The rate of reaction 2a did not change. Problem solving standards
Speed chemical reactions The branch of chemistry that studies the rate and mechanism of chemical reactions is called chemical kinetics. The rate of a chemical reaction is the number of elementary acts of interaction per unit of time in a unit of reaction space. This definition is valid for both homogeneous and heterogeneous processes. In the first case, the reaction space is the volume of the reaction vessel, and in the second, 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 speed 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 decision 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? 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.
LESSON 10 10th grade(first year of study)
Fundamentals of chemical kinetics. State of chemical equilibrium Plan
1. Chemical kinetics and the field of its study.
2. Rate of homogeneous and heterogeneous reactions.
3. Dependence of the reaction rate on various factors: the nature of the reactants, the concentration of the reagents (law of mass action), temperature (van't Hoff rule), catalyst.
4. Reversible and irreversible chemical reactions.
5. Chemical equilibrium and conditions for its displacement. Le Chatelier's principle.
The branch of chemistry that studies the rates and mechanisms of chemical reactions is called chemical kinetics. One of the main concepts in this section is the concept of the rate of a chemical reaction. Some chemical reactions occur almost instantly (for example, a neutralization reaction in solution), others take thousands of years (for example, the transformation of graphite into clay during the weathering of rocks).
The rate of a homogeneous reaction is the amount of a substance that reacts or is formed as a result of a reaction per unit time per unit volume of the system:
In other words, the rate of a homogeneous reaction is equal to the change in the molar concentration of any of the reacting substances per unit time. The reaction rate is a positive quantity, therefore, when expressing it through a change in the concentration of the reaction product, a “+” sign is given, and when the reagent concentration changes, a “–” sign is given.
The rate of a heterogeneous reaction is the amount of substance that reacts or is formed as a result of a reaction per unit time per unit surface area of the phase:
The most important factors influencing the rate of a chemical reaction are the nature and concentration of the reagents, temperature, and the presence of a catalyst.
Influence nature of the reagents manifests itself in the fact that, under the same conditions, different substances interact with each other at different rates, for example:
When increasing reagent concentrations the number of collisions between particles increases, which leads to an increase in the reaction rate. The quantitative dependence of the reaction rate on the concentration of reagents is expressed by the law of effective mass (K.M. Guldberg and P. Waage, 1867; N.I. Beketov , 1865). The rate of a homogeneous chemical reaction at a constant temperature is directly proportional to the product of the concentration of the reacting substances in powers equal to their stoichiometric coefficients (concentrations of solid substances are not taken into account), for example:
where A and B are gases or liquids, k – reaction rate constant equal to the reaction rate at a reactant concentration of 1 mol/l. Constant k depends on the properties of the reacting substances and temperature, but does not depend on the concentration of the substances.
Dependence of reaction speed on temperature is described by the experimental rule of Van t-Goff (1884). When the temperature increases by 10°, the rate of most chemical reactions increases by 2–4 times:
where is the temperature coefficient.
Catalyst is a substance that changes the rate of a chemical reaction, but is not consumed as a result of this reaction. There are positive catalysts (specific and universal), negative (inhibitors) and biological (enzymes, or enzymes). The change in reaction rate in the presence of catalysts is called catalysis. There are homogeneous and heterogeneous catalysis. If the reactants and the catalyst are in the same state of aggregation, catalysis is homogeneous; in different – heterogeneous.
Homogeneous catalysis:
heterogeneous catalysis:
The mechanism of action of catalysts is very complex and not fully understood. There is a hypothesis about the formation of intermediate compounds between the reagent and the catalyst:
A + cat. ,
B AB + cat.
Promoters are used to enhance the action of catalysts; There are also catalytic poisons that weaken the effect of catalysts.
The rate of a heterogeneous reaction is affected by interfacial area(the degree of grinding of the substance) and the rate of supply of reagents and removal of reaction products from the phase interface.
All chemical reactions are divided into two types: reversible and irreversible.
Chemical reactions that proceed in only one direction are called irreversible., i.e. the products of these reactions do not interact with each other to form the starting materials. Conditions for the irreversibility of a reaction are the formation of a precipitate, gas or weak electrolyte. For example:
BaCl 2 + H 2 SO 4 = BaSO 4 + 2HCl,
K 2 S + 2HCl = 2KCl + H 2 S,
HCl + NaOH = NaCl + H 2 O.
Reversible reactions are those that occur simultaneously in the forward and reverse directions., For example:
When a reversible chemical reaction occurs, the rate of the direct reaction initially has a maximum value, and then decreases due to a decrease in the concentration of the starting substances. The reverse reaction, on the contrary, at the initial moment of time has a minimum speed, which gradually increases. Thus, at a certain point in time there comes state chemical equilibrium , at which the rate of the forward reaction is equal to the rate of the reverse reaction. The state of chemical equilibrium is dynamic - both forward and reverse reactions continue to occur, but since their rates are equal, the concentrations of all substances in the reaction system do not change. These concentrations are called equilibrium.
The ratio of the rate constants of forward and reverse reactions is a constant value and is called the equilibrium constant ( TO R ) . Solid concentrations are not included in the equilibrium constant expression. The equilibrium constant of the reaction depends on temperature and pressure, but does not depend on the concentration of the reactants and on the presence of a catalyst, which accelerates the progress of both forward and reverse reactions. The more TO p, the higher the practical yield of reaction products. If TO p > 1, then the reaction products predominate in the system; If TO R< 1, в системе преобладают реагенты.
Chemical equilibrium is mobile, i.e. when external conditions change, the speed of the forward or reverse reaction may increase. The direction of the equilibrium shift is determined by the principle formulated by the French scientist Le Chatelier in 1884. If an external influence is exerted on an equilibrium system, then the equilibrium shifts towards the reaction that counteracts this influence. Equilibrium shifts are affected by changes in reactant concentrations, temperature, and pressure.
An increase in the concentration of reagents and the removal of products lead to a shift in equilibrium towards the direct reaction.
When the system is heated, the equilibrium shifts towards the endothermic reaction, and when cooled, towards the exothermic reaction.
For reactions involving gaseous substances, an increase in pressure shifts the equilibrium towards a reaction that occurs with a decrease in the number of gas molecules. If the reaction proceeds without changing the number of molecules of gaseous substances, then the change in pressure does not in any way affect the shift in equilibrium.
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 a reaction and the time it takes to occur are inversely related proportional dependence. 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, 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).
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 at 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 tests 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 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 No. 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 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 velocity 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 for the content of the drug in the human body to decrease 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 research it was found that within 24 hours 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 an accident Chernobyl nuclear power plant(1986) there was a release of the radionuclide Cs-137, 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 of pesticide hydrolysis at 25 0 C is equal to 0.32 s - 1. The initial concentration of the pesticide in the sample was 2.5 mol/l. Calculate how long it 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.
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 in 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 the 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, based on the law of mass action, we will compose and solve kinetic equations for irreversible reactions of a whole order.
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 life time 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 the Chernobyl accident, is 29.7 years. After what time will the amount of this isotope be less than 1% of the original? (answer)
2-4. The half-life of the radioactive isotope 90 Sr, which enters the atmosphere when nuclear tests, - 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 . What is the half-life of N 2 O 5? What will be the pressure in the system after a) 10 s, b) 10 min, if the initial pressure was 500 mm Hg? Art. (answer)
2-7. The first order reaction is carried out with 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 an 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.