1. In a vessel, gas A with an amount of substance of 4.5 mol and gas B with an amount of substance of 3 mol were mixed. Gases A and B react in accordance with the equation A + B = C. After some time, gas C was formed in the system with an amount of substance of 2 mol. What quantities of unreacted gases A and B remain in the system?
From the reaction equation it follows that:
Dn(A) = Dn(B) = Dn(C) = 2 mol,
where Dn is the change in the amount of substance during the reaction.
Therefore, what remains in the vessel is:
n 2 (A) = n 1 (A) - Dn(A); n 2 (A) = (4.5 - 2) mol = 2.5 mol;
n 2 (B) = n 1 (B) - Dn(B); n 2 (B) = (3 - 2) mol = 1 mol.
2. The reaction proceeds according to the equation: 2A + B ⇄ C and is second order in substance A and first in 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 forward reaction at the moment when 50% of substance B reacts if the initial concentrations are: C(A) = 10 mol/l; C(B) = 5 mol/l. How will the rate of a chemical reaction change?
C(B) that entered into the reaction is equal to:
C(B) = 0.5 5 = 2.5 mol/l.
Accordingly, C(A) that 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) = 10 - 5 = 5 mol/l,
C(B) = 5 - 2.5 = 2.5 mol/l.
The rate of the forward reaction will be equal to:
The rate of the 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 = C and has the first order for substance A and the second for substance B. The initial concentrations of the substances are: C(A) = 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 decreases by 0.3 × 2 = 0.6 mol/l. After the reaction occurs, the concentrations are:
4. The rates of forward 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 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 concentrations of all three gases will increase by the same amount, and the rates of both reactions will become correspondingly equal:
The reaction rate ratios are:
Thus, the rate of the forward reaction will increase by 27 times, the reverse reaction by 9.
5. The reaction at a temperature of 50 0 C proceeds in 2 minutes 15 s. How long will it take for this reaction to complete at a temperature of 70 0 C, if in this temperature range the temperature coefficient of rate g is 3?
As the temperature increases from 50 to 70 0 C, the reaction rate increases in accordance with the Van't Hoff rule:
Where = 70 0 C, = 50 0 C, a and are the reaction rates at given temperatures.
We get:
those. the reaction rate increases 9 times.
According to the definition, reaction time is inversely proportional to the rate of reaction, therefore:
where and is the reaction time at temperatures And .
From here we get:
Considering that = 135 s (2 min 15 s), we determine the reaction time at temperature :
6. How many times will the rate of a chemical reaction increase when the temperature increases from = 10 0 C to = 80 0 C , if the temperature coefficient of speed g is 2?
From van't Hoff's 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 after 3 hours, 50% of the original amount of the drug remained in the patient’s body. Determine the half-life and rate constant for the reaction of drug removal 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 removed from the body, then t 1/2 = 3 hours. Let's calculate the reaction rate constant from the equation:
8. During laboratory studies of aqueous solutions of the drug, it was found that due to hydrolysis, the concentration of the drug decreased from 0.05 mol/l to 0.03 mol/l per day. Calculate the half-life of the drug hydrolysis reaction.
Since hydrolysis reactions usually occur with a significant excess of water, its concentration can be kept constant. Consequently, during the reaction only the concentration of the drug changes 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 eliminated from the body.
When 75% of the drug is excreted 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 for the reaction of sucrose hydrolysis is 2.31×10 - 3 h - 1. Calculate:
1) 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 equal to:
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 was hydrolyzed.
11. During a certain first-order reaction, 60% of the initial amount of a substance undergoes transformation in 30 minutes. Determine what part of the substance will remain after 1 hour.
1. After 30 minutes, the amount of remaining substance will be:
C 1 = C 0 - 0.6 C 0 = 0.4 × C 0.
i.e., the ratio C 0 /C 1 is 2.5.
2. Let's find the reaction rate constant:
3. The amount of substance C2 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 the rate of a chemical reaction called?
2. What is the true rate of a homogeneous reaction?
3. What is the dimension of the rate of a homogeneous reaction?
4. What is the rate of a heterogeneous reaction called?
5. What is the dimension of the rate of a heterogeneous reaction?
6. List the factors influencing the speed of the reaction.
7. Formulate the law of mass action.
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 the order of reaction? 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 a reaction?
13. Define simple and complex reactions. Give a classification of complex reactions.
14. Formulate Van't Hoff's rule. Give a mathematical expression for van't Hoff's rule.
15. How does the reaction rate depend on the activation energy? Write the Arrhenius equation.
16. What is an activated complex? Why do reactions proceed through the stages of formation of activated complexes?
17. What is 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 #1
1. The reaction between substances A and B is expressed by the equation 2A + B = C and is second order for substance A and first order for substance B. The initial concentrations of substances are: C 0 (A) = 0.4 mol/l; C 0 (B) = 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. How many degrees must the temperature be increased for the reaction rate to increase 64 times? The temperature coefficient of the reaction rate g is equal to 2.
a) when the pressure in the system doubles?
b) when the volume of gases doubles?
Option No. 2
1. The reaction proceeds according to the equation: A + B = C and is of 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 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 later the reaction would end 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 increases by 3 times?
Option #3
1. The reaction is expressed by the equation: A + B = C and has first order in substance A and substance B. At initial concentrations C 0 (A) = 3 mol/l and C 0 (B) = 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 when the temperature increases from 10 to 70 0 C, if the temperature coefficient of the rate g is 2?
3. The reaction rate A (s) + 2B (gas) = C (s) is expressed by the equation: 
How will the reaction rate change if the concentration of B is doubled?
Option No. 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 for it to end at 80 0 C if the temperature coefficient of speed g is 3?
3. The rate of reaction 3A + B = C is expressed by the equation: 
How many times will the rate of the forward reaction change:
a) when the concentration of substance A doubles?
b) with a simultaneous decrease in the concentration of the starting substances by 2 times?
Option #5
1. The rate of a certain reaction increased 8 times when the temperature increased from 40 to 70 0 C. Determine the value of g.
2. The reaction proceeds according to the equation: A + 3B = 2C and is of first order in substance A and second in substance B. The initial concentrations of substances are: C 0 (A) = 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 forward and reverse reactions occurring in the gas phase and obeying the equations change:
Option #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 forward reaction is described by the equation 
How many times will the rate of the forward reaction decrease after 0.5 mol of A reacts?
2. By how many degrees must 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 = B, the order of which is estimated as 0.5, with an isothermal decrease in pressure in the system by 3 times?
Option No. 7
1. The reaction between substances A and B proceeds according to the equation: A + 2B = C and is of first order in substance A and substance B. The initial concentrations of the reacting substances were: C 0 (A) = 1.5 mol/l; C 0 (B) = 3 mol/l; k = 0.4. Calculate the rate of the chemical reaction at the initial moment of time and after some time, when 75% of A has reacted.
2. What is the temperature coefficient of rate g, if with an increase in temperature by 30 0 C, the reaction rate increases 27 times?
3. How will the rates of forward and reverse reactions occurring in the gas phase and obeying the equations change:
with an isothermal increase in pressure by a factor of 2?
Option No. 8
1. In a 1 liter solution containing 1 mol of substance A and 2 mol of substance B, the following reaction occurs: A + 3B = 2C + D. The direct reaction is first order in substance A and second order in substance B. How many times will the rate of the direct reaction decrease? reaction after 0.65 mol of substance A has reacted?
2. When the temperature increases from -5 to +5 0 C, the rate of bacterial hydrolysis (enzymatic process) increases 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) = B (gas) + C (solid) be increased so that the rate of the direct reaction, which is a second-order reaction, increases 4 times?
Option No. 9
1. The reaction proceeds according to the equation: 2A + B = 2C and is second order in substance A and first order 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: C 0 (A) = 2 mol/l; C 0 (B) = 1 mol/l. How will the rate of a chemical reaction change?
2. When the temperature increased from 10 to 50 0 C, the reaction rate increased 16 times. Determine the temperature coefficient of speed g.
3. The reaction proceeds according to the equation: A + B = C + D + E and has first order in substance A and zero in substance B. How will the rate of the direct reaction change after diluting the reacting mixture by 3 times?
Option No. 10
1. The reaction proceeds according to the equation: A + 2B = AB 2 and is first order in substance A and 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) = 0.8 mol/l and the reaction rate at the time of formation of 0.2 mol/l substance AB 2.
2. How many times will the rate of a chemical reaction increase when the temperature increases 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 how long it will take to reduce the content of the drug in the human body by 8 times.
Option No. 11
1. The reaction proceeds according to the equation: A + B = 2C and is of first order in substance A and substance B. The initial concentrations of substances are: C 0 (A) = 0.3 mol/l; C 0 (B) = 0.5 mol/l; k = 0.1. Find the initial reaction rate and the reaction rate after some 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 rate g equal to 2, calculate how many minutes later would the same reaction end 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 eliminated from the body.
Option No. 12
1. The reaction proceeds according to the equation: A + 2B = C and is of first order in substance A and second in substance B. The initial concentrations of substances are: C 0 (A) = 0.9 mol/l; C 0 (B) = 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 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 C the speed increases by 27 times?
3. The half-life of a certain first-order reaction is 30 minutes. Calculate what portion of the original amount will remain after 1 hour.
Option No. 13
1. The reaction proceeds according to the equation: 2A + B = 2C and is second order in substance A and first order in 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) = 0.9 mol/l and the reaction rate at the time of formation of 0.1 mol of substance C.
2. At a temperature of 10 0 C, the reaction takes place in 80 minutes. At what temperature will the reaction complete in 20 minutes if the temperature coefficient of rate g is 2?
3. During 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 is a first-order reaction.
Option No. 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 = 2C. The forward reaction is first order with respect to substance A and second order with respect to substance B. How will the rate of the forward reaction change after 0.5 mol of gas A reacts?
2. When the temperature of the system increased from 10 to 50 0 C, 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 radionuclide Cs-137 was released, the half-life of which is 30 years. Calculate what part of the radionuclide that entered the body remains at the present time.
Option No. 15
1. The reaction proceeds according to the equation: A + B = C has the first order in substance A and in substance B. At the initial concentrations of substances C 0 (A) = 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 for 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 how long it will take for the pesticide concentration to decrease to 0.01 mol/l.
Option No. 16
1. The decomposition reaction proceeds according to the equation: 2A = 2B + C and is of second order in substance A. The rate constant of this reaction at 200 0 C is 0.05. Initial concentration C(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 (solid) + 3B (gas) = 2C (solv), which has zero order in substance A and third order in substance B, if the pressure in the system is increased by 3 times?
3. During a certain 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 No. 17
1. The interaction of gases proceeds according to the equation: A + 2B = 2C and is of the first order in substance A and second in substance B. The initial concentrations of gases are equal to: C 0 (A) = 2 mol/l; C 0 (B) = 4 mol/l; k = 0.02. Calculate the rate of the direct reaction at the initial time and after some time, when 50% of substance A has reacted.
2. At 20 0 C the reaction occurs in 2 minutes. How long will it take for the same reaction to occur 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 equal to 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 No. 18
1. The reaction proceeds according to the equation: 2A + B = 2C and is of first order in substance A and substance B. The reaction rate is 0.5 mol/l×s. The initial concentrations of substances are: C(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 occurs in 2 minutes. How long will it take for the same reaction to occur at 50 0 C if g = 2?
3. The rate constant for the inversion reaction of cane sugar at 25 0 C is equal to 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.
Problem 325.
Find the value of the rate constant for the reaction A + B ⇒ AB, if at concentrations of substances A and B equal to 0.05 and 0.01 mol/l, respectively, the reaction rate is 5 .
10 -5 mol/(l. min).
Solution:
Speed chemical reaction is expressed by the equation:
v- ,k- reaction rate constant
Answer: 0.1/mol. min.
Problem 326.
How many times will the rate of the reaction 2A + B ⇒ A 2 B change if the concentration of substance A is increased by 2 times, and the concentration of substance B is decreased by 2 times?
Solution:
v- ,k- reaction rate constant, [A] and [B] – concentrations of starting substances.
Due to an increase in the concentration of substance A by 2 times and a decrease in the concentration of substance B by 2 times, the reaction rate will be expressed by the equation:
Comparing the expressions for v and v" we find that the reaction rate has increased by 2 times.
Answer: increased by 2 times.
Problem 327.
How many times should the concentration of substance B 2 in the system be increased?
2A 2(g) + B 2(g) = 2A 2 B, so that when the concentration of substance A decreases by 4 times, the rate of the direct reaction does not change?
Solution:
The concentration of substance A was reduced by 4 times. We denote the change in the concentration of substance B by x. Then, before the concentration of substance A changes, the reaction rate can be expressed by the equation:
v- ,k- reaction rate constant, [A] and [B] – concentrations of starting substances.
After changing the concentration of substance A 2, the reaction rate will be expressed by the equation:
According to the conditions of the problem, v = v" or
Thus, it is necessary to increase the concentration of substance B 2 in the system 2A 2 (g) + B 2 (g) = 2A 2 B by 16 times, so that when the concentration of substance A 2 decreases by 4 times, the rate of the direct reaction does not change.
Answer: 16 times.
Problem 328.
Two vessels of the same capacity are introduced: into the first - 1 mole of gas A and 2 moles of gas B, into the second - 2 moles of gas A and 1 mole of gas B. The temperature in both vessels is the same. Will the reaction rate between gases A and B in these vessels differ if the reaction rate is expressed by: a) equation b) equation
Solution:
a) If the reaction rate is expressed by the equation, then, taking into account the concentrations of substances A and B in the vessels, we write down the expressions for the reaction rates for the vessels:
Thus,
b) If the reaction rate is expressed by the equation, then, taking into account the concentrations of substances A and B in the vessels, we write down the expressions for the reaction rates for the vessels:
Thus, 
Answer: a) no, b) yes.
Problem 329.
Some time after the start of the reaction 3A+B ⇒ 2C+D concentrations of substances were: [A] = 0.03 mol/l; [B] =0.01 mol/l; [C] = 0.008 mol/l. What are the initial concentrations of substances A and B?
Solution:
To find the concentrations of substances A and B, we take into account that, according to the reaction equation, from 3 moles of substance A and 1 mole of substance B, 1 mole of substance C is formed. Since, according to the conditions of the problem, 0.008 moles of substance C were formed in each liter of the system, then it was consumed 0.012 moles of substance A (3/2 .
0.008 = 0.012) and 0.004 mol of substance B (1/2 .
0.008 = 0.004). Thus, the initial concentrations of substances A and B will be equal:
[A] 0 = 0.03 + 0.012 = 0.042 mol/l;
[B] 0 = 0.01 + 0.004 = 0.014 mol/l.
Answer:[A] 0 = 0.042 mol/l; [B] 0 = 0.014 mol/l.
Problem 330.
In the system CO + C1 2 = COC1 2, the concentration was increased from 0.03 to 0.12 mol/l, and the chlorine concentration from 0.02 to 0.06 mol/l. How many times did the rate of the forward reaction increase?
Solution:
Before the concentration changes, the reaction rate can be expressed by the equation:
v is the reaction rate, k is the reaction rate constant, [CO] and are the concentrations of the starting substances.
After increasing the concentration of reactants, the reaction rate is:
Let's calculate how many times the reaction rate has increased:
Answer: 12 times.
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 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, the surface on which the reaction occurs. Since the interaction changes the concentrations of reagents or reaction products per unit time. In this case, there is no need to monitor changes 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 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, 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 - k[A][B], and they speak of a bimolecular reaction; when a collision of three molecules occurs in an elementary act, the dependence of speed on concentration is true: v - k [A] [B] [C], and they speak of a trimolecular reaction. In all analyzed dependencies: v - reaction rate; [A], [B], [C] - concentrations of reacting substances; k - proportionality coefficient; called the reaction rate constant. v = k, when the concentrations of reactants or their product are equal to unity. 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 the 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: 2СО + 02 = 2С02. According to the law of mass action v - k[C0]2. 2) Let us denote [CO] = a; = b, then: v = k a2 b. 3) When the concentration of the starting substances increases by 3 times, we obtain: [CO] = 3a, a = 3b. 4) Calculate the rate of reaction 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 when the temperature increases by 40 °C if the temperature coefficient of the reaction rate is 3? Given: At = 40 °C Y - 3 Find: 2 Solution: 1) According to Van't Hoff's rule: h-U vt2 = vh y 10, 40 and, - vt > 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 is 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] = 10 mol/l [B] = 6 mol/l Find: "start! ^ Solution: 1) Find the reaction rate at the initial moment: v - k[A]2 [B], r> = 0.8 102 b - 480 mol - l sec"1. beginning 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) From the reaction equation it follows 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] = 10 - 4.8 = 5.2 mol/l. 4) Calculate if: d) = 0.8 * 5.22 3.6 = 77.9 mol l "1 * sec"1. Answer: g>begin ~ 480 mol l sec"1, g/ = 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 complete at a temperature of 60 °C, if in this temperature range the temperature coefficient of the reaction rate is 2? Given: t1 = 30 °C t2 = 60 °C 7 = 2 t = 2 min = 120 sec Find: h Solution: 1) In accordance with the van’t Hoff rule: vt - = y 1 vt - = 23 = 8. Vt 2) The reaction speed is inversely proportional to the reaction time, therefore: Answer: t = 15 sec. Questions and tasks for independent solution 1. Define reaction rate. Give examples of reactions occurring 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 a positive and in which a negative sign is needed on the right side of the expression. 3. On what factors does the rate of a chemical reaction depend? 4. What is called activation energy? What factor influences the rate of a chemical reaction does it characterize? 5. What explains the strong increase in reaction rate with increasing temperature? 6. Define the basic law of chemical kinetics - the law of mass action. Who and when was it formulated? 7. What is the rate constant of a chemical reaction called 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 in which inhibitors are used. 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 = 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 when the temperature increases 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 reaction A + B = C increases three times with every 10 °C increase in temperature. How many times will the reaction rate increase when the temperature increases by 50 °C? 16. How many times will the rate of the reaction between 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 when the temperature increases by 40 °C (y = 2)? 18. How will the rate of the reaction 2NO + 02 ^ 2N02 change if the pressure in the system is doubled? 19. How many times should the concentration of hydrogen in the system N2 + 3H2^2NH3 be increased so that the reaction rate increases by 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 when: a) the concentration of nitric oxide doubles; b) chlorine concentration doubled; c) the concentrations of both substances are doubled? . 21. At 150 °C, some reaction ends in 16 minutes. Taking the temperature coefficient equal to 2.5, calculate the time period after which the same reaction will end at 80 °C. 22. How many degrees must the temperature be increased for the reaction rate to increase 32 times? The temperature coefficient of the reaction rate is 2. 23. At 30 °C, the reaction occurs in 3 minutes. How long will it take for the same reaction to occur 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.
Test questions and tasks
1. The speed of chemical reactions, the difference between average speed and instantaneous speed.
2. Write down the mathematical expression for the law of mass action for chemical reactions:
2A + B = A 2 V
4Fe + 3O 2 = 2Fe 2 O 3
3. Dependence of the rate of a chemical reaction on the nature of the reacting substances and on temperature. Van't Hoff's law, Arrhenius equation. Homogeneous and heterogeneous catalysis. Examples. Mechanism of action of the catalyst. Activation energy of a chemical reaction.
4. The rate constant for the reaction A + 2B = AB 2 is equal to 2 10 -3 l/(mol s). Calculate its speed at the initial moment, when C A = C B = 0.4 mol/l and after some time. At this point, the concentration of substance AB 2 was 0.1 mol/l.
5. combustion of methane in oxygen if the oxygen concentration is increased 5 times?
6. The chemical reaction proceeds according to the equation A + B = C. At the initial moment of time, C A = 2.7 mol/l, C B = 2.5 mol/l. After 0.5 hours, the concentration of substance A decreased and became equal to CA = 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 so that the rate of the chemical reaction 2NO 2 + O 2 = 2NO 2 increases 1000 times?
8. How many times will the rate of a chemical reaction change when the temperature decreases from 70 to 30 0 C if the temperature coefficient is 3?
9. How many degrees must the temperature be increased to increase the rate of a chemical reaction by 81 times? The temperature coefficient of the reaction rate is 3?
10. Calculate the temperature coefficient of a certain chemical reaction if, with an increase in temperature from 10 to 50 0 C, the rate of the chemical reaction increased 16 times.
Examples of completing tasks
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 will the rate of a chemical reaction change?
4Al(k) + 3O 2 (g) = 2Al 2 O 3 (k),
if the oxygen concentration is increased by 3 times?
Solution
1. We write down the expression for the dependence of the rate of a chemical reaction on the concentration of reactants: V 1 = k 3 .
2. When the oxygen concentration increases by 3 times, the rate of the chemical reaction increases: V 2 = k 3 .
V 2 / V 1 = ¾¾¾¾¾¾¾¾ = 27
Answer. When the oxygen concentration increases by 3 times, the rate of the chemical reaction increases by 27 times.
Example 3. How will the rate of a chemical reaction change?
2Al(k) + 3Cl 2 (g) = 2AlCl 3 (k)
when the pressure doubles?
Solution.
1. We write down the expression for the dependence of the rate of a chemical reaction on the concentration of reactants: V 1 = k 3 .
2. When the pressure doubles, the chlorine concentration also doubles. Therefore, V 2 = k 3.
3. The change in the rate of a chemical reaction is
V 2 / V 1 = ¾¾¾¾¾¾¾ = 8
Answer. When the pressure doubles, the rate of this chemical reaction increases 8 times.
Example 4. The temperature coefficient of the rate of a chemical reaction is 2.5. How will its speed change a) when the temperature of the reaction mixture increases from 60 to 100 o C; b) when the temperature drops from 50 to 30 o C.
Solution
1. The dependence of the rate of a chemical reaction on temperature is determined by the Van't Hoff rule. Its mathematical expression is:
V 2 = V 1 γ (t2 - t1) / 10.
Therefore, a) V 2 / V 1 = 2.5 (100-60) / 10 = 2.5 4 = 39.06;
b) V 2 / V 1 = 2.5 (30-50) / 10 = 2.5 -2 = 1/ 6.25 = 0.16.
Answer. When the temperature increases by 40 o, the rate of this reaction increases by 39.06 times; when the temperature decreases 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 a temperature of 50 o C.
Subject. Chemical equilibrium
Test questions and tasks
1. Reversible and irreversible chemical reactions. Give examples. The main signs of irreversibility of reactions. False chemical equilibrium.
2. Law of mass action for reversible chemical reactions. Physical meaning of the chemical equilibrium constant.
3. Write down the expression for the chemical equilibrium constant for the following chemical reactions:
3Fe(k) + 4H 2 O(g) Fe 3 O 4 (k) + 4H 2 (g)
CaO(k) + CO 2 (g) CaCO 3 (k)
Ca(k) + C(k) +3/2O 2 (g) CaCO 3 (k)
4. Le Chatelier's principle. Give examples.
5. How does an increase in pressure affect the 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(k) + CO 2 (g) 2CO(g)
6. The chemical equilibrium in the following reactions will shift in the direction of the forward or reverse reaction as the temperature decreases:
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 > 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 shift the chemical equilibrium towards a direct reaction:
C(k) + 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) = 2SO 3 (g) was established at the following concentrations of reactants: = 0.2 mol/l, = 0.05 mol/l, = 0.09 mol/l. How will the rate of the forward reaction and the rate of the reverse reaction change 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) = 2HCl (g), if the initial concentrations C (H 2) = 0.5 mol/l, C (Cl 2) = 1.5 mol/l, and the equilibrium concentration of hydrogen chloride = 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) = 11.2 g, m(Cl 2) = 14.2 g, m(COCl 2) = 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 completing tasks
Example 1. Write a mathematical expression for the chemical equilibrium constant of the reaction Ca 3 N 2 (k) + 6H 2 O (g) = 3Ca(OH) 2 (k) + 2NH 3 (g).
Solution. The mathematical expression for the chemical equilibrium constant (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) = Co(k) + CO 2 (g), calculate the chemical equilibrium constant if 80% of CO has reacted by the time of equilibrium, the initial concentration of CO is 1.88 mol/l.
Solution
1. Mathematical expression for the chemical equilibrium constant Kc = /.
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% - has entered into a chemical reaction:
[CO] = C (CO)ref. – C (CO) react. = 1.88 – (1.88 80)/ 100 =
0.376 mol/l.
The equilibrium concentration of CO 2 is equal to:
[CO 2 ] = C (CO) reaction = (1.88 80)/ 100 = 1.504 mol/l.
3. In the mathematical expression for the chemical equilibrium constant, we substitute the values of the equilibrium concentrations of CO and CO 2:
Kc = 1.504/ 0.376 = 4.
Answer. The chemical equilibrium constant of this reaction is 4; which indicates that at this point 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(k) + CO 2 (g) + H 2 O(g) = (NiOH) 2 CO 3 (k) DH o be shifted?< 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.
Solution
1. In accordance with Le Chatelier's principle, an increase in pressure shifts the equilibrium of a chemical reaction in a direction that is accompanied by a decrease in the volume of the reaction system. As pressure increases, the equilibrium of this reaction shifts to the right (the rate of the forward reaction is higher than the reverse reaction).
2. In accordance with Le Chatelier's principle, an increase in temperature shifts the chemical equilibrium towards an endothermic reaction. Consequently, as the temperature increases, the equilibrium of this reaction shifts to the left (the rate of the reverse reaction is higher than the forward reaction).
3. To increase the yield of the product of the chemical reaction of the formation of nickel (II) hydroxycarbonate, the pressure should be increased and the temperature reduced.
Example 4. Write an expression for the chemical equilibrium constant of the reaction:
MgO(k) + H 2 (g) = Mg(k) + H 2 O(l).
Does increasing pressure affect the shift in chemical equilibrium?
Solution. For heterogeneous reactions in the expression for rate.
Example 4.1. How will the reaction rate of each reaction change?
2NO (g) + Cl 2 (g) = 2NOCI (g) (1); CaO (k) + CO 2 (g) = CaCO 3 (k) (2),
if in each system the pressure 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, and therefore is not included in the equation of the law of mass action.
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 = D. The initial concentrations are: C A = 5 mol/l, C B = 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 mass action v = . At the initial moment, the speed v 1 = 0.4 × 5 2 × 3.5 = 35. After some time, 60% of substance A will remain in the reaction mixture, i.e., the concentration of substance A will become equal to 5 × 0.6 = 3 mol /l. This means that the concentration of A 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 = 0.4 × 3 2 × 2.5 = 9.
Example 4.3. Some time after the start of the reaction
2NO + O 2 = 2NO 2 concentrations of substances were (mol/l): = 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 based on the reaction equation, according to which 2 mol of NO is consumed to form 2 mol 2NO 2. According to the conditions of the problem, 0.216 mol NO 2 was formed, for which 0.216 mol NO was consumed. This means that the initial NO concentration is:
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 required, 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: = 0.12 + 0.108 = 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 of its occurrence will change at 283 K if the temperature coefficient of the reaction rate is 2.
Solution. Using Van't Hoff's rule, we find how many times the reaction rate will change:
2 –4 = .
The reaction rate decreases by 16 times. The rate of the reaction and the time it takes to occur are inversely proportional. 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 3H 2 + CO = CH 4 + H 2 O
The initial concentrations of the reactants were (mol/l): = 0.8; CCO = 0.6. How will the reaction rate change if the hydrogen concentration is increased to 1.2 mol/l and the carbon monoxide concentration is increased to 0.9 mol/l?
(Answer: will increase 5 times).
№ 4.2 . The decomposition reaction of N 2 O follows the equation 2N 2 O = 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 reaction rate 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, with a decrease in temperature 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 o C it takes 3 hours. The temperature coefficient of the reaction rate is 3 ( Answer: 32.6 o C).
№ 4.6. How will the reaction rate CO + Cl 2 = COCl 2 change if the pressure is increased 3 times and at the same time the temperature is increased by 30 o C (γ = 2)?
(Answer: will increase 72 times).
№ 4.7 . The reactions proceed according to the equations
C (k) + O 2 (g) = CO 2 (g) (1); 2CO (g) + O 2 (g) = 2CO 2 (g) (2)
How will the rate of (1) and (2) reactions change if in each system: a) reduce the pressure 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 by (1) 3, (2) 27 times);
b) will decrease by (1) 3, (2) 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 = 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) = SO 2 (g) (1); 2SO 2 (g) + O 2 (g) = 2SO 3 (g) (2)
How will the rate of (1) and (2) reactions change if in each system: a) increase the pressure 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) 4, (2) 64 (fold);
b) will increase by (1) 4, (2) 64 times); c) will increase by (1) and (2) 4 times).
№ 4.10 . The rate constant for 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 was equal to 0.6 mol/l. Calculate what CA and the reaction rate became equal to. ( 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): = 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): CCO = 0.5; = 0.6; = 0.4; = 0.2. Calculate the concentrations of all substances participating 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 = CO 2 change if:
a) increase the volume of the reaction vessel 3 times; b) increase the concentration of CO by 3 times; c) increase the temperature by 40 o C (γ = 2)? ( Answer: a) will decrease by 27 times; b) will increase 9 times; c) will increase 16 times).
№ 4.14 . At 10 o C the reaction ends in 20 minutes. How long will the reaction last when the temperature rises to 40 o C if the temperature coefficient is 3? ( Answer: 44.4 s).
№ 4.15 . How many times should it be increased?
a) the concentration of CO in the system 2CO = CO 2 + C, so that the reaction rate increases 4 times?
b) the concentration of hydrogen in the system N 2 + 3H 2 = 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 NO 2 formation increases by 10 3 times? ( Answer: 2 times; 4.64 times; 10 times).
№ 4.16 . Reaction rate A + 2B = AB 2 at C A = 0.15 mol/l and
C B = 0.4 mol/l is equal to 2.4 ∙ 10 −3. Determine the rate constant and reaction rate when the concentration of B becomes 0.2 mol/L. ( Answer: 0,1; 2 ∙ 10 -4).
№ 4.17 . How will the rate of reaction 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 o C (γ = 2)? ( Answer: will increase 72 times).
№ 4.18. The reaction follows 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): = 0.009; = 0.02; = 0.003. Calculate: = 0.7 mol/l).
