Security questions and tasks
1. Speed chemical reactions, the difference between average speed and instantaneous speed.
2. Write it down mathematical expression 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 average speed within 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 temperature coefficient equals 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 chemical equilibrium constants.
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 of NO 2, 1 mol of O 2 is required, and to obtain 0.216 mol of 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 initial speed 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 decreases 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).
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 rate of reaction between gases A and B in these vessels differ if the rate of reaction 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.
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: 1) calculation of reaction rates and determination of kinetic curves, i.e. 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 concentrations of reactants per unit time. For reaction
a A+ b B+... d D+ e E+...
the reaction rate is determined as follows:
where square brackets indicate the concentration of the 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 mass action:
The rate of a chemical reaction at each moment of time is proportional to the current concentrations of the reactants, raised to certain powers:
,
Where k- rate constant (independent of concentration); x, y- some numbers that are called order of reaction by substance A and B, respectively. In general, these numbers 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 steps called elementary reactions. An elementary reaction is usually understood as a single act of formation or rupture of a chemical bond, proceeding through the formation of a transition complex. The number of particles participating 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 overall order is equal to the molecularity, and the orders by substance 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 rate of reaction and the rate of NOBr consumption?
Solution. By definition, the reaction rate is:
Mol/(l.s).
From the same definition it follows that the rate of NOBr consumption is equal to the rate of NO formation 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 equal to 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 reaction rate at [B] = 1.5 mol/L.
Solution. According to the law of mass action, at any moment of time the reaction rate is equal to:
.
By the time when [A] = 1.5 mol/l, 0.5 mol/l of substances A and B have reacted, so [B] = 3 – 0.5 = 2.5 mol/l. The rate constant is:
L/(mol. s).
By the time 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:
Mol/(l.s).
TASKS
1-1. How is the rate of the ammonia synthesis reaction 1/2 N 2 + 3/2 H 2 = NH 3 expressed in terms of 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 = NH 3 change if the reaction equation is written as N 2 + 3H 2 = 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 quantities 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 reaction products? (answer)
1-6. How many times will the rate of the gas-phase elementary reaction A = 2D increase when the pressure increases by 3 times? (answer)
1-7. Determine the order of the reaction if the rate constant has the dimension l 2 / (mol 2 . s). (answer)
1-8. The rate constant of a 2nd order gas reaction at 25 o C is equal to 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 the total pressure. (answer)
1-10. The rate constants for the forward and reverse reactions are 2.2 and 3.8 l/(mol. s). By which of the following mechanisms can these reactions occur: 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 a 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 equal to 1.5 mol/l. 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 equal to 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 the concentrations of A and B will the initial reaction rate be maximum at a fixed total pressure? (answer)
2. Kinetics of simple reactions
In this section, we will compose and solve kinetic equations for irreversible reactions of a whole order based on the law of mass action.
0th order reactions. The rate of these reactions does not depend on concentration:
,
where [A] is the concentration of the starting substance. Zero order occurs in heterogeneous and photochemical reactions.
1st order reactions. 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 this notation, the kinetic equation for the 1st order reaction and its solution have the form:
The solution to the kinetic equation is also written in another form, convenient for analyzing the reaction order:
.
The time during which half of substance A decays is called the half-life t 1/2. It is defined by the equation x(t 1/2) = a/2 and equal
2nd order reactions. In reactions of type A + B D + ..., the rate is directly proportional to the product of 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) identical 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-lives of substances A and B are 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 whose 14 C content was 72% of normal. How old is the tree?
Solution. Radioactive decay is a 1st order reaction. The rate constant is:
The lifetime of a tree can be found from solving the kinetic equation, taking into account the fact that [A] = 0.72. [A] 0:
Example 2-2. It has been established that a 2nd order reaction (one reagent) is 75% complete in 92 minutes 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. Let us write the solution of the kinetic equation for a 2nd order reaction with one reagent twice:
,
where, by condition, a= 0.24 M, t 1 = 92 min, x 1 = 0.75. 0.24 = 0.18 M, 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 we denote the half-life of A by t 1/2, and the decay time of A by 75% by 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 order of the reaction n.Solution. Let us write the solution of the kinetic equation for the reaction twice n-th order with one reagent:
and divide one expression by another. Constants k And a 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 to the kinetic equation, prove that for 1st order reactions the time t x, during which the degree of conversion of the starting substance reaches x, does not depend on the initial concentration. (answer)2-2. The first order reaction proceeds 30% in 7 minutes. 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 Chernobyl accident, - 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's assume that the body of a newborn child 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 o C is equal to 3.38. 10 -5 s -1 . Why equal to the period 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 varying amounts of the starting material. Will the tangents to the initial sections of the kinetic curves intersect at one point on the x-axis? Explain your answer. (answer)
2-8. The first order reaction A 2B occurs in the gas phase. The initial pressure is p 0 (B missing). Find the dependence of total pressure on time. After what time will the pressure increase by 1.5 times compared to the original? What is the progress of the reaction by this time? (answer)
2-9. The second order reaction 2A B occurs in the gas phase. The initial pressure is p 0 (B missing). Find the dependence of total pressure on time. After what time will the pressure decrease by 1.5 times compared to the original? What is the progress 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 o C. A solution was prepared containing 0.004 M nitroethane and 0.005 M NaOH. How long will it take for 90% of nitroethane to react?
2-13. The rate constant for the recombination of H + and FG - (phenylglyoxynate) ions into the UFG molecule at 298 K is equal to k= 10 11.59 l/(mol. s). Calculate the time it takes for the reaction to complete 99.999% if the initial concentrations of both ions are 0.001 mol/L. (answer)
2-14. The rate of oxidation of 1-butanol by hypochlorous acid does not depend on the alcohol concentration and is proportional to 2. How long will it take for the oxidation reaction at 298 K to complete 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 ethyl acetate solution is saponified by a 0.002 M NaOH solution by 10% in 23 minutes. After how many minutes will it be saponified to the same degree with a 0.005 M KOH solution? Consider that this reaction is of 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 hour, the concentration of substance A decreased to 0.020 mol/l. Calculate the rate constant and half-lives of both substances.
Irreversible reactions
1. How will the rate of 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?
2. How many times should the concentration of substance B 2 in the system 2A 2 (g) + B 2 (g) ® 2A 2 B (g) be increased so that when the concentration of substance A decreases by 4 times, the rate of the direct reaction does not change?
3. In the system CO + C1 2 ® COC1 2, the concentration of CO was increased from 0.03 to 0.12 mol/l, and the concentration of C1 2 - from 0.02 to 0.06 mol/l. How many times did the rate of the forward reaction increase?
4. How will the rate of the direct reaction N 2 (g) + 3H (g) ® 2 NH 3 change if a) the pressure in the system is increased by 3 times; b) reduce the volume by 2 times; c) increase the concentration of N 2 by 4 times?
5. How many times should the pressure be increased so that the rate of formation of NO 2 by the reaction 2NO + O 2 ® 2 NO 2 increases 1000 times?
6. The reaction between carbon monoxide (II) and chlorine proceeds according to the equation CO + C1 2 ® COC1 2. How will the reaction rate change when a) the CO concentration increases by 2 times; b) concentration of C1 2 2 times; c) the concentrations of both substances are 2 times?
7. The reaction takes place in the gas phase. The reaction involves two substances A and B. It is known that when the concentration of component A is doubled, the rate increases 2 times, and when the concentration of component B doubles, the rate increases 4 times. Write an equation for the reaction that occurs. How will the reaction rate change when the total pressure increases by 3 times?
8. The reaction rate of the interaction of substances A, B and D is studied. At constant concentrations of B and D, an increase in the concentration of substance A by 4 times leads to an increase in the rate by 16 times. If the concentration of substance B increases by 2 times at constant concentrations of substances A and D, then the speed increases only 2 times. At constant concentrations of A and B, doubling the concentration of substance D leads to a 4-fold increase in speed. Write an equation for the reaction.
9. Determine the rate of the chemical reaction A(g) + B(g) ® AB(g), if the reaction rate constant is 2 × 10 -1 l × mol -1 × s, and the concentrations of substances A and B are respectively 0.025 and 0 .01 mol/l. Calculate the reaction rate when the pressure increases by 3 times.
10. Find the value of the rate constant for the reaction A + 2B ® AB 2, if at the concentrations of substances A and B, respectively equal to 0.1 and 0.05 mol/l, the reaction rate is 7 × 10 -5 mol/(l×s) .
11. In a vessel with a volume of 2 liters, 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 react in accordance with the equation A + B = C. After 20 seconds, a gas with an amount of substance of 2 mol was formed in the system. Determine the average reaction rate. What quantities of substances A and B did not react?
12. The reaction between substances A and B is expressed by the equation A + B ® C. The initial concentrations are [A] O = 0.03 mol/l, [B] O = 0.05 mol/l. The reaction rate constant is 0.4. Find the initial reaction rate and the reaction rate after some time, when the concentration of the resulting substance C becomes equal to 0.01 mol/l.
13. Reaction between gaseous substances A and B are expressed by the equation A + B ® C. The initial concentrations of substances are [A] 0 = 0.03 mol/l, [B] 0 = 0.03 mol/l. The reaction rate constant is 0.1. After some time, the concentration of substance A decreased by 0.015 mol/l. How many times must the total pressure be increased so that the rate of a chemical reaction becomes equal to the original rate?
14. How many degrees must the temperature be increased for the reaction rate to increase 27 times? The temperature coefficient of the reaction rate is 3.
15. At 20 o C the reaction proceeds in 2 minutes. How long will this reaction take to occur a) at 50 o C, b) at 0 o C? The temperature coefficient of the reaction rate is 2.
16. At a temperature of 30 o C the reaction takes place in 25 minutes, and at 50 o C in 4 minutes. Calculate the temperature coefficient of the reaction rate.
17. The reaction rate at 0 o C is 1 mol/l×s. Calculate the rate of this reaction at 30 o C if the temperature coefficient of rate is 3.
18. With an increase in temperature by 50 o C, the reaction rate increased 32 times. Calculate the temperature coefficient of the rate of a chemical reaction.
19. Two reactions occur at 25 o C at the same rate. The temperature coefficient of the rate of the first reaction is 2.0, and the second is 2.5. Find the ratio of the rates of these reactions at 95 o C.
20. What is the activation energy of the reaction if, with an increase in temperature from 290 to 300 K, the reaction rate increases by 2 times?
21. How many times will the rate of a reaction occurring at 298 K increase if, as a result of using a catalyst, it was possible to reduce the activation energy by 4 kJ/mol?
22. What is the value of the activation energy of the reaction, the rate of which at 300 K is 10 times greater than at 280 K.
23. The activation energy of the reaction O 3 (g) +NO(g) ® O 2 (g) +NO 2 (g) is 40 kJ/mol. How many times will the reaction rate change when the temperature increases from 27 to 37 o C?
24. One catalyst reduces the activation energy at 300 K by 20 kJ/mol, and the other by 40 kJ/mol. Which catalyst is more effective? Justify the answer by calculating the ratio of reaction rates when using a particular catalyst.
25. At 150 o C, some reaction ends in 16 minutes. Taking the temperature coefficient of the reaction rate equal to 2.5, calculate the time after which this reaction will end if it is carried out a) at 200 o C, b) at 80 o C.
26. When the temperature increases by 10 o C, the rate of a chemical reaction doubles. At 20 o C it is equal to 0.04 mol/(l×s). What will be the rate of this reaction at a) 40 o C, b) 0 o C?
27. At 20 o C, the rate of the chemical reaction is 0.04 mol/(l×s). Calculate the rate of this reaction at 70 o C, if it is known that the activation energy is 70 kJ/mol.
28. Calculate the temperature coefficient of the reaction g, if the rate constant of this reaction at 120 o C is equal to 5.88 × 10 -4, and at 170 o C - 6.7 × 10 -2.
29. How many times will the rate of a chemical reaction change when the temperature increases from 300 K to 400 K, if the temperature coefficient g = 2? What is the activation energy for this reaction?
30. How many times will the rate of the chemical reaction A + 2B ® C increase when the pressure in the system increases 4 times and the temperature simultaneously increases by 40 o C. The reactants are gases. The temperature coefficient of the reaction is 2.
31. How many times will the rate of the chemical reaction 2A(g) + B(g) ® 2C(g) decrease when the pressure of all substances in the system decreases by 3 times and the temperature of the system decreases by 30 o C? The temperature coefficient of the reaction rate g is 2.
32. The reaction between gaseous substances A and B is expressed by the equation A + B ® C. The initial concentrations of the substances are [A] 0 = 0.05 mol/l and [B] 0 = 0.05 mol/l. After some time, the concentration of substances decreased by half. Determine how it is necessary to change the temperature so that the reaction rate becomes equal to the initial rate, if a) the temperature coefficient of the reaction is 2, b) the activation energy is 70 kJ, the reaction temperature is 27 o C?
33. It is known that when the temperature increases from 290 to 300 K, the rate of a chemical reaction doubles. Calculate the activation energy. How will the rate of this reaction change at 310 K if a catalyst is introduced into the system that lowers the activation energy of this reaction by 10 kJ/mol?
Chemical equilibrium
1. At a certain temperature, equilibrium in the 2NO 2 «2NO+O 2 system was established at concentrations = 0.4 mol/l, = 0.2 mol/l, = 0.1 mol/l. Find the equilibrium constant and the initial concentration of NO 2 if the initial oxygen concentration is zero. What conditions will promote a shift in equilibrium towards the formation of NO if the direct reaction is endothermic?
2. The equilibrium constant of the system A+B«C+D is equal to unity. What percentage of substance A will be converted if you mix 3 moles of substance A and 5 moles of substance B? What conditions will contribute to a shift in equilibrium towards the formation of B if the direct reaction is exothermic?
3. For the system
CO (G) + H 2 O (G) “CO 2 (G) + H 2 (G)
0 = 0 =0.03 mol/l, 0 = 0 =0. Calculate the equilibrium constant if the equilibrium concentration of carbon dioxide is 0.01 mol/l. What conditions will contribute to a shift in equilibrium towards the formation of CO if the direct reaction is endothermic?
4. For the system
2NO (G) +Cl 2 (G) “2NOCl (G)
0 =0.5 mol/l, 0 =0.2 mol/l, 0 =0 mol/l. Find the equilibrium constant if by the time of its onset 20% of nitric oxide has reacted. What conditions will contribute to a shift in equilibrium towards the formation of NOCl if the direct reaction is exothermic?
H 2(G) + I 2(G) «2HI (G) ,
if 1 mole of iodine and 2 moles of hydrogen are placed in a vessel with a capacity of 10 liters (KC = 50). What conditions will contribute to a shift in equilibrium towards the formation of iodine if the direct reaction is exothermic?
6. For the system CO (G) + H 2 O (G) “CO 2 (G) + H 2 (G), 0 = 0 =1 mol/l, 0 = 0 =0. Calculate the composition of the equilibrium mixture (% vol.), if the equilibrium constant K C = 1. What conditions will contribute to a shift in equilibrium towards the formation of hydrogen if the reverse reaction is exothermic?
7. In a closed vessel the reaction AB (G) “A (G) + B (G) takes place. Equilibrium constant K C =0.04. Find the initial concentration of AB if the equilibrium concentration of AB is 0.02 mol/l. What conditions will contribute to a shift in equilibrium towards the formation of A if the reverse reaction is exothermic?
8. In a closed vessel with a volume of 10 liters at a temperature of 800˚C, the equilibrium CaCO 3 (T) “CaO (T) + CO 2 (G) has been established. Equilibrium constant K P =300 kPa. What mass of CaCO 3 decomposed? What conditions will contribute to a shift in equilibrium towards the formation of carbon dioxide if the direct reaction is endothermic?
9. In a closed vessel at a certain temperature, the equilibrium Fe (T) + H 2 O (G) “FeO (T) + H 2 (G) has been established. Determine the fraction of reacted water if K P = 1 and the initial partial pressure of hydrogen is zero. What conditions will contribute to a shift in equilibrium towards the formation of hydrogen if the reverse reaction is exothermic?
10. Determine the equilibrium concentration of hydrogen in the system 2HI (G) “H 2 (G) + I 2 (G) if the initial concentration of HI was 0.05 mol/l and the equilibrium constant K C = 0.02. What conditions will contribute to a shift in equilibrium towards the formation of HI if the direct reaction is endothermic?
