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Chemistry · Textbook solutions

Chemical Kinetics

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 49 questions

Worked Examples

10 q

Solved Examples

Worked · 10
  1. Eg 3.1
    From the concentrations of C4H9Cl\text{C}_4\text{H}_9\text{Cl} (butyl chloride) at different times given below, calculate the average rate of the reaction: C4H9Cl+H2O→C4H9OH+HCl\text{C}_4\text{H}_9\text{Cl} + \text{H}_2\text{O} \rightarrow \text{C}_4\text{H}_9\text{OH} + \text{HCl} during different intervals of time.
    t/st/\text{s}050100150200300400700800
    [C4H9Cl]/mol L−1[\text{C}_4\text{H}_9\text{Cl}]/\text{mol L}^{-1}0.1000.09050.08200.07410.06710.05490.04390.02100.017
  2. Eg 3.2
    The decomposition of N2O5\text{N}_2\text{O}_5 in CCl4\text{CCl}_4 at 318K has been studied by monitoring the concentration of N2O5\text{N}_2\text{O}_5 in the solution. Initially the concentration of N2O5\text{N}_2\text{O}_5 is 2.33 mol L−12.33\,\text{mol L}^{-1} and after 184 minutes, it is reduced to 2.08 mol L−12.08\,\text{mol L}^{-1}. The reaction takes place according to the equation 2 N2O5 (g)→4 NO2 (g)+O2 (g)2\,\text{N}_2\text{O}_5\,(g) \rightarrow 4\,\text{NO}_2\,(g) + \text{O}_2\,(g) Calculate the average rate of this reaction in terms of hours, minutes and seconds. What is the rate of production of NO2\text{NO}_2 during this period?
  3. Eg 3.3
    Calculate the overall order of a reaction which has the rate expression (a) Rate =k [A]1/2 [B]3/2= k\,[\text{A}]^{1/2}\,[\text{B}]^{3/2} (b) Rate =k [A]3/2 [B]−1= k\,[\text{A}]^{3/2}\,[\text{B}]^{-1}
  4. Eg 3.4
    Identify the reaction order from each of the following rate constants. (i) k=2.3×10−5 L mol−1s−1k = 2.3 \times 10^{-5}\,\text{L mol}^{-1}\text{s}^{-1} (ii) k=3×10−4 s−1k = 3 \times 10^{-4}\,\text{s}^{-1}
  5. Eg 3.5
    The initial concentration of N2O5\text{N}_2\text{O}_5 in the following first order reaction N2O5(g)→2 NO2(g)+12O2(g)\text{N}_2\text{O}_5(g) \rightarrow 2\,\text{NO}_2(g) + \tfrac{1}{2}\text{O}_2(g) was 1.24×10−2 mol L−11.24 \times 10^{-2}\,\text{mol L}^{-1} at 318 K318\,\text{K}. The concentration of N2O5\text{N}_2\text{O}_5 after 60 minutes was 0.20×10−2 mol L−10.20 \times 10^{-2}\,\text{mol L}^{-1}. Calculate the rate constant of the reaction at 318 K318\,\text{K}.
  6. Eg 3.6
    The following data were obtained during the first order thermal decomposition of N2O5(g)\text{N}_2\text{O}_5(g) at constant volume: 2N2O5(g)→2N2O4(g)+O2(g)2\text{N}_2\text{O}_5(g) \rightarrow 2\text{N}_2\text{O}_4(g) + \text{O}_2(g)
    S.No.Time/sTotal Pressure/(atm)
    1.000.50.5
    2.1001000.5120.512
    Calculate the rate constant.
  7. Eg 3.7
    A first order reaction is found to have a rate constant, k=5.5×10−14 s−1k = 5.5 \times 10^{-14}\,\text{s}^{-1}. Find the half-life of the reaction.
  8. Eg 3.8
    Show that in a first order reaction, time required for completion of 99.9% is 10 times of half-life (t1/2)(t_{1/2}) of the reaction.
  9. Eg 3.9
    The rate constants of a reaction at 500K and 700K are 0.02 s−10.02\,\text{s}^{-1} and 0.07 s−10.07\,\text{s}^{-1} respectively. Calculate the values of EaE_a and AA.
  10. Eg 3.10
    The first order rate constant for the decomposition of ethyl iodide by the reaction C2H5I(g)→C2H4(g)+HI(g)\text{C}_2\text{H}_5\text{I(g)} \rightarrow \text{C}_2\text{H}_4\text{(g)} + \text{HI(g)} at 600K is 1.60×10−5 s−11.60 \times 10^{-5}\,\text{s}^{-1}. Its energy of activation is 209 kJ/mol209\,\text{kJ/mol}. Calculate the rate constant of the reaction at 700K.

Intext Questions

9 q
  1. Intext 3.1
    For the reaction R→P\text{R} \rightarrow \text{P}, the concentration of a reactant changes from 0.03M to 0.02M in 25 minutes. Calculate the average rate of reaction using units of time both in minutes and seconds.
  2. Intext 3.2
    In a reaction, 2A→2\text{A} \rightarrow Products, the concentration of A decreases from 0.5 mol L−10.5\,\text{mol L}^{-1} to 0.4 mol L−10.4\,\text{mol L}^{-1} in 10 minutes. Calculate the rate during this interval?
  3. Intext 3.3
    For a reaction, A+B→Product\text{A} + \text{B} \rightarrow \text{Product}; the rate law is given by, r=k [A]1/2[B]2r = k\,[\text{A}]^{1/2}[\text{B}]^{2}. What is the order of the reaction?
  4. Intext 3.4
    The conversion of molecules X to Y follows second order kinetics. If concentration of X is increased to three times how will it affect the rate of formation of Y ?
  5. Intext 3.5
    A first order reaction has a rate constant 1.15×10−3 s−11.15 \times 10^{-3}\,\text{s}^{-1}. How long will 5 g5\,\text{g} of this reactant take to reduce to 3 g3\,\text{g}?
  6. Intext 3.6
    Time required to decompose SO2Cl2\text{SO}_2\text{Cl}_2 to half of its initial amount is 60 minutes. If the decomposition is a first order reaction, calculate the rate constant of the reaction.
  7. Intext 3.7
    What will be the effect of temperature on rate constant ?
  8. Intext 3.8
    The rate of the chemical reaction doubles for an increase of 10K in absolute temperature from 298K. Calculate EaE_a.
  9. Intext 3.9
    The activation energy for the reaction 2 HI(g)→H2+I2(g)2\,\text{HI(g)} \rightarrow \text{H}_2 + \text{I}_2\text{(g)} is 209.5 kJ mol−1209.5\,\text{kJ mol}^{-1} at 581K. Calculate the fraction of molecules of reactants having energy equal to or greater than activation energy?

Exercises

30 q
  1. Ex 3.1
    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)3\text{NO}(g) \rightarrow \text{N}_2\text{O}(g) Rate =k[NO]2= k[\text{NO}]^2 (ii) H2O2(aq)+3I−(aq)+2H+→2H2O(l)+I3−\text{H}_2\text{O}_2(aq) + 3\text{I}^-(aq) + 2\text{H}^+ \rightarrow 2\text{H}_2\text{O}(l) + \text{I}_3^- Rate =k[H2O2][I−]= k[\text{H}_2\text{O}_2][\text{I}^-] (iii) CH3CHO(g)→CH4(g)+CO(g)\text{CH}_3\text{CHO}(g) \rightarrow \text{CH}_4(g) + \text{CO}(g) Rate =k[CH3CHO]3/2= k[\text{CH}_3\text{CHO}]^{3/2} (iv) C2H5Cl(g)→C2H4(g)+HCl(g)\text{C}_2\text{H}_5\text{Cl}(g) \rightarrow \text{C}_2\text{H}_4(g) + \text{HCl}(g) Rate =k[C2H5Cl]= k[\text{C}_2\text{H}_5\text{Cl}]
  2. Ex 3.2
    For the reaction: 2A+B→A2B2\text{A} + \text{B} \rightarrow \text{A}_2\text{B} the rate =k[A][B]2= k[\text{A}][\text{B}]^2 with k=2.0×10−6 mol−2 L2 s−1k = 2.0 \times 10^{-6}\,\text{mol}^{-2}\,\text{L}^{2}\,\text{s}^{-1}. Calculate the initial rate of the reaction when [A]=0.1 mol L−1[\text{A}] = 0.1\,\text{mol L}^{-1}, [B]=0.2 mol L−1[\text{B}] = 0.2\,\text{mol L}^{-1}. Calculate the rate of reaction after [A][\text{A}] is reduced to 0.06 mol L−10.06\,\text{mol L}^{-1}.
  3. Ex 3.3
    The decomposition of NH3\text{NH}_3 on platinum surface is zero order reaction. What are the rates of production of N2\text{N}_2 and H2\text{H}_2 if k=2.5×10−4 mol−1 L s−1k = 2.5 \times 10^{-4}\,\text{mol}^{-1}\,\text{L}\,\text{s}^{-1}?
  4. Ex 3.4
    The decomposition of dimethyl ether leads to the formation of CH4\text{CH}_4, H2\text{H}_2 and CO\text{CO} and the reaction rate is given by Rate =k [CH3OCH3]3/2= k\,[\text{CH}_3\text{OCH}_3]^{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(pCH3OCH3)3/2= k\left(p_{\text{CH}_3\text{OCH}_3}\right)^{3/2} If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constants?
  5. Ex 3.5
    Mention the factors that affect the rate of a chemical reaction.
  6. Ex 3.6
    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. Ex 3.7
    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. Ex 3.8
    In a pseudo first order reaction in water, the following results were obtained:
    t/st/\text{s}0306090
    [A]/mol L−1[\text{A}]/\text{mol L}^{-1}0.550.310.170.085
    Calculate the average rate of reaction between the time interval 30 to 60 seconds.
  9. Ex 3.9
    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. Ex 3.10
    In a reaction between A and B, the initial rate of reaction (r0)(r_0) was measured for different initial concentrations of A and B as given below:
    A/mol L−1\text{A}/\text{mol L}^{-1}0.200.200.40
    B/mol L−1\text{B}/\text{mol L}^{-1}0.300.100.05
    r0/mol L−1s−1r_0/\text{mol L}^{-1}\text{s}^{-1}5.07×10−55.07 \times 10^{-5}5.07×10−55.07 \times 10^{-5}1.43×10−41.43 \times 10^{-4}
    What is the order of the reaction with respect to A and B?
  11. Ex 3.11
    The following results have been obtained during the kinetic studies of the reaction: 2A+B→C+D2\text{A} + \text{B} \rightarrow \text{C} + \text{D}
    Experiment[A]/mol L−1[\text{A}]/\text{mol L}^{-1}[B]/mol L−1[\text{B}]/\text{mol L}^{-1}Initial rate of formation of D/mol L−1min−1\text{D}/\text{mol L}^{-1}\text{min}^{-1}
    I0.10.16.0×10−36.0 \times 10^{-3}
    II0.30.27.2×10−27.2 \times 10^{-2}
    III0.30.42.88×10−12.88 \times 10^{-1}
    IV0.40.12.40×10−22.40 \times 10^{-2}
    Determine the rate law and the rate constant for the reaction.
  12. Ex 3.12
    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:
    Experiment[A]/mol L−1[\text{A}]/\text{mol L}^{-1}[B]/mol L−1[\text{B}]/\text{mol L}^{-1}Initial rate/mol L−1min−1\text{mol L}^{-1}\text{min}^{-1}
    I0.10.12.0×10−22.0 \times 10^{-2}
    II-0.24.0×10−24.0 \times 10^{-2}
    III0.40.4-
    IV-0.22.0×10−22.0 \times 10^{-2}
  13. Ex 3.13
    Calculate the half-life of a first order reaction from their rate constants given below: (i) 200 s−1200\,\text{s}^{-1} (ii) 2 min−12\,\text{min}^{-1} (iii) 4 years−14\,\text{years}^{-1}
  14. Ex 3.14
    The half-life for radioactive decay of 14C^{14}\text{C} is 5730 years. An archaeological artifact containing wood had only 80% of the 14C^{14}\text{C} found in a living tree. Estimate the age of the sample.
  15. Ex 3.15
    The experimental data for decomposition of N2O5\text{N}_2\text{O}_5 [2N2O5→4NO2+O2][2\text{N}_2\text{O}_5 \rightarrow 4\text{NO}_2 + \text{O}_2] in gas phase at 318K are given below:
    t/st/\text{s}0400800120016002000240028003200
    102×[N2O5]/mol L−110^2 \times [\text{N}_2\text{O}_5]/\text{mol L}^{-1}1.631.361.140.930.780.640.530.430.35
    (i) Plot [N2O5][\text{N}_2\text{O}_5] against tt. (ii) Find the half-life period for the reaction. (iii) Draw a graph between log⁡[N2O5]\log[\text{N}_2\text{O}_5] and tt. (iv) What is the rate law ? (v) Calculate the rate constant. (vi) Calculate the half-life period from kk and compare it with (ii).
  16. Ex 3.16
    The rate constant for a first order reaction is 60 s−160\,\text{s}^{-1}. How much time will it take to reduce the initial concentration of the reactant to its 1/16th1/16^{\text{th}} value?
  17. Ex 3.17
    During nuclear explosion, one of the products is 90Sr^{90}\text{Sr} with half-life of 28.1 years. If 1 μg1\,\mu\text{g} of 90Sr^{90}\text{Sr} 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. Ex 3.18
    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. Ex 3.19
    A first order reaction takes 40 min for 30% decomposition. Calculate t1/2t_{1/2}.
  20. Ex 3.20
    For the decomposition of azoisopropane to hexane and nitrogen at 543 K, the following data are obtained.
    tt (sec)P(mm of Hg)
    035.0
    36054.0
    72063.0
    Calculate the rate constant.
  21. Ex 3.21
    The following data were obtained during the first order thermal decomposition of SO2Cl2\text{SO}_2\text{Cl}_2 at a constant volume. SO2Cl2(g)→SO2(g)+Cl2(g)\text{SO}_2\text{Cl}_2(g) \rightarrow \text{SO}_2(g) + \text{Cl}_2(g)
    ExperimentTime/s−1\text{s}^{-1}Total pressure/atm
    100.5
    21000.6
    Calculate the rate of the reaction when total pressure is 0.65 atm.
  22. Ex 3.22
    The rate constant for the decomposition of N2O5\text{N}_2\text{O}_5 at various temperatures is given below:
    T/∘CT/^\circ\text{C}020406080
    105×k/s−110^5 \times k/\text{s}^{-1}0.07871.7025.71782140
    Draw a graph between ln⁡k\ln k and 1/T1/T and calculate the values of AA and EaE_a. Predict the rate constant at 30∘30^\circ and 50∘C50^\circ\text{C}.
  23. Ex 3.23
    The rate constant for the decomposition of hydrocarbons is 2.418×10−5 s−12.418 \times 10^{-5}\,\text{s}^{-1} at 546 K. If the energy of activation is 179.9 kJ/mol179.9\,\text{kJ/mol}, what will be the value of pre-exponential factor.
  24. Ex 3.24
    Consider a certain reaction A→\text{A} \rightarrow Products with k=2.0×10−2 s−1k = 2.0 \times 10^{-2}\,\text{s}^{-1}. Calculate the concentration of AA remaining after 100 s if the initial concentration of AA is 1.0 mol L−11.0\,\text{mol L}^{-1}.
  25. Ex 3.25
    Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law, with t1/2=3.00t_{1/2} = 3.00 hours. What fraction of sample of sucrose remains after 8 hours ?
  26. Ex 3.26
    The decomposition of hydrocarbon follows the equation k=(4.5×1011 s−1) e−28000 K/Tk = (4.5 \times 10^{11}\,\text{s}^{-1})\,e^{-28000\,\text{K}/T} Calculate EaE_a.
  27. Ex 3.27
    The rate constant for the first order decomposition of H2O2\text{H}_2\text{O}_2 is given by the following equation: log⁡k=14.34−1.25×104 K/T\log k = 14.34 - 1.25 \times 10^{4}\,\text{K}/T Calculate EaE_a for this reaction and at what temperature will its half-period be 256 minutes?
  28. Ex 3.28
    The decomposition of A into product has value of kk as 4.5×103 s−14.5 \times 10^{3}\,\text{s}^{-1} at 10∘C10^\circ\text{C} and energy of activation 60 kJ mol−160\,\text{kJ mol}^{-1}. At what temperature would kk be 1.5×104 s−11.5 \times 10^{4}\,\text{s}^{-1}?
  29. Ex 3.29
    The time required for 10% completion of a first order reaction at 298K is equal to that required for its 25% completion at 308K. If the value of AA is 4×1010 s−14 \times 10^{10}\,\text{s}^{-1}. Calculate kk at 318K and EaE_a.
  30. Ex 3.30
    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.