Chapter 3 Solutions — Chemical Kinetics

Exercises

1. 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
   • (ii) H₂O₂(aq) + 3I⁻(aq) + 2H⁺ -> 2H₂O(l) + I₃⁻ Rate = k[H₂O₂][I⁻]
   • (iii) CH₃CHO(g) -> CH₄(g) + CO(g) Rate = k[CH₃CHO]^(3/2)
   • (iv) C₂H₅Cl(g) -> C₂H₄(g) + HCl(g) Rate = k[C₂H₅Cl]
2. 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 when [A] = 0.1 mol L⁻¹, [B] = 0.2 mol L⁻¹. Calculate the rate of reaction after [A] is reduced to 0.06 mol L⁻¹.
3. 3.
   The decomposition of NH₃ on platinum surface is zero order reaction. What are the rates of production of N₂ and H₂ if k = 2.5 × 10⁻⁴ mol L⁻¹ 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). The rate of reaction is followed by increase in pressure in a closed vessel, so the rate can also be expressed in terms of the partial pressure of dimethyl ether, i.e., Rate = k(p_CH₃OCH₃)^(3/2). If the pressure is measured in bar and time in minutes, then what…
5. 5.
   Mention the factors that affect the rate of a chemical reaction.
6. 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?
7. 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?
8. 8.
   In a pseudo first order reaction in water, the following results were obtained: t/s: 0, 30, 60, 90 [A]/mol L⁻¹: 0.55, 0.31, 0.17, 0.085 Calculate the average rate of reaction between the time interval 30 to 60 seconds.
9. 9.
   A reaction is first order in A and second order in B.

   • (i) Write the differential rate equation.
   • (ii) How is the rate affected on increasing the concentration of B three times?
   • (iii) How is the rate affected when the concentrations of both A and B are doubled?
10. 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: A/mol L⁻¹: 0.20 | 0.20 | 0.40 B/mol L⁻¹: 0.30 | 0.10 | 0.05 r₀/mol L⁻¹ s⁻¹: 5.07 × 10⁻⁵ | 5.07 × 10⁻⁵ | 1.43 × 10⁻⁴ What is the order of the reaction with respect to A and B?
11. 11.
    The following results have been obtained during the kinetic studies of the reaction: 2A + B -> C + D Exp I: [A]=0.1, [B]=0.1, rate=6.0 × 10⁻³ mol L⁻¹ min⁻¹ Exp II: [A]=0.3, [B]=0.2, rate=7.2 × 10⁻² mol L⁻¹ min⁻¹ Exp III: [A]=0.3, [B]=0.4, rate=2.88 × 10⁻¹ mol L⁻¹ min⁻¹ Exp IV: [A]=0.4, [B]=0.1, rate=2.40 × 10⁻² mol L⁻¹ min⁻¹ Determine the rate law and the rate constant for the reaction.
12. 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: Exp I: [A]=0.1, [B]=0.1, rate=2.0 × 10⁻² mol L⁻¹ min⁻¹ Exp II: [A]=?, [B]=0.2, rate=4.0 × 10⁻² mol L⁻¹ min⁻¹ Exp III: [A]=0.4, [B]=0.4, rate=? Exp IV: [A]=?, [B]=0.2, rate=2.0 × 10⁻² mol L⁻¹ min⁻¹
13. 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
14. 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.
15. 15.
    The experimental data for decomposition of N₂O₅ [2N₂O₅ -> 4NO₂ + O₂] in gas phase at 318 K are given below: t/s: 0, 400, 800, 1200, 1600, 2000, 2400, 2800, 3200 10² × [N₂O₅]/mol L⁻¹: 1.63, 1.36, 1.14, 0.93, 0.78, 0.64, 0.53, 0.43, 0.35

    • (i) Plot [N₂O₅] against t.
    • (ii) Find the half-life period for the reaction.
    • (iii) Draw a graph between log[N₂O₅] and t.
    • (iv) What is the rate law?
    • (v) Calculate…
16. 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?
17. 17.
    During nuclear explosion, one of the products is ⁹⁰Sr with half-life of 28.1 years. If 1 mg of ⁹⁰Sr was absorbed in the bones of a newly born baby instead of calcium, how much of it will remain after 10 years and 60 years if it is not lost metabolically.
18. 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.
19. 19.
    A first order reaction takes 40 min for 30% decomposition. Calculate t_(1/2).
20. 20.
    For the decomposition of azoisopropane to hexane and nitrogen at 543 K, the following data are obtained: t(sec): 0, 360, 720 P(mm Hg): 35.0, 54.0, 63.0 Calculate the rate constant.
21. 21.
    The following data were obtained during the first order thermal decomposition of SO₂Cl₂ at a constant volume: SO₂Cl₂(g) -> SO₂(g) + Cl₂(g) Expt 1: Time = 0 s, Total pressure = 0.5 atm Expt 2: Time = 100 s, Total pressure = 0.6 atm Calculate the rate of the reaction when total pressure is 0.65 atm.
22. 22.
    The rate constant for the decomposition of N₂O₅ at various temperatures is given below: T/°C: 0, 20, 40, 60, 80 10⁵ × k/s⁻¹: 0.0787, 1.70, 25.7, 178, 2140 Draw a graph between ln k and 1/T and calculate the values of A and Ea. Predict the rate constant at 30°C and 50°C.
23. 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.
24. 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.
25. 25.
    Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law, with t_(1/2) = 3.00 hours. What fraction of sample of sucrose remains after 8 hours?
26. 26.
    The decomposition of hydrocarbon follows the equation k = (4.5 × 10¹¹ s⁻¹) e^(-28000K/T). Calculate Ea.
27. 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. Calculate Ea for this reaction and at what temperature will its half-period be 256 minutes?
28. 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?
29. 29.
    The time required for 10% completion of a first order reaction at 298 K is equal to that required for its 25% completion at 308 K. If the value of A is 4 × 10¹⁰ s⁻¹, calculate k at 318 K and Ea.
30. 30.
    The rate of a reaction quadruples when the temperature changes from 293 K to 313 K. Calculate the energy of activation of the reaction assuming that it does not change with temperature.