 0.12 mol / l; [C] \u003d 0.216 mol / l. Find the equilibrium constant of the reaction and the initial concentrations of substances A and B.

Decision.According to the law of mass action, the equilibrium constant of this reaction is expressed by the equation

Substituting these tasks into it, we get:

According to the reaction equation, 1 mol C is formed from 1 mol A and 2 mol B. Since, according to the condition of the problem, 0.216 mol of substance C was formed in each liter of the system, 0.216 mol A and 0.216 2 \u003d 0.432 mol B were consumed. Thus , the required initial concentrations are equal to:

[A] \u003d 0.06 + 0.116 \u003d 0.276 mol / L;

[B] \u003d 0.12 + 0.432 \u003d 0.552 mol / l.

Example 4.This reaction takes place according to the equation A + B \u003d 2C. Determine the equilibrium concentrations of the reacting substances if the initial concentrations of substances A and B are 0.5 and 0.7 mol / L, respectively, and the equilibrium constant of the reaction TOp \u003d 50.

Decision.By the time of equilibrium, the concentrations of the starting substances A and B will decrease, and the concentration of the reaction product C will increase. For each mole of substances A and B, 2 moles of substance C are formed; therefore, if the decrease in the concentration of substances A and B is denoted by x mol, then the increase in the concentration of substance C will be equal to 2 x mole.

Equilibrium concentrations of reactants will be:

[A] \u003d (0.5 - x) mol / l; [B] \u003d (0.7 - x) mol / l; [C] \u003d 2 x mol / l.

46x 2 -60x +17,5=0.

Solving the equation, we get: x 1 = 0,86; x 2 \u003d 0.44. By the condition of the problem, the value x 2. Hence, the equilibrium concentrations of the reactants are equal: [A] \u003d 0.5 - 0.44 \u003d 0.06 mol / l; [B] \u003d 0.7 - 0.44 \u003d \u003d 0.26 mol / l; [C] \u003d 0.44 * 2 \u003d 0.88 mol / l.

Example 5... Calculate how many times the rate of a chemical reaction will increase with an increase in temperature by 40 ° C, if the temperature coefficient of this reaction is 3.

Decision.The dependence of the rate of a chemical reaction on temperature is expressed by the Van't Hoff rule of thumb.

In this example, the temperature has increased by 40 ° C,

Consequently, the reaction rate increased by 3 4 \u003d 81 times.

Self-study questions

1. Formulate the law of action of the masses, Van't Hoff's law, Le Chatelier's principle.

2. What are the factors influencing the speed of the reaction.

3. What is called the equilibrium constant, what does it depend on and what does it characterize?

4. The reaction proceeds according to the equation 4HCI (g) + O 2 (g) \u003d 2H 2 O (g) + 2CI 2 (g). How will the reaction rate change if the pressure in the system is increased by 3 times?

5. How many times should the hydrogen concentration be increased so that the rate of the reaction N 2 (g) + 3H 2 (g) ®2NH 3 (g) increases 1000 times? How should the pressure be changed to achieve the same acceleration of the reaction?

6. In which direction the balance is shifted: a) when the temperature rises; b) with increasing pressure:

2H 2 (g) + O 2 (g) ⇆2H 2 O (steam) + 249.9 kJ

2SO 2 (g) + O 2 (g) ⇆2SO 3 (g) + 198.4 kJ

7. The equilibrium of the 2NO (g) + O 2 (g) ®2NO 2 (g) system was established at the following concentrations of substances: \u003d 0.08 mol / l; \u003d 0.03 mol / l; \u003d 0.01 mol / l. Calculate the equilibrium constant and the starting NO and O 2 concentrations if the starting NO 2 concentration is zero.

1. How will the rate of the direct reaction A (g) + 2B (g) → AB 2 change if the pressure in the system is increased by 4 times?

a) the speed will decrease 10 times;

b) the speed will not change;

c) the speed will increase 16 times;

d) the speed will increase 64 times.

2. The temperature coefficient of the rate of some reaction is 2.0. How will the speed of this reaction change if you lower it by 40 degrees?

a) will increase by 8 times;

b) decrease by 8;

c) decrease by 16 times;

d) will increase 16 times.

3. In a homogeneous system A + B \u003d 2C equilibrium concentrations of reacting gases (mol / l): [A] \u003d 0.06; [B] \u003d 0.2; [C] \u003d 0.8. Calculate the equilibrium constant of the system.

4. For the reaction NO (g) + O 2 (g) \u003d NO 2 (g) at 25 ° C Cr \u003d 0.1. What is the ∆G response?

a) 23.5 kJ / mol;

b) -5.7 J / mol;

c) -44.8 kJ / mol;

d) 22.44 kJ / mol.

5. In which direction will the equilibrium shift with decreasing temperature in the reaction:

C 2 H 4 (g) + 3O 2 (g) \u003d 2CO 2 (g) + 2H 2 O (g) (∆H o \u003d -1323 kJ ) ?

a) will shift to the right;

b) will shift to the left;

c) the balance will not change.

1. In a vessel, gas A was mixed with the amount of substance 4.5 mol and gas B with the amount of substance 3 mol. Gases A and B react in accordance with the equation A + B \u003d C. After a while, gas C was formed in the system with an amount of 2 mol. How much of unreacted gases A and B are left in the system?

It follows from the reaction equation that:

Dn (A) \u003d Dn (B) \u003d Dn (C) \u003d 2 mol,

where Dn is the change in the amount of a substance during the reaction.

Therefore, the following remains in the vessel:

n 2 (A) \u003d n 1 (A) - Dn (A); n 2 (A) \u003d (4.5 - 2) mol \u003d 2.5 mol;

n 2 (B) \u003d n 1 (B) - Dn (B); n 2 (B) \u003d (3 - 2) mol \u003d 1 mol.

2. The reaction proceeds according to the equation: 2A + B ⇄ C and has the second order in substance A and the first in substance B. At the initial time, the reaction rate is 15 mol / l × s. Calculate the rate constant and the rate of the direct reaction at the moment when 50% of substance B reacts, if the initial concentrations are equal: C (A) \u003d 10 mol / l; C (B) \u003d 5 mol / L. How will the rate of a chemical reaction change?

C (B) reacted is equal to:

C (B) \u003d 0.5 · 5 \u003d 2.5 mol / L.

Accordingly, the reaction С (A) is equal to:

2 mol / L A - 1 mol / L B

C (A) - 2.5 mol / L B

C (A) and C (B) after the reaction:

C (A) \u003d 10 - 5 \u003d 5 mol / l,

C (B) \u003d 5 - 2.5 \u003d 2.5 mol / L.

The direct reaction rate will be equal to:

The rate of the chemical reaction will change:

that is, it will decrease by 8 times.

3. The reaction between substances A and B is expressed by the equation: A + 2B \u003d C and has the first order in substance A and the second in substance B. The initial concentrations of substances are equal: C (A) \u003d 2 mol / l; C (B) \u003d 4 mol / l; the rate constant is 1.0. Find the initial reaction rate and the rate after a certain time, when the concentration of substance A decreases by 0.3 mol / L.

According to the law of mass action:

If the concentration of substance A decreases by 0.3 mol / l, then the concentration of substance B will decrease by 0.3 × 2 \u003d 0.6 mol / l. After the reaction proceeds, the concentrations are:

4. The rates of direct and reverse gas-phase reactions occurring in a closed vessel are expressed by the equations:

According to the law of effective masses, the rates of direct and reverse reactions under initial conditions are equal:

An increase in pressure by 3 times for gaseous systems leads to a decrease in the volume of the gas mixture by 3 times, the concentration of all three gases will increase by the same amount, and the rates of both reactions will become, respectively, equal:

The reaction rate ratios are:

Thus, the speed of the forward reaction will increase by 27 times, the reverse - by 9.

5. The reaction at a temperature of 50 0 С proceeds in 2 minutes 15 seconds. How long will this reaction take at a temperature of 70 0 С if the temperature coefficient of the rate g is equal to 3 in a given temperature range?

With an increase in temperature from 50 to 70 0 С, the reaction rate in accordance with the Van't Hoff rule increases:

where \u003d 70 0 С, \u003d 50 0 С, a and are the reaction rates at these temperatures.

We get:

those. the reaction rate increases 9 times.

By definition, the reaction time is inversely proportional to the reaction rate, therefore:

where and is the reaction time at temperatures and .

From here we get:

Considering that \u003d 135 s (2 min 15 s), we determine the reaction time at a temperature :

6. How many times will the rate of the chemical reaction increase when the temperature rises from \u003d 10 0 C to \u003d 80 0 С , if the temperature coefficient of speed g is 2?

From the Van't Hoff rule:

The reaction speed will increase 128 times.

7. When studying the kinetics of drug elimination from the patient's body, it was found that 50% of the initial amount of the drug remained in the patient's body in 3 hours. Determine the half-life and the reaction rate constant for the elimination of the drug from the human body, if it is known that this is a first-order reaction.

Since during a given period of time 50% of the drug was excreted from the body, t 1/2 \u003d 3 hours. The reaction rate constant is calculated from the equation:

8. In laboratory studies of aqueous solutions of the drug, it was found that due to hydrolysis, the concentration of the drug per day decreased from 0.05 mol / l to 0.03 mol / l. Calculate the half-life of the drug hydrolysis reaction.

Since hydrolysis reactions usually take place with a significant excess of water, its concentration can be constant. Therefore, in the course of the reaction, only the concentration of the drug changes and the hydrolysis reaction can be considered a first-order reaction.

The value of the reaction rate constant is found from the equation:

9. The half-life of the drug from the patient's body (first-order reaction) is 5 hours. Determine the time during which 75% of the drug will be excreted from the body.

When 75% of the drug is removed from the body, the C / C 0 ratio will be 0.25. In this case, it is convenient to use the formula:

,

10. The rate constant of the sucrose hydrolysis reaction is 2.31 × 10 - 3 h - 1. Calculate:

1) the half-life of the reaction;

2) the time during which 20% of sucrose will undergo hydrolysis;

3) what part of glucose will undergo hydrolysis after 5 days.

1. The half-life is:

2. After 20% sucrose undergoes hydrolysis, the C / C 0 ratio will be 0.8. Hence:

3. After 5 days (120 hours), the C / C 0 ratio will be:

Therefore, 24% of glucose was hydrolyzed.

11. In the course of some first-order reaction, 60% of the initial amount of the substance is converted in 30 minutes. Determine how much of the substance remains after 1 hour.

1. After 30 minutes, the amount of the remaining substance will be:

C 1 \u003d C 0 - 0.6 C 0 \u003d 0.4 × C 0.

that is, the C 0 / C 1 ratio is 2.5.

2. Find the reaction rate constant:

3. The amount of substance C 2 remaining after 1 hour is determined by the formula:

Thus, after 1 hour, 16% of the original substance will remain.

Questions for self-control

1. What is called the rate of a chemical reaction?

2. What is called the true rate of a homogeneous reaction?

3. What is the dimension of the rate of a homogeneous reaction?

4. What is called the rate of a heterogeneous reaction?

5. What is the dimension of the rate of a heterogeneous reaction?

6. List the factors influencing the reaction rate.

7. Formulate the law of the masses at work.

8. What is the physical meaning of the reaction rate constant? What does the reaction rate constant depend on and what does it not depend on?

9. What is called the order of reaction? Give examples of reaction equations of the zero, first, second and third orders.

10. Does the dimension of the reaction rate constant depend on the order of the reaction?

11. What is called the molecularity of a reaction?

13. Define simple and complex reactions. Give the classification of complex reactions.

14. Formulate the Van't Hoff rule. Give a mathematical expression for the Van't Hoff rule.

15. How does the reaction rate depend on the activation energy? Write the Arrhenius equation.

16. What is an activated complex? Why do the reactions proceed through the stages of the formation of activated complexes?

17. What is called a catalyst? Homogeneous and heterogeneous catalysis. Why are reactions faster in the presence of catalysts?

18. What is enzymatic catalysis? Write the Michaelis-Menten equation.

Variants of tasks for independent solution

Option number 1

1. The reaction between substances A and B is expressed by the equation 2A + B \u003d C and has the second order in substance A and the first in substance B. The initial concentrations of substances are: C 0 (A) \u003d 0.4 mol / l; C 0 (B) \u003d 0.8 mol / l; k \u003d 0.6. Find the initial reaction rate and the rate after a certain time, when the concentration of substance A decreases by 0.2 mol / L.

2. How many degrees should the temperature be increased for the reaction rate to increase 64 times? The temperature coefficient of the reaction rate is equal to 2.

a) when the pressure in the system doubles?

b) when the volume of gases increases by 2 times?

Option number 2

1. The reaction proceeds according to the equation: A + B \u003d C and has the first order in substance A and in substance B. The concentration of A was increased from 2 to 8 mol / l, and the concentration of B from 3 to 9 mol / l. How many times has the speed of the direct reaction increased?

2. At 150 0 С, the reaction ends in 10 minutes. Taking the temperature coefficient g equal to 2, calculate how many minutes the reaction would have ended at 170 0 C.

3. The reaction rate is expressed by the equation: How many times will the reaction rate change with an increase in the concentration of the starting substances by 3 times?

Option number 3

1. The reaction is expressed by the equation: A + B \u003d C and has the first order in substance A and in substance B. At initial concentrations C 0 (A) \u003d 3 mol / l and C 0 (B) \u003d 5 mol / l, the rate of the direct reaction is equal to 0.3 mol / L × s. Determine the rate constant and the reaction rate after a while, when the concentration of A decreases by 2 mol / L.

2. How many times will the rate of a chemical reaction increase with an increase in temperature from 10 to 70 0 С, if the temperature coefficient of the rate g is equal to 2?

3. The reaction rate A (tv) + 2B (gas) \u003d \u200b\u200bC (tv) is expressed by the equation: How will the reaction rate change if the B concentration is doubled?

Option number 4

1. The reaction proceeds according to the equation: 2A + B \u003d 2C and has the second order in substance A and the first in substance B. Calculate the speed of the direct reaction at the moment when 40% of substance B reacts, if the initial concentrations are equal: C 0 (A) \u003d 8 mol / l; C 0 (B) \u003d 4 mol / l; k \u003d 0.4.

2. Some reaction at 100 0 C ends in 5 minutes. How long will it take to end at 80 0 С, if the temperature coefficient of the rate g is 3?

3. The reaction rate 3A + B \u003d C is expressed by the equation: How many times will the speed of the direct reaction change:

a) when the concentration of substance A is doubled?

b) while reducing the concentration of the starting substances by 2 times?

Option number 5

1. The rate of some reaction with an increase in temperature from 40 to 70 0 С has increased 8 times. Determine the value of g.

2. The reaction proceeds according to the equation: A + 3B \u003d 2C and has the first order in substance A and the second in substance B. The initial concentrations of substances are equal: C 0 (A) \u003d 2 mol / l; C 0 (B) \u003d 6 mol / l; k \u003d 1. Calculate the initial rate of the direct reaction and the rate at the moment when the concentration of substance A has decreased by 1 mol / L. How will the rate of a chemical reaction change?

3. How will the rates of the forward and reverse reactions that take place in the gas phase and obey the equations:

Option number 6

1. In a closed vessel there is a mixture of gases consisting of 1 mol A and 3 mol B, which reacts according to the equation: A + 3B \u003d 2C. The direct reaction rate is described by the equation How many times will the rate of the direct reaction decrease after 0.5 mol of A has reacted?

2. How many degrees should the temperature be increased for the reaction rate to increase 9 times if the temperature coefficient of the rate g is 3?

3. How will the rate of the direct gas-phase reaction change: 2A \u003d B, the order of which is estimated as 0.5, with an isothermal decrease in pressure in the system by a factor of 3?

Option number 7

1. The reaction between substances A and B proceeds according to the equation: A + 2B \u003d C and has the first order in substance A and in substance B. The initial concentrations of the reacting substances were: C 0 (A) \u003d 1.5 mol / l; C 0 (B) \u003d 3 mol / l; k \u003d 0.4. Calculate the rate of a chemical reaction at the initial moment of time and after a certain time, when 75% A reacts.

2. What is the temperature coefficient of the rate g, if with an increase in temperature by 30 0 С the reaction rate increases 27 times?

3. How will the rates of the forward and reverse reactions that take place in the gas phase and obey the equations:

with an isothermal increase in pressure by 2 times?

Option number 8

1. In a solution of 1 liter, containing 1 mol of substance A and 2 mol of substance B, the reaction proceeds: A + 3B \u003d 2C + D. The direct reaction has the first order in substance A and the second in substance B. How many times will the speed of the straight line decrease reaction after 0.65 mol of substance A have reacted?

2. When the temperature rises from -5 to +5 0 С, the rate of bacterial hydrolysis (enzymatic process) increases by 4 times. Find the value of the temperature coefficient of the reaction rate g.

3. How many times should the concentration of substance A in the system 2A (gas) \u003d \u200b\u200bB (gas) + C (tv.) Be increased so that the rate of the direct reaction, which is a second-order reaction, increases 4 times?

Option number 9

1. The reaction proceeds according to the equation: 2A + B \u003d 2C and has the second order in substance A and the first in substance B. The rate of the direct reaction is 8 mol / l × s. Calculate the rate constant and the rate of the direct reaction at the moment when 30% of substance B reacts, if the initial concentrations are equal: C 0 (A) \u003d 2 mol / l; C 0 (B) \u003d 1 mol / l. How will the rate of a chemical reaction change?

2. With an increase in temperature from 10 to 50 0 С, the reaction rate increased 16 times. Determine the temperature coefficient of speed g.

3. The reaction proceeds according to the equation: A + B \u003d C + D + E and has the first order in substance A and zero in substance B. How will the rate of the direct reaction change after diluting the reaction mixture by 3 times?

Option number 10

1. The reaction proceeds according to the equation: A + 2B \u003d AB 2 and has the first order in substance A and the second in substance B. The reaction rate constant is 0.01. Calculate the reaction rate at initial concentrations: C 0 (A) \u003d 0.8 mol / l; C 0 (B) \u003d 0.8 mol / l and the reaction rate by the time of formation of 0.2 mol / l of substance AB 2.

2. How many times will the rate of a chemical reaction increase when the temperature rises from 30 to 60 0 С, if the temperature coefficient of the rate g is 3?

3. The half-life of the drug from the patient's body (first-order reaction) is 6 hours. Determine how long the content of the drug in the human body will decrease by 8 times.

Option number 11

1. The reaction proceeds according to the equation: A + B \u003d 2C and has the first order in substance A and in substance B. The initial concentrations of substances are equal: C 0 (A) \u003d 0.3 mol / l; C 0 (B) \u003d 0.5 mol / l; k \u003d 0.1. Find the initial reaction rate and the reaction rate after a certain time, when the concentration of A decreases by 0.1 mol / L.

2. At 100 0 C some reaction ends in 16 minutes. Taking the temperature coefficient of the rate g equal to 2, calculate how many minutes the same reaction would have ended at 140 0 С?

3. The half-life of the drug from the patient's body (first-order reaction) is 2 hours. Determine the time during which 99% of the drug will be excreted from the body.

Option number 12

1. The reaction proceeds according to the equation: A + 2B \u003d C and has the first order in substance A and second in substance B. The initial concentrations of substances are equal: C 0 (A) \u003d 0.9 mol / l; C 0 (B) \u003d 1.5 mol / l; k \u003d 0.6. Find the initial reaction rate and the rate after a certain time, when 50% of substance A is consumed.

2. What is the temperature coefficient of the rate of a chemical reaction g , if with an increase in temperature by 30 0 С the speed increases by 27 times?

3. The half-life of some first-order reaction is 30 minutes. Calculate what part of the original amount will remain in 1 hour.

Option number 13

1. The reaction proceeds according to the equation: 2A + B \u003d 2C and is of the second order in substance A and the first in substance B. The reaction rate constant is 5 × 10 - 2. Calculate the reaction rate at initial concentrations C 0 (A) \u003d 0.4 mol / l; C 0 (B) \u003d 0.9 mol / L and the reaction rate by the time of formation of 0.1 mol of substance C.

2. At a temperature of 10 0 C, the reaction proceeds in 80 minutes. At what temperature will the reaction complete in 20 minutes if the temperature coefficient of the rate g is 2?

3. In the course of laboratory studies, it was found that the concentration of the drug in the patient's body per day decreased from 0.1 mol / l to 0.02 mol / l. Calculate the half-life of the drug, assuming that this is a first-order reaction.

Option number 14

1. In a closed vessel with a volume of 1 liter, there is a mixture of gases, consisting of 1 mol of gas A and 3 mol of gas B, which reacts according to the equation: A + 3B \u003d 2C. The direct reaction is first order in substance A and second in substance B. How will the rate of the direct reaction change after 0.5 mol of gas A has reacted?

2. With an increase in the temperature of the system from 10 to 50 0 С, the rate of the chemical reaction increased 16 times. Determine the temperature coefficient of the reaction rate g .

3. During the accident at the Chernobyl nuclear power plant (1986), the Cs-137 radionuclide was released, with a half-life of 30 years. Calculate how much of the radionuclide that has entered the body remains at the present time.

Option number 15

1. The reaction proceeds according to the equation: A + B \u003d C has the first order in substance A and in substance B. At initial concentrations of substances C 0 (A) \u003d 0.6 mol / l; With 0 (B) \u003d 0.8 mol / l, the reaction rate is 0.03 mol / l × s. Determine the rate constant and the reaction rate after a while, when the concentration of substance A decreases by 0.3 mol / L.

2. The reaction rate at 0 0 С is equal to 1 mol / l × s. Calculate the rate of this reaction at 30 0 С, if the temperature coefficient of the rate of reaction is 3.

3. The rate constant of pesticide hydrolysis at 25 0 С is equal to 0.32 s - 1. The initial concentration of the pesticide in the sample was 2.5 mol / L. Calculate how long it takes for the pesticide concentration to decrease to 0.01 mol / l.

Option number 16

1. The decomposition reaction proceeds according to the equation: 2A \u003d 2B + C and has the second order in substance A. The rate constant of this reaction at 200 0 С is equal to 0.05. Initial concentration C (A) \u003d 2 mol / L. Determine the reaction rate at the specified temperature at the initial moment and at the moment when 80% of substance A decomposes.

2. How will the rate of the direct reaction change: 2A (tv) + 3B (gas) \u003d \u200b\u200b2C (tv), which has a zero order in substance A and third in substance B, if the pressure in the system is increased by 3 times?

3. In the course of some first-order reaction, 20% of the initial amount of the substance is converted in 45 minutes. Determine how much of the substance will remain after 1.5 hours.

Option number 17

1. The interaction of gases proceeds according to the equation: A + 2B \u003d 2C and has the first order in substance A and second in substance B. The initial gas concentrations are equal: C 0 (A) \u003d 2 mol / l; C 0 (B) \u003d 4 mol / l; k \u003d 0.02. Calculate the speed of the direct reaction at the initial moment of time and after some time, when 50% of substance A has reacted.

2. At 20 0 С the reaction proceeds in 2 minutes. How long will the same reaction take at 0 0 С if g \u003d 2?

3. Formic acid decomposes into carbon monoxide (IV) and hydrogen on the gold surface. The rate constant of this reaction at 140 0 С is 5.5 × 10 - 4 min –1, and at 185 0 С it is 9.2 × 10 –3 min –1. Determine the activation energy of this reaction.

Option number 18

1. The reaction proceeds according to the equation: 2A + B \u003d 2C and has the first order in substance A and in substance B. The reaction rate is 0.5 mol / l × s. The initial concentrations of substances are: C (A) \u003d 6 mol / l; C (B) \u003d 3 mol / L. Determine the rate constant of this reaction and the reaction rate after a while, when the concentration of substance B decreases by 1 mol / L.

2. At 20 0 С the reaction proceeds in 2 minutes. How long will the same reaction take at 50 0 С, if g \u003d 2?

3. The rate constant of the cane sugar inversion reaction at 25 ° C is 9.67 × 10 - 3 min - 1, and at 40 ° C it is 73.4 × 10 - 3 min –1. Determine the activation energy of this reaction in the specified temperature range.

LESSON 10 10th grade (first year of study)

Fundamentals of Chemical Kinetics. Chemical equilibrium Plan

1. Chemical kinetics and the area of \u200b\u200bits study.

2. Rate of homogeneous and heterogeneous reaction.

3. Dependence of the reaction rate on various factors: the nature of the reactants, the concentration of the reactants (law of mass action), temperature (Van't Hoff's rule), catalyst.

4. Reversible and irreversible chemical reactions.

5. Chemical equilibrium and conditions for its displacement. Le Chatelier's principle.

The branch of chemistry that studies the rates and mechanisms of chemical reactions is called chemical kinetics. One of the main concepts in this section is the concept of the rate of a chemical reaction. Some chemical reactions occur almost instantaneously (for example, the reaction of neutralization in solution), others over the course of millennia (for example, the transformation of graphite into clay during the weathering of rocks).

The rate of a homogeneous reaction is the amount of a substance that enters into a reaction or is formed as a result of a reaction per unit time per unit volume of the system:

In other words, the rate of a homogeneous reaction is equal to the change in the molar concentration of any of the reacting substances per unit time. The reaction rate is a positive value, therefore, if it is expressed through a change in the concentration of the reaction product, a "+" sign is put, and when the concentration of the reagent changes, the "-" sign is put.

The rate of a heterogeneous reaction is the amount of a substance entering into a reaction or formed as a result of a reaction per unit of time per unit of phase surface:

The most important factors affecting the rate of a chemical reaction are the nature and concentration of reagents, temperature, and the presence of a catalyst.

Influence nature of reagents manifests itself in the fact that under the same conditions, different substances interact with each other at different rates, for example:

When increasing concentration of reagents the number of collisions between particles increases, which leads to an increase in the reaction rate. Quantitatively, the dependence of the reaction rate on the concentration of reagents is expressed in terms of the efficiency of the reaction (K.M. Guldberg and P. Waage, 1867; N.I. Beketov , 1865). The rate of a homogeneous chemical reaction at constant temperature is directly proportional to the product of the concentration of the reacting substances in powers equal to their stoichiometric coefficients (the concentration of solids is not taken into account in this case), for example:

where A and B are gases or liquids, k - a reaction rate constant equal to the reaction rate at a reactant concentration of 1 mol / l. Constant k depends on the properties of the reacting substances and temperature, but does not depend on the concentration of substances.

The dependence of the reaction rate on temperature described by the experimental rule of W ant-Goffa (1884). When the temperature rises by 10 °, the rate of most chemical reactions increases by 2-4 times:

where is the temperature coefficient.

Catalyst is called a substance that changes the rate of a chemical reaction, but is not consumed as a result of this reaction. Distinguish between positive catalysts (specific and universal), negative (inhibitors) and biological (enzymes, or enzymes). The change in the reaction rate in the presence of catalysts is called catalysis... Distinguish between homogeneous and heterogeneous catalysis. If the reactants and the catalyst are in the same state of aggregation, the catalysis is homogeneous; in different - heterogeneous.

Homogeneous catalysis:

heterogeneous catalysis:

The mechanism of action of catalysts is very complex and not fully understood. There is a hypothesis about the formation of intermediate compounds between the reagent and the catalyst:

A + cat. ,

In AB + cat.

To enhance the action of catalysts, promoters are used; there are also catalytic poisons that weaken the effect of catalysts.

The rate of a heterogeneous reaction is influenced by interface size (the degree of fineness of the substance) and the rate of supply of reagents and removal of reaction products from the interface.

All chemical reactions are divided into two types: reversible and irreversible.

Chemical reactions occurring in only one direction are called irreversible., i.e. the products of these reactions do not interact with each other to form the starting materials. The conditions for the irreversibility of the reaction are the formation of a precipitate, gas or a weak electrolyte. For instance:

BaCl 2 + H 2 SO 4 \u003d BaSO 4 + 2HCl,

K 2 S + 2HCl \u003d 2KCl + H 2 S,

HCl + NaOH \u003d NaCl + H 2 O.

Reversible reactions are reactions that occur simultaneously in the forward and reverse directions., eg:

When a reversible chemical reaction proceeds, the rate of the direct reaction first has a maximum value, and then decreases due to a decrease in the concentration of the starting substances. The reverse reaction, on the contrary, at the initial moment of time has a minimum speed, which gradually increases. Thus, at a certain point in time, state of chemical equilibrium, at which the rate of the forward reaction is equal to the rate of the reverse reaction. The state of chemical equilibrium is dynamic - both direct and reverse reactions continue to proceed, but since their rates are equal, the concentrations of all substances in the reaction system do not change. These concentrations are called equilibrium.

The ratio of the rate constants of the forward and reverse reactions is a constant and is called the equilibrium constant ( TO r ) ... Solid concentrations are not included in the expression for the equilibrium constant. The equilibrium constant of the reaction depends on temperature and pressure, but does not depend on the concentration of the reactants and on the presence of a catalyst, which accelerates both the forward and reverse reactions. The more TOp, the higher the practical yield of the reaction products. If a TO p\u003e 1, then the reaction products prevail in the system; if a TO R< 1, в системе преобладают реагенты.

Chemical equilibrium is mobile, i.e. when the external conditions change, the speed of the forward or reverse reaction can increase. The direction of the displacement of the equilibrium is determined by the principle formulated by the French scientist Le Chatelier in 1884. If an external influence is exerted on the equilibrium system, then the equilibrium is shifted towards the reaction that counteracts this influence. The shift in equilibrium is affected by changes in the concentration of reagents, temperature and pressure.

An increase in the concentration of reagents and the withdrawal of products lead to a shift in equilibrium towards the direct reaction.

When the system is heated, the equilibrium shifts towards the endothermic reaction, while cooling - towards the exothermic one.

For reactions in which gaseous substances take part, an increase in pressure shifts the equilibrium towards a reaction proceeding with a decrease in the number of gas molecules. If the reaction proceeds without changing the number of molecules of gaseous substances, then the change in pressure does not in any way affect the displacement of equilibrium.

Test questions and tasks

1. The speed of chemical reactions, the difference between the average speed and the instant.

2. Write down the mathematical expression for the law of mass action for chemical reactions:

2A + B \u003d A 2 B

4Fe + 3O 2 \u003d 2Fe 2 O 3

3. Dependence of the rate of a chemical reaction on the nature of the reacting substances, on temperature. Van't Hoff's law, Arrhenius equation. Homogeneous and heterogeneous catalysis. Examples. The mechanism of action of the catalyst. Activation energy of a chemical reaction.

4. The rate constant of the reaction A + 2B \u003d AB 2 is equal to 2 10 -3 l / (mol s). Calculate its rate at the initial moment, when C A \u003d C B \u003d 0.4 mol / l and after a while. At this point, the concentration of the substance AB 2 was 0.1 mol / l.

5. combustion of methane in oxygen, if the oxygen concentration is increased by 5 times?

6. The chemical reaction proceeds according to the equation A + B \u003d C. At the initial moment of time, C A \u003d 2.7 mol / l, C B \u003d 2.5 mol / l. After 0.5 hour, the concentration of substance A decreased and became equal to C A \u003d 2.5 mol / l. Calculate the concentration of substances B and C at this moment and the average speed in the specified period of time.

7. How many times should the pressure be increased to increase the rate of the chemical reaction 2NO 2 + O 2 \u003d 2NO 2 1000 times?

8. How many times will the rate of a chemical reaction change with a decrease in temperature from 70 to 30 0 С, if the temperature coefficient is 3.

9. How many degrees do you need to raise the temperature for the rate of chemical reaction to increase 81 times? The temperature coefficient of the reaction rate is 3?

10. Calculate the temperature coefficient of a certain chemical reaction, if the rate of the chemical reaction increased 16 times with an increase in temperature from 10 to 50 0 С.

Examples of assignments

Example 1. Write a mathematical expression for the law of mass action for the following chemical reactions:

Answer. For reaction (1), the rate depends only on the concentration of SO 2, for reaction (2) - only on the concentration of H 2.

Example 2.How the rate of a chemical reaction will change

4Al (c) + 3O 2 (g) \u003d 2Al 2 O 3 (c),

if the oxygen concentration is increased by 3 times?

Decision

1. We write down the expression for the dependence of the rate of a chemical reaction on the concentration of reactants: V 1 \u003d k 3.

2. With an increase in the oxygen concentration by 3 times, the rate of the chemical reaction increases: V 2 \u003d k 3.

V 2 / V 1 \u003d ¾¾¾¾¾¾¾¾ \u003d 27

Answer.With an increase in the oxygen concentration by 3 times, the rate of the chemical reaction increases by 27 times.

Example 3.How the rate of a chemical reaction will change

2Al (q) + 3Cl 2 (g) \u003d 2AlCl 3 (q)

when the pressure increases 2 times?

Decision.

1. We write down the expression for the dependence of the rate of a chemical reaction on the concentration of reactants: V 1 \u003d k 3.

2. When the pressure is increased by 2 times, the chlorine concentration also increases by 2 times. Therefore, V 2 \u003d k 3.

3. The change in the rate of a chemical reaction is

V 2 / V 1 \u003d ¾¾¾¾¾¾¾ \u003d 8

Answer.When the pressure increases by 2 times, the rate of this chemical reaction increases by 8 times.

Example 4. The temperature coefficient of the rate of a chemical reaction is 2.5. How will its rate change a) with an increase in the temperature of the reaction mixture from 60 to 100 about C; b) when the temperature drops from 50 to 30 o C.

Decision

1. The dependence of the rate of a chemical reaction on temperature is determined by the Van't Hoff rule. Its mathematical expression:

V 2 \u003d V 1 γ (t2 - t1) / 10.

Therefore, a) V 2 / V 1 \u003d 2.5 (100-60) / 10 \u003d 2.5 4 \u003d 39.06;

b) V 2 / V 1 \u003d 2.5 (30-50) / 10 \u003d 2.5 -2 \u003d 1 / 6.25 \u003d 0.16.

Answer. When the temperature rises by 40 o, the rate of this reaction increases 39.06 times, when the temperature drops by 20 o, the rate of the chemical reaction decreases by 6.25 times and is only 0.16 of the rate of the chemical reaction at 50 o C.

Theme. Chemical equilibrium

Test questions and tasks

1. Reversible and irreversible chemical reactions. Give examples. The main signs of irreversible reactions. False chemical equilibrium.

2. The law of mass action for reversible chemical reactions. The physical meaning of the constant of chemical equilibrium.

3. Write down the expression for the chemical equilibrium constant for the following chemical reactions:

3Fe (c) + 4H 2 O (g) Fe 3 O 4 (c) + 4H 2 (g)

CaO (c) + CO 2 (g) CaCO 3 (c)

Ca (c) + C (c) + 3 / 2O 2 (g) CaCO 3 (c)

4. Le Chatelier's principle. Give examples.

5. How does an increase in pressure affect a shift in chemical equilibrium in the following reactions:

H 2 (g) + J 2 (g) 2HJ (g)

CO (g) + Cl 2 (g) COCl 2 (g)

2NO (g) + O 2 (g) 2NO 2 (g)

C (q) + CO 2 (g) 2CO (g)

6. In the direction of the direct or reverse reaction, the chemical equilibrium will shift in the following reactions with decreasing temperature:

2H 2 S (g) + 3O 2 (g) 2SO 2 (g) + 2H 2 O (g) DH< 0

2N 2 (g) + O 2 (g) 2N 2 O (g) DH\u003e 0

2SO 2 (g) + O 2 (g) 2SO 3 (g) + 192.74 kJ

N 2 O 4 (g) 2NO 2 (g) - 54.47 kJ

7. What factors can be used to shift the chemical equilibrium towards a direct reaction:

C (c) + H 2 O (g) CO (g) + H 2 (g) - 129.89 kJ

N 2 (g) + 3H 2 (g) 2NH 3 (g) DH< 0

8. Chemical equilibrium in the reaction 2SO 2 (g) + O 2 (g) \u003d 2SO 3 (g) was established at the following concentrations of reactants: \u003d 0.2 mol / l, \u003d 0.05 mol / l, \u003d 0.09 mol / l. How will the rate of the forward reaction change, the rate of the reverse reaction, if the volume of the gas mixture is reduced by 3 times?

9. Calculate the equilibrium concentration of hydrogen and chlorine in the chemical reaction: H 2 (g) + Cl 2 (g) \u003d 2HCl (g), if the initial concentration C (H 2) \u003d 0.5 mol / l, C (Cl 2) \u003d 1.5 mol / l, and the equilibrium concentration of hydrogen chloride \u003d 0.8 mol / l. Calculate the chemical equilibrium constant.

10. At a certain temperature, the composition of the equilibrium mixture is as follows: m (CO) \u003d 11.2 g, m (Cl 2) \u003d 14.2 g, m (COCl 2) \u003d 19.8 g, its volume is 10 liters. Calculate the equilibrium constant of the chemical reaction CO (g) + Cl 2 (g) COCl 2 (g)

Examples of assignments

Example 1.Write the mathematical expression for the chemical equilibrium constant of the reaction Ca 3 N 2 (k) + 6H 2 O (g) \u003d 3Ca (OH) 2 (k) + 2NH 3 (g).

Decision.The mathematical expression for the constant of chemical equilibrium (the law of mass action for reversible reactions) does not take into account the participation of substances in the solid and liquid phases. Hence,

Answer. The equilibrium constant is determined by the ratio of the equilibrium concentrations of ammonia and water in the gas phase.

Example 2. For the reaction CoO (k) + CO (g) \u003d Co (k) + CO 2 (g), calculate the constant of chemical equilibrium, if 80% CO has reacted by the moment of equilibrium, the initial concentration of CO is 1.88 mol / L.

Decision

1. Mathematical expression for the constant of chemical equilibrium Kc \u003d /.

2. Equilibrium concentrations of CO and CO 2. The equilibrium concentration of CO will be less than the initial one (part of the substance - 80% - entered into a chemical reaction:

[CO] \u003d C (CO) ref. - C (CO) proreag. \u003d 1.88 - (1.88 80) / 100 \u003d

0.376 mol / L.

The equilibrium concentration of CO 2 is equal to:

[CO 2] \u003d C (CO) reaction \u003d (1.88 · 80) / 100 \u003d 1.504 mol / l.

3. In the mathematical expression for the constant of chemical equilibrium, we substitute the values \u200b\u200bof the equilibrium concentrations of CO and CO 2:

Kc \u003d 1.504 / 0.376 \u003d 4.

Answer. The chemical equilibrium constant for this reaction is 4; which indicates that at this moment in time the rate of the forward reaction is 4 times higher than the rate of the reverse reaction.

Example 3.In which direction will the chemical equilibrium of the reaction 2NiO (к) + CO 2 (g) + H 2 O (g) \u003d (NiOH) 2 CO 3 (к) DH o< 0

a) with increasing pressure, b) with increasing temperature? Suggest the optimal change in the thermodynamic parameters T and P to increase the yield of the reaction product.

Decision

1. In accordance with the Le Chatelier principle, an increase in pressure shifts the equilibrium of a chemical reaction in the direction that is accompanied by a decrease in the volume of the reaction system. With increasing pressure, the equilibrium of this reaction shifts to the right (the rate of the forward reaction is higher than that of the reverse one).

2. In accordance with Le Chatelier's principle, an increase in temperature shifts the chemical equilibrium towards an endothermic reaction. Consequently, with increasing temperature, the equilibrium of this reaction shifts to the left (the rate of the reverse reaction is higher than that of the direct one).

3. To increase the yield of the product of the chemical reaction of formation of nickel (II) hydroxycarbonate, increase the pressure and decrease the temperature.

Example 4.Write an expression for the chemical equilibrium constant of a reaction:

MgO (c) + H 2 (g) \u003d Mg (c) + H 2 O (g).

Does increasing pressure affect chemical equilibrium shift?

Decision. For heterogeneous reactions in the expression for the speed.

Rate of chemical reactions The branch of chemistry that studies the rate and mechanism of chemical reactions is called chemical kinetics. The rate of a chemical reaction is the number of elementary acts of interaction per unit time in a unit of reaction space. This definition is valid for both homogeneous and heterogeneous processes. In the first case, the reaction space is the volume of the reaction vessel, and in the second, the surface on which the reaction takes place. Since the interaction changes the concentration of reagents or reaction products per unit time. In this case, there is no need to monitor the change in the concentration of all substances participating in the reaction, since its stoichiometric equation establishes the relationship between the concentrations of the reactants. The concentration of reactants is most often expressed by the number of moles in 1 liter (mol / l). The rate of a chemical reaction depends on the nature of the reacting substances, concentration, temperature, the size of the contact surface of the substances, the presence of catalysts and others. , and talk about a monomolecular reaction; when a collision of two different molecules occurs in an elementary act, the dependence has the following form: u - to [A] [B], and they speak of a bimolecular reaction; when in an elementary act there is a collision of three molecules, for the dependence of the velocity on the concentration it is true: v - to [A] [B] [C], and they speak of a trimolecular reaction. In all analyzed dependencies: v - reaction rate; [A], [B], [C] - the concentration of reactants; k - coefficient of proportionality; called the reaction rate constant. v \u003d k, when the concentrations of reactants or their product are equal to one. The rate constant depends on the nature of the reactants and on temperature. The dependence of the rate of simple reactions (i.e., reactions proceeding through one elementary act) on concentration is described by the law of mass action established by K. Guldberg and P. Waage in 1867: the rate of a chemical reaction is directly proportional to the product of the concentration of reactants raised to the power their stoichiometric coefficients. For example, for the reaction 2NO + 02 \u003d 2N02; v - k2 and will increase three times Find: Solution: 1) Write down the reaction equation: 2СО + 02 \u003d 2С02. According to the law of mass action, v is k [C0] 2. 2) We denote [CO] \u003d a; \u003d B, then: v \u003d k a2 b. 3) With an increase in the concentration of the starting substances in 3 times we get: [CO] \u003d 3a, a \u003d 3b. 4) We calculate the reaction rate u1: - k9a23b - k27a% a if k27 D2b 27 v to a2b Answer: 27 times. Example 3 How many times will the rate of a chemical reaction increase with an increase in temperature by 40 ° C, if the temperature coefficient of the rate of reaction is equal to 3? Given: At \u003d 40 ° С Y - 3 Find: 2 Solution: 1) According to the van't Hoff rule: h-U vt2 \u003d vh у 10, 40 and, - vt\u003e 3 10 - vt -81. 2 1 1 Answer: 81 times. a Example 4 The reaction between substances A and B proceeds according to the scheme 2A + B * »C. The concentration of substance A is 10 mol / l, and of substance B - 6 mol / l. The reaction rate constant is 0.8 L2 4 mol "2 sec" 1. Calculate the rate of the chemical reaction at the initial moment, as well as at the moment when 60% of substance B remains in the reaction mixture. Given: k - 0.8 l2 mol "2 sec" 1 [A] \u003d 10 mol / l [B] \u003d 6 mol / l Find: "start! ^ Solution: 1) Find the reaction rate at the initial moment: v - k [A] 2 [B], r\u003e \u003d 0.8 102 b - 480 mol - l sec" 1. start 2) After some time, 60% of substance B will remain in the reaction mixture. Then: Therefore, [B] decreased by: 6 - 3.6 \u003d 2.4 mol / l. 3) It follows from the reaction equation that substances A and B interact with each other in a ratio of 2: 1, therefore [A] decreased by 4.8 mol / l and became equal to: [A] \u003d 10 - 4.8 \u003d 5.2 mol / l. 4) We calculate if: d) \u003d 0.8 * 5.22 3.6 \u003d 77.9 mol l "1 * sec" 1. Answer: r\u003e start ~ 480 mol l sec "1, g / \u003d 77.9 mol l-1 sec" 1. Example 5 The reaction at a temperature of 30 ° C proceeds in 2 minutes. How long does this reaction take at a temperature of 60 ° C if the temperature coefficient of the reaction rate is 2 in a given temperature range? Given: t1 \u003d 30 ° С t2 \u003d 60 ° С 7 \u003d 2 t \u003d 2 min \u003d 120 sec Find: h Solution: 1) In accordance with the Van't Hoff rule: vt - \u003d у ω 1 vt - \u003d 23 \u003d 8. Vt 2) The reaction speed is inversely proportional to the reaction time, therefore: Answer: t \u003d 15 sec. Questions and tasks for independent solution 1. Give the definition of the reaction rate. Give examples of reactions going at different rates. 2. The expression for the true rate of a chemical reaction proceeding at a constant volume of the system is written as follows: dC v \u003d ± -. d t Indicate in which cases positive and negative signs are required on the right side of the expression. 3. What factors determine the rate of a chemical reaction? 4. What is called activation energy? The influence of which factor on the rate of a chemical reaction does it characterize? 5. What explains the strong increase in the reaction rate with increasing temperature? 6. Give a definition to the basic law of chemical kinetics - the law of mass action. By whom and when was it formulated? 7. What is called the rate constant of a chemical reaction and what factors does it depend on? 8. What is a catalyst and how does it affect the rate of a chemical reaction? 9. Give examples of processes that use inhibitors. 10. What are promoters and where are they used? 11. What substances are called "catalytic poisons"? Give examples of such substances. 12. What is homogeneous and heterogeneous catalysis? Give examples of processes using their catalytic processes. 13. How will the reaction rate 2С0 + 02 \u003d 2С02 change, if the volume of the gas mixture is reduced by 2 times? 14. How many times will the rate of a chemical reaction increase with an increase in temperature from 10 ° C to 40 ° C, if it is known that with an increase in temperature by 10 ° C, the reaction rate will double? 15. The rate of reaction A + B \u003d C increases threefold with an increase in temperature for every 10 ° C. How many times will the reaction rate increase when the temperature rises by 50 ° C? 16. How many times will the reaction rate of the interaction of hydrogen and bromine increase if the concentration of the initial substances is increased by 4 times? 17. How many times will the reaction rate increase when the temperature rises by 40 ° C (y \u003d 2)? 18. How will the reaction rate of 2NO + 02 ^ 2N02 change if the pressure in the system is doubled? 19. How many times should the hydrogen concentration in the N2 + 3H2 ^ 2NH3 system be increased for the reaction rate to increase 125 times? 20. The reaction between nitrogen oxide (II) and chlorine proceeds according to the equation 2NO + C12 2NOC1; How will the reaction rate change with an increase in: a) the concentration of nitric oxide by two times; b) the concentration of chlorine is twice; c) the concentration of both substances is twice? ... 21. At 150 ° C, some reaction ends in 16 minutes. Taking the temperature coefficient equal to 2.5, calculate after what period of time the same reaction will end at 80 ° C. 22. How many degrees should the temperature be increased in order for the reaction rate to increase 32 times. The temperature coefficient of the reaction rate is 2. 23. At 30 ° C, the reaction proceeds in 3 minutes. How long will the same reaction take at 50 ° C, if the temperature coefficient of the reaction rate is 3. 24. At a temperature of 40 ° C, the reaction proceeds in 36 minutes, and at 60 ° C - in 4 minutes. Calculate the temperature coefficient of the reaction rate. 25. The reaction rate at 10 ° C is 2 mol / L. Calculate the rate of this reaction at 50 ° C if the temperature coefficient of the rate of reaction is 2.