5.2. KINETICS OF COMPLEX CHEMICAL REACTIONS

Task 1

1.What are the main kinetic relationships governing simple and complex reactions?

2.The quantum yield of a photochemical reaction is not equal to one. How can it be explained?

3.What chemical reactions are considered as reversible? What is a general formula for the rate of a reversible reaction?

4.Draw the kinetic curves for a first-order parallel reaction (k1 = k2).

5.In the reaction, 2Н2 + О2 → 2Н2О, the following kinetic equation is determined: w = k [H2] [O2]4/3. What is the total order of this reaction? Explain your answer. Suggest a mechanism for this reaction.

6.In the reaction of the conversion of γ-oxybutyric acid into lactone

the concentration of the latter in different moments of time has been changed as follows:

The initial concentration of acid was 0.1823 mol/L, the equilibrium

concentration of lacton, x∞ = 0.1328 mol/L. Determine the kinetic constants of the direct and reverse reactions.

Task 2

1.Can it be decided whether the reaction is complex or simple based on variation of the reaction order?

2.What are free radicals?

3.What equations are used for calculation of the rate constants of reversible first-order reactions?

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4.Draw the curves of the dependence of the concentration of the substances, A and B, on time for parallel reactions given below in the case when k1 > k2.

k1 B A

2 C

5.The reaction of the photochemical chlorination of formic acid in a gas phase can be described by the following scheme:

Cl2 + hν → 2Cl∙

Cl∙ + НСООН → НCl + НООС∙

Cl2 + НООС∙→ НCl + СО2 + Сl∙

Cl∙ + wall → Cl2 (ads.)

Show the stages of chain initiation, chain propagation, and chain termination.

6.The following experimental data were obtained for the reaction of isomerization of β-oxycrotonic ester into acetoacetic ester at 25°C:

The equilibrium concentration of acetoacetic ester (x∞) is 0.288 mol/L. Calculate the rate constants of the direct and reverse reactions.

Task 3

1.What postulates are used upon deducing the kinetic equations for reversible and parallel reactions?

2.What is the main quantitative characteristic of photochemical reactions?

3.Write down the kinetic equation for the following reaction:

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5. Prove that the kinetics of the reaction

kk

А1 →В 2 →С

is described by the equation

− dd[Aτ ] = dd[Cτ ]

6.The rate of the chemical transformation of the substance, A, is characterized by the equation

− d[Adτ ] = (k1 + k2 + k3 )[A].

Task 5

1.What is meant by the mechanism of a chemical reaction?

2.Which of the chemical reactions are called consecutive? Give examples.

3.The reaction

CH4 + Cl2 + hν → CH3Cl + HCl

proceeds via a chain mechanism according to the following scheme: Cl2 + hν → 2Cl∙

CH4 + Cl∙ → СH3∙ + HCl

СH3∙ + Cl2 → СH3Cl + Сl∙

СH3∙ + СH3∙ → C2H6

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4. The rate of a chemical reaction is described by the equation

ddτx = k1(a − x)(b − x) −k2 (c + x) .

To which type of reactions does this reaction belong? Give its schematic representation.

5.Write down the differential equations of the rate of the change in the concentration of the reactant, A, and the rate of accumulation of the reaction products, B and C, for the following reaction:

6. The quantum yield of the acetone photolysis

hν

(CH3 )2 CO → C2H6 +CO

upon the light exposure with a wavelength of 300 nm makes 0.2. If the intensity of the absorbed light equals 10–2 J/s, then how many moles of carbon monoxide is formed per one second?

Task 7

1.What values can take the order of a complex reaction?

2.Give the scheme of an unbranched chain reaction.

3.Can the kinetic constant, k1, be determined in the reaction,

k1 B

A

2 C ,

by measuring only the current concentrations of A and B?

4.By what kind of an equation is the overall reaction rate described in the case of the following parallel reactions:

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k

A 1 →B

k

A +C 2 → B + D ?

5. Decomposition of N2O5 proceeds through the following mechanism:

k

1 →

N2O5 ← NO2 + NO3 k2

k

NO2 + NO3 2 →NO2 +O2 + NO

Assuming that the concentration of NO3 is constant, derive the kinetic equation for the decomomposition of N2O5.

6. Fot the reaction

the rate constants, k1 and k2, at 25°С equal 0.00685 and 0.00254 min-1, respectively. If the initial concentration of acid is 0.1823 mol/L, then what fractional amount of the starting material is converted into lactone in 100 min from the reaction start?

Task 8

1.What is called "quantum yield of a photochemical reaction"? What range of values can it take?

2.How can complex reactions be classified based on the mutual influence of their separate steps?

3.Illustrate schematically kinetic curves for a first-order reversible reaction.

4.A branched chain reaction of the oxidation of hydrogen includes the following steps:

H∙ + O2 → OH∙ + ∙O∙

∙O∙ + H2 → OH∙ + H∙

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kk

А1→В 2 →С

stipulating that k1 > k2.

4. What equation does describe the rate of the reversible reaction,

5.Designating the change in the concentration of phenol via x and the initial concentration of phenol and acid via а and b, respectively, write down the rate equation for the nitration reaction of phenol, which proceeds by the following scheme:

6.Calculate the rate constants of the direct and reverse reactions for the reversible first-order reaction

Upon reaching the equilibrium state, 23.2% of ammonium thiocyanate is converted into thiourea.

Task 10

1.How can we reveal that a particular chemical reaction has a complex mechanism?

2.Name the reasons, by which chain reactions are initiated.

3.What data are required for the calculation of the k1 value in the reaction

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3.Represent schematically the kinetic curves for parallel reaction of the first order in the case when k1 = k2.

4.The rate of a particular reaction is described by the equation,

ddτx = k1(a − x)2 −(b − x) −k2 (c + x)(c + x) .

To which type of complex reactions does it belong? Give its schematic representation.

5. Prove that the equality,

− dd[Aτ ]= dd[Cτ ],

is applicable under the stationary conditions to the reaction,

k k .

A 1→B 2 →C

6. For the reaction

The initial concentration of A is а = 0.1823 mol/L. Determine the rate constants for the direct and reverse reactions.

Task 15

1.What is “the mechanism of a chemical reaction”?

2.What are the main points of the method of stationary concentrations?

3.What are the reasons for chain termination in the reactions, which proceeds by a chain mechanism?

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4. Write down the differential equation describing the rate of the reaction,

5. For the reaction

write down the relationships between the rates and the rate constants, k1 + k2, under the condition of inequality of the initial concentrations of reactants.

6.What will be the concentration of А in 4.3 min after the start in the reaction

Ak1 k2 B

C

k3 D

considering that its initial concentration was 44.7 mol/L, and the sum, k1 + k2 + k3, equals 0.115 min–1.

Task 16

1.Name differences in the kinetics of simple and complex reactions.

2.What signs indicate that the reaction goes by a chain mechanism?

3.What equation is used for calculation of the rate constants of first-order parallel reactions?

4.Show graphically the change in the concentration of reagents over time in a consecutive reaction,

Ak1→ B k2 → C .

5.The rate of some chemical reaction is described by the following equation:

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