1. Gas A was mixed in a vessel with a quantity of substance 4.5 mol and gas B with a quantity of substance 3 mol. Gases A and B react in accordance with the equation A + B \u003d C. After some time, gas C was formed in the system with a substance of 2 mol. What quantities of unreacted gases A and B remained in the system?
It follows from the reaction equation that:
Dn(A) = Dn(B) = Dn(C) = 2 mol,
where Dn is the change in the amount of a substance during the reaction.
Therefore, in the vessel remains:
n 2 (A) = n 1 (A) - Dn(A); n 2 (A) \u003d (4.5 - 2) mol \u003d 2.5 mol;
n 2 (B) = 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 for substance A and the first for substance B. At the initial moment of 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: С(A) = 10 mol/l; C(B) = 5 mol/l. How will the rate of a chemical reaction change?
С(B), which has entered into the reaction, is equal to:
C(B) \u003d 0.5 5 \u003d 2.5 mol / l.
Accordingly, C(A), which has entered into the reaction, 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 rate of the direct reaction will be:
The rate of a chemical reaction will change:
i.e., 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 for substance A and the second for substance B. The initial concentrations of substances are: C (A) \u003d 2 mol / l; C(B) = 4 mol/l; the rate constant is 1.0. Find the initial rate of the reaction and the rate after some 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 = 0.6 mol/l. After the reaction, 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 mass action, the rates of forward and reverse reactions at initial conditions are equal:
An increase in pressure by a factor of 3 for gaseous systems leads to a decrease in the volume of the gas mixture by a factor of 3, the concentrations 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 rate of the forward reaction will increase by 27 times, the reverse - by 9.
5. The reaction at a temperature of 50 0 C proceeds in 2 minutes 15 seconds. How long will it take for this reaction to end at a temperature of 70 0 C, if the temperature coefficient of the rate g is 3 in this temperature range?
With an increase in temperature from 50 to 70 0 C, the reaction rate increases in accordance with the van't Hoff rule:
Where = 70 0 C, \u003d 50 0 С, a and - reaction rates at given temperatures.
We get:
those. the reaction rate increases by 9 times.
According to the definition, the reaction time is inversely proportional to the rate of the reaction, therefore:
where and is the reaction time at temperatures And .
From here we get:
Given that = 135 s (2 min 15 s), we determine the reaction time at a temperature :
6. How many times will the rate of a chemical reaction increase with an increase in temperature from = 10 0 C to = 80 0 С , if the temperature coefficient of speed g is equal to 2?
From the van't Hoff rule:
The reaction rate will increase 128 times.
7. When studying the kinetics of excretion medicinal product from the patient's body, it was found that in 3 hours 50% of the original amount remained in the patient's body medicinal product. Determine the half-life and rate constant of the elimination reaction of the drug from the human body, if it is known that this is a first-order reaction.
Since for a given period of time 50% of the drug was removed from the body, then t 1/2 = 3 hours. We calculate the reaction rate constant 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 hydrolysis reaction of the drug.
Since hydrolysis reactions usually proceed with a significant excess of water, its concentration can be constant. Consequently, only the concentration of the drug changes during the reaction, and the hydrolysis reaction can be considered a first-order reaction.
We find the value of the reaction rate constant 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 removed from the body.
With the removal of 75% of the drug 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 undergoes hydrolysis;
3) what part of glucose will undergo hydrolysis after 5 days.
1. The half-life is:
2. After 20% of sucrose has undergone hydrolysis, the C/C 0 ratio will be 0.8. Hence:
3. After 5 days (120 hours), the C / C 0 ratio will be:
Consequently, 24% of glucose underwent hydrolysis.
11. In the course of some first-order reaction, 60% of the initial amount of the substance is converted in 30 minutes. Determine what part of the substance will remain 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.
i.e., 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 that affect the reaction rate.
7. Formulate the law of mass action.
8. What is the physical meaning of the reaction rate constant? What does the rate constant of a reaction depend on and what does it not depend on?
9. What is called the reaction order? Give examples of reaction equations of 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 the reaction?
13. Define simple and complex reactions. Give a 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 reactions proceed through the stages of formation activated complexes?
17. What is called a catalyst? Homogeneous and heterogeneous catalysis. Why do reactions proceed 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 for substance A and the first for 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 = 0.6. Find the initial rate of the reaction and the rate after some time, when the concentration of substance A decreases by 0.2 mol/l.
2. By how many degrees should the temperature be raised so that the reaction rate increases by 64 times? The temperature coefficient of the reaction rate g is 2.
a) when the pressure in the system doubles?
b) with an increase in the volume of gases by 2 times?
Option number 2
1. The reaction proceeds according to the equation: A + B = 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. By how much did the rate of the forward reaction increase?
2. At 150 0 C, 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 when the concentration of the starting substances is increased 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 equal to 0.3 mol/l×s. Determine the rate constant and the reaction rate after some time, 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 C, if the temperature coefficient of the rate g is 2?
3. The reaction rate A (tv) + 2B (gas) = C (tv) is expressed by the equation: 
How will the reaction rate change if the concentration of B is doubled?
Option number 4
1. The reaction proceeds according to the equation: 2A + B = 2C and has the second order for substance A and the first for substance B. Calculate the rate of the direct reaction at the moment when 40% of substance B reacts if the initial concentrations are: C 0 (A) = 8 mol/l; C 0 (B) = 4 mol/l; k = 0.4.
2. Some reaction at 100 0 C ends in 5 minutes. How long will it take to end at 80 0 C if the temperature coefficient of velocity g is 3?
3. The reaction rate 3A + B = C is expressed by the equation: 
How many times will the rate of the direct reaction change?
a) when the concentration of substance A is doubled?
b) with a simultaneous decrease in the concentration of the starting substances by 2 times?
Option number 5
1. The rate of a certain reaction with an increase in temperature from 40 to 70 0 C increased by 8 times. Determine the value of g.
2. The reaction proceeds according to the equation: A + 3B \u003d 2C and has the first order for substance A and the second for substance B. The initial concentrations of substances are: C 0 (A) \u003d 2 mol / l; C 0 (B) = 6 mol/l; k = 1. Calculate the initial rate of the forward reaction and the rate at the moment when the concentration of substance A decreased by 1 mol/l. How will the rate of a chemical reaction change?
3. How will the rates of direct and reverse reactions occurring in the gas phase and obeying the equations change:
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 = 2C. The rate of the direct reaction is described by the equation 
How many times will the rate of the direct reaction decrease after 0.5 mol A has reacted?
2. By how many degrees should the temperature be increased so that the reaction rate increases by 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 = B, the order of which is estimated as 0.5, with an isothermal decrease in pressure in the system by 3 times?
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) = 3 mol/l; k = 0.4. Calculate the rate of a chemical reaction at the initial moment of time and after some time, when 75% A has reacted.
2. What is the temperature coefficient of the rate g if, with an increase in temperature by 30 0 C, the reaction rate increases by 27 times?
3. How will the rates of direct and reverse reactions occurring in the gas phase and obeying the equations change:
with an isothermal increase in pressure by 2 times?
Option number 8
1. In a 1 liter solution 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 direct decrease reaction after 0.65 mol of substance A?
2. When the temperature rises from -5 to +5 0 C, 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 be increased in the system 2A (gas) \u003d B (gas) + C (solid) so that the rate of the direct reaction, which is a second-order reaction, increases by 4 times?
Option number 9
1. The reaction proceeds according to the equation: 2A + B = 2C and has the second order for substance A and the first for 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: C 0 (A) = 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 C, the reaction rate increased by 16 times. Determine the temperature coefficient of velocity g.
3. The reaction proceeds according to the equation: A + B = C + D + E and has the first order for substance A and zero for substance B. How will the rate of the direct reaction change after diluting the reacting 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) = 0.8 mol/l; C 0 (B) \u003d 0.8 mol / l and the reaction rate at 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 with an increase in temperature from 30 to 60 0 C, 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 the time for which 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: C 0 (A) \u003d 0.3 mol / l; C 0 (B) \u003d 0.5 mol / l; k = 0.1. Find the initial reaction rate and the reaction rate after some time, when the concentration 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 in how many minutes the same reaction would have ended at 140 0 C?
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 removed from the body.
Option number 12
1. The reaction proceeds according to the equation: A + 2B \u003d C and has the first order for substance A and the second for substance B. The initial concentrations of substances are: C 0 (A) \u003d 0.9 mol / l; C 0 (B) \u003d 1.5 mol / l; k = 0.6. Find the initial rate of the reaction and the rate after some time, when 50% of substance A has been consumed.
2. What is the temperature coefficient of the chemical reaction rate g , if with an increase in temperature by 30 0 C, 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 after 1 hour.
Option number 13
1. The reaction proceeds according to the equation: 2A + B = 2C and has the second order for substance A and the first for substance B. The reaction rate constant is 5 × 10 - 2. Calculate the reaction rate at initial concentrations C 0 (A) = 0.4 mol/l; C 0 (B) \u003d 0.9 mol / l and the reaction rate by the time 0.1 mol of substance C is formed.
2. At a temperature of 10 0 C, the reaction proceeds in 80 minutes. At what temperature will the reaction be completed in 20 minutes if the temperature coefficient of the rate g is 2?
3. In the course of laboratory studies, it was found that during the day the concentration of the drug in the patient's body decreased from 0.1 mol/l to 0.02 mol/l. Calculate the half-life of the drug, assuming that this reaction is of the first order.
Option number 14
1. In a closed vessel with a volume of 1 l 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 = 2C. The direct reaction has the first order in substance A and the 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 C, the rate of the chemical reaction increased by 16 times. Determine the temperature coefficient of the reaction rate g .
3. During the accident at the Chernobyl nuclear power plant (1986), the radionuclide Cs-137 was released, the half-life of which is 30 years. Calculate what part of the radionuclide that has entered the body has remained 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; C 0 (B) = 0.8 mol/l, the reaction rate is 0.03 mol/l×s. Determine the rate constant and the reaction rate after some time, when the concentration of substance A decreases by 0.3 mol/l.
2. The reaction rate at 0 0 C is 1 mol/l×s. Calculate the rate of this reaction at 30 0 C if the temperature coefficient of the reaction rate is 3.
3. The rate constant of pesticide hydrolysis at 25 0 C is 0.32 s - 1 . The initial concentration of the pesticide in the sample was 2.5 mol/L. Calculate the time it takes for the pesticide concentration to drop 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 C is 0.05. Initial concentration С(A) = 2 mol/l. Determine the reaction rate at the indicated temperature at the initial moment and at the moment when 80% of substance A has decomposed.
2. How will the rate of the direct reaction change: 2A (tv) + 3B (gas) \u003d 2C (tv), which has the zero order for substance A and the third for 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 undergoes transformation in 45 minutes. Determine what part 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 terms of substance A and the second in terms of substance B. The initial concentrations of gases are: C 0 (A) \u003d 2 mol / l; C 0 (B) = 4 mol/l; k = 0.02. Calculate the rate 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 C, the reaction proceeds in 2 minutes. How long will the same reaction take at 0 0 C if g = 2?
3. Formic acid decomposes into carbon monoxide (IV) and hydrogen on the surface of gold. The rate constant of this reaction at 140 0 C is 5.5×10 - 4 min -1 , and at 185 0 C 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 = 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 equal: С(A) = 6 mol/l; C(B) = 3 mol/l. Determine the rate constant of this reaction and the rate of the reaction after some time, when the concentration of substance B decreases by 1 mol/l.
2. At 20 0 C, the reaction proceeds in 2 minutes. How long will the same reaction take at 50 0 C if g = 2?
3. The rate constant of the cane sugar inversion reaction at 25 0 C is 9.67×10 - 3 min - 1 , and at 40 0 C it is 73.4 × 10 - 3 min -1 . Determine the activation energy of this reaction in the specified temperature range.
Speed 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 of 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 case, the surface on which the reaction takes place. Since during the interaction the concentrations of reactants or reaction products change per unit of 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 ratio between the concentrations of the reagents. The concentration of the reactants is most often expressed as 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 speak of a monomolecular reaction; when two different molecules collide in an elementary act, the dependence has the following form: u - k[A][B], and one speaks of a bimolecular reaction; when three molecules collide in an elementary act, the dependence of the velocity on concentration is true: v - k[A] [B] [C], and one speaks of a trimolecular reaction. In all analyzed dependencies: v is the reaction rate; [A], [B], [C] - concentrations of reactants; k - coefficient of proportionality; called the rate constant of the reaction. v = k when the concentrations of the reactants or their product are equal to one. The rate constant depends on the nature of the reactants and on the temperature. The dependence of the rate of simple reactions (i.e., reactions occurring 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 reacting substances raised to the power their stoichiometric coefficients. For example, for the reaction 2NO + 02 = 2N02; v - k2 and will increase three times Find: Solution: 1) Write the reaction equation: 2CO + 02 = 2CO2. According to the law of mass action, v - k[C0]2. 2) Denote [CO] = a; = b, then: v = k a2 b. 3) With an increase in the concentration of the starting substances by a factor of 3, we get: [CO] = 3a, a = 3b. 4) Calculate the reaction rate u1: - k9a23b - k27a% a if k27 D2b 27 v k 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 reaction rate is 3? Given: At \u003d 40 ° С Y - 3 Find: 2 Solution: 1) According to the van't Hoff rule: h-U vt2 \u003d vh y 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 substance B - b mol / l. The reaction rate constant is 0.8 l2 4 mol "2 sec"1. Calculate the rate of a 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] = 10 mol / l [B] = 6 mol / l Find: "beginning! ^ Solution: 1) Find the reaction rate at the initial moment: v - k [A] 2 [B], r> \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 = 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>beginning ~ 480 mol l sec "1, r / \u003d 77.9 mol l-1 sec" 1. Example 5 The reaction at a temperature of 30 °C proceeds in 2 minutes. How long will it take for this reaction to end at a temperature of 60 ° C, if in a given temperature range the temperature coefficient of the reaction rate is 2? 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 y u 1 vt - \u003d 23 \u003d 8. Vt 2) The reaction rate is inversely proportional to the reaction time, therefore: Answer: t=15sec. Questions and tasks for independent solution 1. Define the reaction rate. Give examples of reactions proceeding at different rates. 2. The expression for the true rate of a chemical reaction occurring at a constant volume of the system is written as follows: dC v = ±--. d t Indicate in which cases positive and in which negative signs are needed on the right side of the expression. 3. What factors determine the rate of a chemical reaction? 4. What is called the activation energy? What factor influences the rate of a chemical reaction? 5. What explains the strong increase in the reaction rate with increasing temperature? 6. Define 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 2CO + 02 = 2CO2 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 increase by 2 times? 15. The rate of the reaction A + B \u003d C with an increase in temperature for every 10 ° C increases three times. By 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 concentrations of the starting substances are increased by 4 times? 17. How many times will the reaction rate increase with an increase in temperature by 40 ° C (y \u003d 2)? 18. How will the reaction rate 2NO + 02 ^ 2N02 change if the pressure in the system is doubled? 19. How many times should the concentration of hydrogen in the N2 + 3H2^ 2NH3 system be increased in order for the reaction rate to increase 125 times? 20. The reaction between nitric oxide (II) and chlorine proceeds according to the equation 2NO + C12 2NOC1; how the reaction rate will change with an increase in: a) the concentration of nitric oxide twice; b) chlorine concentration doubled; c) the concentration of both substances doubled? . 21. At 150°C some reaction is complete in 16 minutes. Assuming a temperature coefficient of 2.5, calculate how long it will take for the same reaction to end at 80°C. 22. By how many degrees should the temperature be increased so that the reaction rate increases by 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 reaction rate is 2.
Example 4.1. How will the reaction rate of each reaction change?
2NO (g) + Cl 2 (g) = 2NOCI (g) (1); CaO (c) + CO 2 (g) \u003d CaCO 3 (c) (2),
if the pressure in each system is increased by 3 times?
Solution. Reaction (1) is homogeneous and, according to the law of mass action, the initial reaction rate is v = k∙ ∙ ; reaction (2) is heterogeneous, and its rate is expressed by the equation v = k∙ . The concentration of substances in the solid phase (CaO in this reaction) does not change during the reaction, therefore it is not included in the mass action law equation.
An increase in pressure in each of the systems by 3 times will lead to a decrease in the volume of the system by 3 times and an increase in the concentration of each of the reacting gaseous substances by 3 times. At new concentrations of reaction rates: v" = k∙(3) 2 ∙3 = 27 k∙ ∙ (1) and v" = k 3 (2). Comparing the expressions for the rates v and v", we find that the rate of reaction (1) increases by 27 times, and reaction (2) by 3 times.
Example 4.2. The reaction between substances A and B is expressed by the equation 2A + B \u003d D. The initial concentrations are: C A \u003d 5 mol / l, C B \u003d 3.5 mol / l. The rate constant is 0.4. Calculate the reaction rate at the initial moment and at the moment when 60% of substance A remains in the reaction mixture.
Solution. According to the law of action of masses v = . At the initial moment, the speed v 1 \u003d 0.4 × 5 2 × 3.5 \u003d 35. After some time, 60% of substance A will remain in the reaction mixture, i.e., the concentration of substance A will become 5 × 0.6 \u003d 3 mol / l. This means that the concentration of A has decreased by 5 - 3 = 2 mol / l. Since A and B interact with each other in a ratio of 2:1, the concentration of substance B decreased by 1 mol and became equal to 3.5 - 1 = 2.5 mol / l. Therefore, v 2 \u003d 0.4 × 3 2 × 2.5 \u003d 9.
Example 4.3. Some time after the start of the reaction
2NO + O 2 \u003d 2NO 2 concentrations of substances were (mol / l): \u003d 0.06;
0.12; = 0.216. Find the initial concentrations of NO and O 2 .
Solution. The initial concentrations of NO and O 2 are found on the basis of the reaction equation, according to which 2 mol of NO is spent on the formation of 2 mol 2NO 2. According to the condition of the problem, 0.216 mol NO 2 was formed, for which 0.216 mol NO was spent. Hence, the initial concentration of NO is equal to:
0.06 + 0.216 = 0.276 mol/L.
According to the reaction equation for the formation of 2 mol NO 2, 1 mol O 2 is needed, and to obtain 0.216 mol NO 2, 0.216 / 2 = 0.108 mol / O 2 is required. The initial concentration of O 2 is: \u003d 0.12 + 0.108 \u003d 0.228 mol / l.
Thus, the initial concentrations were:
0.276 mol/l; = 0.228 mol/l.
Example 4.4. At 323 K some reaction is completed in 30 s. Determine how the reaction rate and time will change at 283 K if the temperature coefficient of the reaction rate is 2.
Solution. According to the van't Hoff rule, we find how many times the reaction rate will change:
2 –4 = .
The reaction rate decreases by 16 times. The rate of a reaction and its time are inversely related. Consequently, the time of this reaction will increase by 16 times and will be 30 × 16 = 480 s = 8 min.
Tasks
№ 4.1 . The reaction proceeds according to the equation 3Н 2 + CO = CH 4 + H 2 O
The initial concentrations of reactants were (mol/l): = 0.8; CCO = 0.6. How will the reaction rate change if the concentration of hydrogen is increased to 1.2 mol/l, and the concentration of carbon monoxide to 0.9 mol/l?
(Answer: will increase 5 times).
№ 4.2 . The decomposition reaction of N 2 O proceeds according to the equation 2N 2 O \u003d 2N 2 + O 2. The reaction rate constant is 5·10 -4 . Initial concentration
0.32 mol/l. Determine the reaction rate at the initial moment and at the moment when 50% N 2 O decomposes. ( Answer: 5,12 . 10 -5 ; 1,28 . 10 -5).
№ 4.3 . The reaction between substances A and B is expressed by the equation
A + 2B = D. Initial concentrations: C A = 0.3 mol / l and C B = 0.4 mol / l. The rate constant is 0.8. Calculate the initial rate of the reaction and determine how the reaction rate changed after some time, when the concentration of substance A decreased by 0.1 mol.
(Answer: 3,84 . 10 -2; decreased by 6 times).
№ 4.4 .What is the temperature coefficient of the reaction rate if, when the temperature drops by 30 ° C, the reaction time increases by 64 times? ( Answer: 4).
№ 4.5 .Calculate at what temperature the reaction will end in 45 minutes, if at 20 ° C it takes 3 hours. The temperature coefficient of the reaction rate is 3 ( Answer: 32.6 about C).
№ 4.6. How will the reaction rate CO + Cl 2 = COCl 2 change if the pressure is increased by 3 times and the temperature is simultaneously increased by 30 ° C (γ = 2)?
(Answer: will increase by 72 times).
№ 4.7 . The reactions proceed according to the equations
C (c) + O 2 (g) \u003d CO 2 (g) (1); 2CO (g) + O 2 (g) \u003d 2CO 2 (g) (2)
How will the rate of (1) and (2) reactions change if in each system: a) the pressure is reduced by 3 times; b) increase the volume of the vessel by 3 times; c) increase the oxygen concentration by 3 times? ( Answer: a) will decrease in (1) by 3, in (2) by 27 times);
b) will decrease in (1) by 3, in (2) by 27 times); c) will increase by (1) and (2) by 3 times).
№ 4.8 . The reaction proceeds according to the equation H 2 + I 2 \u003d 2HI. The rate constant is 0.16. The initial concentrations of hydrogen and iodine are 0.04 mol/l and 0.05 mol/l, respectively. Calculate the initial rate of the reaction and its rate when the concentration of H 2 becomes equal to 0.03 mol / l. ( Answer: 3,2 . 10 -3 ; 1,9 . 10 -3).
№ 4.9 . The oxidation of sulfur and its dioxide proceeds according to the equations:
S (k) + O 2 (g) \u003d SO 2 (g) (1); 2SO 2 (g) + O 2 (g) \u003d 2SO 3 (g) (2)
How will the rate of (1) and (2) reactions change if in each system: a) the pressure is increased by 4 times; b) reduce the volume of the vessel by 4 times; c) increase the oxygen concentration by 4 times? ( Answer: a) will increase by (1) by 4, by (2) by 64 (times);
b) will increase by (1) by 4, by (2) by 64 times); c) will increase by (1) and (2) by 4 times).
№ 4.10 . The rate constant of the reaction 2A + B = D is 0.8. Initial concentrations: C A = 2.5 mol/l and C B = 1.5 mol/l. As a result of the reaction, the concentration of substance C B turned out to be 0.6 mol / l. Calculate what became equal to C A and the rate of reaction. ( Answer: 0.7 mol/l; 0.235).
№ 4.11. The reaction proceeds according to the equation 4HCl + O 2 = 2H 2 O + 2Cl 2
Some time after the start of the reaction, the concentrations of the substances involved in it became (mol / l): \u003d 0.85; = 0.44; = 0.30. Calculate the initial concentrations of HCl and O 2 . ( Answer:= 1.45; = 0.59 mol/l).
№ 4.12 . Initial concentrations of substances in the reaction CO + H 2 O ↔ CO 2 + H 2
were equal (mol/l): C CO = 0.5; = 0.6; = 0.4; = 0.2. Calculate the concentrations of all substances involved in the reaction after 60% H 2 O has reacted. ( Answer: CCO = 0.14; = 0.24; = 0.76; = 0.56 mol/l).
№ 4.13 . How will the reaction rate 2CO + O 2 \u003d CO 2 change if:
a) increase the volume of the reaction vessel 3 times; b) increase the CO concentration by 3 times; c) increase the temperature by 40 o C (γ = 2)? ( Answer: a) will decrease by 27 times; b) will increase by 9 times; c) will increase by 16 times).
№ 4.14 . At 10°C, the reaction is complete in 20 minutes. How long will the reaction last when the temperature rises to 40 ° C, if the temperature coefficient is 3? ( Answer: 44.4 s).
№ 4.15 . How many times should be increased
a) the concentration of CO in the system 2CO \u003d CO 2 + C so that the reaction rate increases by 4 times?
b) the concentration of hydrogen in the system N 2 + 3H 2 \u003d 2NH 3 so that the reaction rate increases 100 times?
c) pressure in the system 2NO + O 2 = 2NO 2 so that the rate of formation of NO 2 increases by 10 3 times? ( Answer: 2 times; 4.64 times; 10 times).
№ 4.16 . The reaction rate A + 2B \u003d AB 2 at C A \u003d 0.15 mol / l and
C B \u003d 0.4 mol / l is equal to 2.4 ∙ 10 -3. Determine the rate constant and the reaction rate when the concentration of B becomes 0.2 mol/l. ( Answer: 0,1; 2 ∙ 10 -4).
№ 4.17 . How will the reaction rate 2A + B = A 2 B change if the concentration of substance A is increased by 3 times, the concentration of substance B is reduced by 2 times, and the temperature is increased by 40 ° C (γ \u003d 2)? ( Answer: will increase by 72 times).
№ 4.18. The reaction proceeds according to the equation 2H 2 S + 3O 2 = 2SO 2 + 2H 2 O.
Some time after the start of the reaction, the concentrations of the substances involved in it became (mol / l): \u003d 0.009; = 0.02; = 0.003. Calculate: = 0.7 mol/l).
SESSION 10 10th grade(first year of study)
Fundamentals of chemical kinetics. State of chemical equilibrium Plan
1. Chemical kinetics and the area of its study.
2. The rate of homogeneous and heterogeneous reactions.
3. The dependence of the reaction rate on various factors: the nature of the reactants, the concentration of the reactants (the law of mass action), the temperature (the van't Hoff rule), the 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 proceed almost instantly (for example, a neutralization reaction in a solution), others take place over 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 of 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 reactants 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 “–”.
The rate of a heterogeneous reaction is the amount of a substance that enters into a reaction or is 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 the reactants, temperature, and the presence of a catalyst.
Influence the nature of the reagents It manifests itself in the fact that under the same conditions, different substances interact with each other at different rates, for example:
With an increase reagent concentrations 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 by the law of action in u u u s u s u s s and s (K.M. Guldberg and P. Waage, 1867; N.I. Beketov , 1865). The rate of a homogeneous chemical reaction at a constant temperature is directly proportional to the product of the concentrations of the reactants in powers equal to their stoichiometric coefficients (the concentrations of solids are not taken into account), for example:
where A and B are gases or liquids, k- reaction rate constant, equal to the reaction rate at a reactant concentration of 1 mol/L. Constant k depends on the properties of the reactants and temperature, but does not depend on the concentration of substances.
The dependence of the reaction rate on temperature is described by the experimental rule of Van t-Goff (1884). With an increase in temperature by 10 °, the rate of most chemical reactions increases by 2–4 times:
where is the temperature coefficient.
Catalyst A substance is called a substance that changes the rate of a chemical reaction, but is not consumed as a result of this reaction. There are 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, 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 reactant 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 action of catalysts.
The rate of a heterogeneous reaction is affected 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.
Irreversible are chemical reactions that proceed in only one direction., 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, a gas, or a weak electrolyte. For example:
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 are reactions that occur simultaneously in the forward and reverse directions., For example:
When a reversible chemical reaction occurs, the rate of the direct reaction initially 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 forward 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 ) . Solids concentrations are not included in the expression of 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 TO p, the higher practical output reaction products. If TO p > 1, then the reaction products predominate in the system; If TO R< 1, в системе преобладают реагенты.
The chemical equilibrium is mobile, i.e. when external conditions change, the rate of the forward or reverse reaction can increase. The direction of equilibrium shift is determined by the principle formulated by the French scientist Le Chatelier in 1884. If an external influence is exerted on an equilibrium system, then the equilibrium is shifted towards the reaction that counteracts this influence. Equilibrium shift is affected by changes in the concentration of reagents, temperature and pressure.
An increase in the concentration of reactants and the withdrawal of products lead to a shift in the equilibrium towards a direct reaction.
When the system is heated, the equilibrium shifts towards the endothermic reaction, and when cooled, it shifts towards the exothermic one.
For reactions involving gaseous substances, an increase in pressure shifts the equilibrium in the direction of 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 a change in pressure does not affect the equilibrium shift in any way.
1. Basic concepts and postulates of chemical kinetics
Chemical kinetics is a branch of physical chemistry that studies the rates of chemical reactions. The main tasks of chemical kinetics are: 1) calculation of reaction rates and determination of kinetic curves, i.e. the dependence of the concentrations of reactants on time ( direct task); 2) determination of reaction mechanisms from kinetic curves ( inverse problem).
The rate of a chemical reaction describes the change in the concentrations of reactants per unit time. For reaction
a A+ b B+... d D+ e E+...
reaction rate is defined as follows:
where square brackets denote the concentration of a substance (usually measured in mol/l), t- time; a, b, d, e- stoichiometric coefficients in the reaction equation.
The reaction rate depends on the nature of the reactants, their concentration, temperature, and the presence of a catalyst. The dependence of the reaction rate on concentration is described by the basic postulate of chemical kinetics - law of acting masses:
The rate of a chemical reaction at each point in time is proportional to the current concentrations of the reactants raised to some powers:
,
Where k- rate constant (independent of concentration); x, y- some numbers that are called order of reaction by substances A and B, respectively. These numbers generally have nothing to do with the coefficients a And b in the reaction equation. Sum of exponents x+ y called general reaction order. The order of the reaction can be positive or negative, integer or fractional.
Most chemical reactions consist of several stages, called elementary reactions. An elementary reaction is usually understood as a single act of formation or cleavage of a chemical bond, proceeding through the formation of a transition complex. The number of particles involved in an elementary reaction is called molecularity reactions. There are only three types of elementary reactions: monomolecular (A B + ...), bimolecular (A + B D + ...) and trimolecular (2A + B D + ...). For elementary reactions, the general order is equal to the molecularity, and the orders in terms of substances are equal to the coefficients in the reaction equation.
EXAMPLES
Example 1-1. The rate of NO formation in the reaction 2NOBr (g) 2NO (g) + Br 2(g) is 1.6 . 10 -4 mol/(l.s). What is the reaction rate and NOBr consumption rate?
Solution. By definition, the rate of a reaction is:
Mole / (l. s).
It follows from the same definition that the NOBr consumption rate is equal to the NO formation rate with the opposite sign:
mol / (l. s).
Example 1-2. In the 2nd order reaction A + B D, the initial concentrations of substances A and B are 2.0 mol/l and 3.0 mol/l, respectively. The reaction rate is 1.2. 10 -3 mol/(l.s) at [A] = 1.5 mol/l. Calculate the rate constant and the reaction rate at [B] = 1.5 mol/L.
Solution. According to the law of mass action, at any given time, the reaction rate is:
.
By the moment when [A] = 1.5 mol/l, 0.5 mol/l of substances A and B have reacted, therefore [B] = 3 – 0.5 = 2.5 mol/l. The rate constant is:
L/(mol. s).
By the moment when [B] = 1.5 mol/l, 1.5 mol/l of substances A and B have reacted, therefore [A] = 2 – 1.5 = 0.5 mol/l. The reaction rate is:
Mole / (l. s).
TASKS
1-1. How is the reaction rate of ammonia synthesis 1/2 N 2 + 3/2 H 2 \u003d NH 3 expressed through the concentrations of nitrogen and hydrogen? (answer)
1-2. How will the rate of the ammonia synthesis reaction 1/2 N 2 + 3/2 H 2 \u003d NH 3 change if the reaction equation is written as N 2 + 3H 2 \u003d 2NH 3? (answer)
1-3. What is the order of elementary reactions: a) Cl + H 2 = HCl + H; b) 2NO + Cl 2 = 2NOCl? (answer)
1-4. Which of the following values can take a) negative; b) fractional values: reaction rate, reaction order, reaction molecularity, rate constant, stoichiometric coefficient? (answer)
1-5. Does the rate of a reaction depend on the concentration of the reaction products? (answer)
1-6. How many times will the rate of the gas-phase elementary reaction A = 2D increase with a 3-fold increase in pressure? (Answer)
1-7. Determine the order of the reaction if the rate constant has the dimension of l 2 / (mol 2. s). (answer)
1-8. The rate constant of the gaseous reaction of the 2nd order at 25 ° C is 10 3 l / (mol. s). What is this constant equal to if the kinetic equation is expressed in terms of pressure in atmospheres? (Answer)
1-9. For gas phase reaction n-th order nA B express the rate of formation of B in terms of total pressure. (Answer)
1-10. The rate constants of the forward and reverse reactions are 2.2 and 3.8 L/(mol s). By which of the following mechanisms can these reactions proceed: a) A + B = D; b) A + B = 2D; c) A = B + D; d) 2A = B. (answer)
1-11. The decomposition reaction 2HI H 2 + I 2 has the 2nd order with a rate constant k= 5.95 . 10 -6 l/(mol. s). Calculate the reaction rate at a pressure of 1 atm and a temperature of 600 K. (answer)
1-12. The rate of the 2nd order reaction A + B D is 2.7 . 10 -7 mol/(l. s) at concentrations of substances A and B, respectively, 3.0. 10 -3 mol/l and 2.0 mol/l. Calculate the rate constant. (Answer)
1-13. In the 2nd order reaction A + B 2D, the initial concentrations of substances A and B are 1.5 mol/L each. The reaction rate is 2.0. 10 -4 mol/(l.s) at [A] = 1.0 mol/l. Calculate the rate constant and reaction rate at [B] = 0.2 mol/l. (answer)
1-14. In the 2nd order reaction A + B 2D, the initial concentrations of substances A and B are 0.5 and 2.5 mol/l, respectively. How many times is the reaction rate at [A] = 0.1 mol/l less than the initial rate? (answer)
1-15. The rate of the gas-phase reaction is described by the equation w = k. [A] 2 . [B]. At what ratio between concentrations A and B will the initial reaction rate be maximum at a fixed total pressure? (answer)
2. Kinetics of simple reactions
In this section, based on the law of mass action, we will compose and solve kinetic equations for irreversible reactions of an integer order.
Reactions of the 0th order. The rate of these reactions does not depend on the concentration:
,
where [A] is the concentration of the starting substance. Zero order occurs in heterogeneous and photochemical reactions.
Reactions of the 1st order. In type A B reactions, the rate is directly proportional to the concentration:
.
When solving kinetic equations, the following notation is often used: initial concentration [A] 0 = a, current concentration [A] = a - x(t), Where x(t) is the concentration of the reacted substance A. In these notations, the kinetic equation for the 1st order reaction and its solution have the form:
The solution of the kinetic equation is also written in another form, convenient for analyzing the reaction order:
.
The time it takes half of substance A to decay is called the half-life t 1/2. It is defined by the equation x(t 1/2) = a/2 and equals
Reactions of the 2nd order. In type A + B D + ... reactions, the rate is directly proportional to the product of the concentrations:
.
Initial concentrations of substances: [A] 0 = a, [B] 0 = b; current concentrations: [A] = a- x(t), [B] = b - x(t).
When solving this equation, two cases are distinguished.
1) the same initial concentrations of substances A and B: a = b. The kinetic equation has the form:
.
The solution to this equation is written in various forms:
The half-life of substances A and B is the same and equal to:
2) The initial concentrations of substances A and B are different: a
b. The kinetic equation has the form: 
.
The solution to this equation can be written as follows:
The half-lives of substances A and B are different: 
.
nth order reactions n A D + ... The kinetic equation has the form:
.
Solution of the kinetic equation:
. (2.1)
The half-life of substance A is inversely proportional to ( n-1)-th degree of initial concentration:
. (2.2)
Example 2-1. The half-life of the radioactive isotope 14 C is 5730 years. During archaeological excavations, a tree was found, the content of 14 C in which is 72% of normal. What is the age of the tree?
Solution. Radioactive decay is a 1st order reaction. The rate constant is:
The lifetime of a tree can be found from the solution of the kinetic equation, taking into account the fact that [A] = 0.72 . [A]0:
Example 2-2. It has been established that the 2nd order reaction (one reagent) is 75% complete in 92 min at an initial reagent concentration of 0.24 M. How long will it take for the reagent concentration to reach 0.16 M under the same conditions?
Solution. We write twice the solution of the kinetic equation for a 2nd order reaction with one reagent:
,
where, by convention, a= 0.24M, t 1 = 92 min, x 1 = 0.75 . 0.24=0.18M, x 2 = 0.24 - 0.16 = 0.08 M. Let's divide one equation by another:
Example 2-3. For an elementary reaction n A B denote the half-life of A through t 1/2 , and the decay time of A by 75% - through t 3/4 . Prove that the ratio t 3/4 / t 1/2 does not depend on the initial concentration, but is determined only by the reaction order n.Solution. We write twice the solution of the kinetic equation for the reaction n-th order with one reagent:
and divide one expression by another. Constants k And a from both expressions will cancel, and we get:
.
This result can be generalized by proving that the ratio of the times for which the degree of conversion is a and b depends only on the order of the reaction:
.
TASKS
2-1. Using the solution of the kinetic equation, prove that for reactions of the 1st order, the time t x, for which the degree of conversion of the initial substance reaches x, does not depend on the initial concentration. (answer)2-2. The first order reaction proceeds by 30% in 7 min. How long will it take for the reaction to be 99% complete? (answer)
2-3. The half-life of the radioactive isotope 137 Cs, which entered the atmosphere as a result of the Chernobyl accident, is 29.7 years. After what time will the amount of this isotope be less than 1% of the original? (answer)
2-4. The half-life of the radioactive isotope 90 Sr, which enters the atmosphere during nuclear tests, is 28.1 years. Let us assume that the body of a newborn child has absorbed 1.00 mg of this isotope. How much strontium will remain in the body after a) 18 years, b) 70 years, if we assume that it is not excreted from the body? (Answer)
2-5. The rate constant for the first order reaction SO 2 Cl 2 = SO 2 + Cl 2 is 2.2. 10 -5 s -1 at 320 o C. What percentage of SO 2 Cl 2 will decompose when kept for 2 hours at this temperature? (Answer)
2-6. 1st order reaction rate constant
2N 2 O 5 (g) 4NO 2 (g) + O 2 (g)
at 25 ° C it is 3.38. 10 -5 s -1 . What is the half-life of N 2 O 5 ? What will be the pressure in the system after a) 10 s, b) 10 min, if the initial pressure was 500 mm Hg. Art. (answer)
2-7. The first order reaction is carried out with different amounts of starting material. Will the tangents to the initial parts of the kinetic curves intersect at one point on the x-axis? Explain the answer. (Answer)
2-8. The first order reaction A 2B proceeds in the gas phase. The initial pressure is p 0 (B is missing). Find the dependence of the total pressure on time. After what time will the pressure increase by 1.5 times compared to the initial one? What is the extent of the reaction by this time? (answer)
2-9. The second order reaction 2A B proceeds in the gas phase. The initial pressure is p 0 (B is missing). Find the dependence of the total pressure on time. After what time will the pressure decrease by 1.5 times compared to the initial one? What is the extent of the reaction by this time? (answer)
2-10. Substance A was mixed with substances B and C in equal concentrations of 1 mol/l. After 1000 s, 50% of substance A remains. How much substance A will remain after 2000 s if the reaction has: a) zero, b) first, c) second, c) third general order? (answer)
2-11. Which of the reactions - first, second or third order - will end faster if the initial concentrations of substances are 1 mol / l and all rate constants expressed in terms of mol / l and s are equal to 1? (answer)
2-12. Reaction
CH 3 CH 2 NO 2 + OH - H 2 O + CH 3 CHNO 2 -
has second order and rate constant k= 39.1 l/(mol. min) at 0 about C. A solution was prepared containing 0.004 M nitroethane and 0.005 M NaOH. How long does it take for 90% nitroethane to react?
2-13. The rate constant for the recombination of H+ and FG - (phenylglyoxinate) ions into a UFH molecule at 298 K is k= 10 11.59 l/(mol. s). Calculate the time during which the reaction has passed by 99.999% if the initial concentrations of both ions are equal to 0.001 mol/l. (answer)
2-14. The rate of oxidation of butanol-1 with hypochlorous acid does not depend on the concentration of alcohol and is proportional to 2 . How long will it take for the oxidation reaction at 298 K to reach 90% if the initial solution contained 0.1 mol/l HClO and 1 mol/l alcohol? The reaction rate constant is k= 24 l/(mol. min). (answer)
2-15. At a certain temperature, a 0.01 M solution of ethyl acetate is saponified with a 0.002 M NaOH solution by 10% in 23 min. After how many minutes will it be saponified to the same degree with 0.005 M KOH solution? Consider that this reaction is of the second order, and the alkalis are completely dissociated. (Answer)
2-16. The second-order reaction A + B P is carried out in a solution with initial concentrations [A] 0 = 0.050 mol/l and [B] 0 = 0.080 mol/l. After 1 h, the concentration of substance A decreased to 0.020 mol/l. Calculate the rate constant and half-lives of both substances.