4.1 From the rate expression for the following reactions, determine their order of reaction and the dimensions of the rate constants.

(i) 3NO(g) → N2O (g) Rate = k[NO]2

4.2 For the reaction: 2A + B → A2B the rate = k[A][B]2 with k = 2.0 × 10–6 mol–2 L2 s–1. Calculate the initial rate of the reaction

4.3 The decomposition of NH3 on the platinum surface is zero order reaction. What are the rates of production of N2 and H2 if k = 2.5 × 10–4 mol–1 L s–1?

4.4 The decomposition of dimethyl ether leads to the formation of CH4, H2 and CO and the reaction rate is given by Rate = k [CH3OCH3]3/2

4.5 Mention the factors that affect the rate of a chemical reaction.

4.6 A reaction is second order with respect to a reactant. How is the rate of reaction affected if the concentration of the reactant is

(i) doubled (ii) reduced to half?

4.7 What is the effect of temperature on the rate constant of a reaction? How can this effect of temperature on rate constant be represented quantitatively?

4.8 In a pseudo first order hydrolysis of ester in water, the following results were obtained:

(i) Calculate the average rate of reaction between the time interval 30 to 60 seconds.

4.9 A reaction is first order in A and second order in B.

(i) Write the differential rate equation.

4.10 In a reaction between A and B, the initial rate of reaction (r0) was measured for different initial concentrations of A and B as given below:

4.11 The following results have been obtained during the kinetic studies of the reaction:

2A + B →C + D

4.12 The reaction between A and B is first order with respect to A and zero order with respect to B. Fill in the blanks in the following table:

4.13 Calculate the half-life of a first order reaction from their rate constants given below:

(i) 200 s–1 (ii) 2 min–1 (iii) 4 years–1

4.14 The half-life for radioactive decay of 14C is 5730 years. An archaeological artifact containing wood had only 80% of the 14C found in a living tree. Estimate the age of the sample.

4.15 The experimental data for decomposition of N2O5

[2N2O5 → 4NO2 + O2]

in gas phase at 318K are given below:

(i) Plot [N2O5] against t.

4.16 The rate constant for a first order reaction is 60 s–1. How much time will it take to reduce the initial concentration of the reactant to its 1/16th value?

4.17 During nuclear explosion, one of the products is 90Sr with half-life of 28.1 years. If 1µg of 90Sr was absorbed in the bones of a newly born baby instead of calcium,

4.18 For a first order reaction, show that time required for 99% completion is twice the time required for the completion of 90% of reaction.

4.19 A first order reaction takes 40 min for 30% decomposition. Calculate t1/2.

4.20 For the decomposition of azoisopropane to hexane and nitrogen at 543 K, the following data are obtained.

4.21 The following data were obtained during the first order thermal decomposition of SO2Cl2 at a constant volume.

4.22 The rate constant for the decomposition of N2O5 at various temperatures is given below:

Draw a graph between ln k and 1/T

4.23 The rate constant for the decomposition of hydrocarbons is 2.418 × 10–5 s–1 at 546 K. If the energy of activation is 179.9 kJ/mol, what will be the value of pre-exponential factor.

4.24 Consider a certain reaction A → Products with k = 2.0 × 10–2 s–1. Calculate the concentration of A remaining after 100 s if the initial concentration of A is 1.0 mol L–1.

4.25 Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law, with t1/2 = 3.00 hours.

4.26 The decomposition of hydrocarbon follows the equation k = (4.5 × 1011 s–1) e-28000K/T Calculate Ea.

4.27 The rate constant for the first order decomposition of H2O2 is given by the following equation:

log k = 14.34 – 1.25 × 104 K/T

4.28 The decomposition of A into product has value of k as 4.5 × 103 s–1 at 10°C and energy of activation 60 kJ mol–1. At what temperature would k be 1.5 × 104 s–1?

4.29 The time required for 10% completion of a first order reaction at 298K is equal to that required for its 25% completion at 308K.

4.30 The rate of a reaction quadruples when the temperature changes from 293 K to 313 K.