Chemistry · Textbook solutions

Chemical Kinetics

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 59 questions

6. Chemical Kinetics — worked examples

13 q

Solved Examples

Worked · 13
  1. Solved Ex.6.1
    For the reaction 2 N2O5(g)⟶4 NO2(g)+O2(g)\mathrm{2\,N_2O_5(g) \longrightarrow 4\,NO_2(g) + O_2(g)} in liquid bromine, N2O5\mathrm{N_2O_5} disappears at a rate of 0.020.02 moles dm−3 sec−1\mathrm{dm^{-3}\ sec^{-1}}. At what rate NO2\mathrm{NO_2} and O2\mathrm{O_2} are formed? What would be the rate of reaction?
  2. Solved Ex.6.2
    Write the rate law for the reaction, A+B⟶P\mathrm{A + B \longrightarrow P} from the following data :
    [A] mol dm−3^{-3} s−1^{-1} (Initial)[B] mol dm−3^{-3} s−1^{-1} (Initial)Initial rate mol dm−3^{-3} s−1^{-1}
    (i) 0.40.24.0×10−54.0 \times 10^{-5}
    (ii) 0.60.26.0×10−56.0 \times 10^{-5}
    (iii) 0.80.43.2×10−43.2 \times 10^{-4}
  3. Solved Ex.6.3
    For the reaction, 2 NOBr(g)⟶2 NO(g)+Br2(g)\mathrm{2\,NOBr(g) \longrightarrow 2\,NO(g) + Br_2(g)}, the rate law is rate =k[NOBr]2= k[\mathrm{NOBr}]^2. If the rate of the reaction is 6.5×10−6 mol L−1 s−16.5 \times 10^{-6}\ \mathrm{mol\ L^{-1}\ s^{-1}} when the concentration of NOBr\mathrm{NOBr} is 2×10−3 mol L−12 \times 10^{-3}\ \mathrm{mol\ L^{-1}}. What would be the rate constant for the reaction?
  4. Solved Ex.6.4
    For the reaction 2NO(g)+2H2(g)⟶N2(g)+2 H2O(g)\mathrm{2NO(g) + 2H_2(g) \longrightarrow N_2(g) + 2\,H_2O(g)}, the rate law is rate =k[NO]2[H2]= k[\mathrm{NO}]^2[\mathrm{H_2}]. What is the order with respect to NO\mathrm{NO} and H2\mathrm{H_2}? What is the overall order of the reaction?
  5. Solved Ex.6.5
    The rate of the reaction, A+B⟶P\mathrm{A + B \longrightarrow P} is 3.6×10−2 mol dm−3 s−13.6 \times 10^{-2}\ \mathrm{mol\ dm^{-3}\ s^{-1}} when [A]=0.2 mol dm−3[\mathrm{A}] = 0.2\ \mathrm{mol\ dm^{-3}} and [B]=0.1 mol dm−3[\mathrm{B}] = 0.1\ \mathrm{mol\ dm^{-3}}. Calculate the rate constant if the reaction is first order in A and second order in B.
  6. Solved Ex.6.6
    Consider, A+B⟶P\mathrm{A + B \longrightarrow P}. If the concentration of A is doubled with [B][\mathrm{B}] being constant, the rate of the reaction doubles. If the concentration of A is tripled and that of B is doubled, the rate increases by a factor 66. What is order of the reaction with respect to each reactant? Determine the overall order of the reaction.
  7. Solved Ex.6.7
    A reaction occurs in the following steps i. NO2(g)+F2(g)⟶NO2F(g)+F(g)\mathrm{NO_2(g) + F_2(g) \longrightarrow NO_2F(g) + F(g)} (slow) ii. F(g)+NO2(g)⟶NO2F(g)\mathrm{F(g) + NO_2(g) \longrightarrow NO_2F(g)} (fast) a. Write the equation of overall reaction. b. Write down rate law. c. Identify the reaction intermediate.
  8. Solved Ex.6.8
    The half life of first order reaction is 990 s990\ \mathrm{s}. If the initial concentration of the reactant is 0.08 mol dm−30.08\ \mathrm{mol\ dm^{-3}}, what concentration would remain after 3535 minutes?
  9. Solved Ex.6.9
    In a first order reaction 60%60\% of the reactant decomposes in 4545 minutes. Calculate the half life for the reaction.
  10. Solved Ex.6.10
    Following data were obtained during the first order decomposition of SO2Cl2\mathrm{SO_2Cl_2} at the constant volume. SO2Cl2(g)⟶SO2(g)+Cl2(g)\mathrm{SO_2Cl_2(g) \longrightarrow SO_2(g) + Cl_2(g)}
    Times/sTotal pressure/bar
    00.5
    1000.6
    Calculate the rate constant of the reaction.
  11. Solved Ex.6.12
    The rate constants for a first order reaction are 0.6 s−10.6\ \mathrm{s^{-1}} at 313 K313\ \mathrm{K} and 0.045 s−10.045\ \mathrm{s^{-1}} at 293 K293\ \mathrm{K}. What is the activation energy?
  12. Solved Ex.6.13
    A first order gas phase reaction has activation energy of 240 kJ mol−1240\ \mathrm{kJ\ mol^{-1}}. If the pre-exponential factor is 1.6×1013 s−11.6 \times 10^{13}\ \mathrm{s^{-1}}. what is the rate constant of the reaction at 600 K600\ \mathrm{K}?
  13. Solved Ex.6.14
    The half life of a first order reaction is 900900 min at 820 K820\ \mathrm{K}. Estimate its half life at 720 K720\ \mathrm{K} if the activation energy is 250 kJ mol−1250\ \mathrm{kJ\ mol^{-1}}.

Exercise

46 q

1. Choose the most correct option.

Practice · 10
  1. Choose the most correct option.
    Ex Q.1 (i)
    The rate law for the reaction aA+bB⟶P\mathrm{aA + bB \longrightarrow P} is rate =k[A] [B]= k[\mathrm{A}]\,[\mathrm{B}]. The rate of reaction doubles if
    1. A.
      concentrations of A and B are both doubled.
    2. B.
      [A] is doubled and [B] is kept constant
    3. C.
      [B] is doubled and [A] is halved
    4. D.
      [A] is kept constant and [B] is halved.
  2. Ex Q.1 (ii)
    The order of the reaction for which the units of rate constant are mol dm−3 s−1\mathrm{mol\ dm^{-3}\ s^{-1}} is
    1. A.
      1
    2. B.
      3
    3. C.
      0
    4. D.
      2
  3. Ex Q.1 (iii)
    The rate constant for the reaction 2 N2O5(g)⟶2 N2O4(g)+O2(g)\mathrm{2\,N_2O_5(g) \longrightarrow 2\,N_2O_4(g) + O_2(g)} is 4.98×10−4 s−14.98 \times 10^{-4}\ \mathrm{s^{-1}}. The order of reaction is
    1. A.
      2
    2. B.
      1
    3. C.
      0
    4. D.
      3
  4. Ex Q.1 (iv)
    Time required for 90 %90\ \% completion of a certain first order reaction is tt. The time required for 99.9 %99.9\ \% completion will be
    1. A.
      tt
    2. B.
      2t2t
    3. C.
      t/2t/2
    4. D.
      3t3t
  5. Ex Q.1 (v)
    Slope of the graph ln⁡[A]t\ln[\mathrm{A}]_t versus tt for first order reaction is
    1. A.
      −k-k
    2. B.
      kk
    3. C.
      k/2.303k/2.303
    4. D.
      −k/2.303-k/2.303
  6. Ex Q.1 (vi)
    What is the half life of a first order reaction if time required to decrease concentration of reactant from 0.8 M0.8\ \mathrm{M} to 0.2 M0.2\ \mathrm{M} is 12 h12\ \mathrm{h}?
    1. A.
      12 h12\ \mathrm{h}
    2. B.
      3 h3\ \mathrm{h}
    3. C.
      1.5 h1.5\ \mathrm{h}
    4. D.
      6 h6\ \mathrm{h}
  7. Ex Q.1 (vii)
    The reaction, 3 ClO⊖⟶ClO3⊖+2 Cl⊖\mathrm{3\,ClO^{\ominus} \longrightarrow ClO_3^{\ominus} + 2\,Cl^{\ominus}} occurs in two steps, (i) 2 ClO−⟶ClO2⊖\mathrm{2\,ClO^{-} \longrightarrow ClO_2^{\ominus}} (ii) ClO2⊖+ClO⊖⟶ClO3⊖+Cl⊖\mathrm{ClO_2^{\ominus} + ClO^{\ominus} \longrightarrow ClO_3^{\ominus} + Cl^{\ominus}} The reaction intermediate is
    1. A.
      Cl⊖\mathrm{Cl^{\ominus}}
    2. B.
      ClO2⊖\mathrm{ClO_2^{\ominus}}
    3. C.
      ClO3⊖\mathrm{ClO_3^{\ominus}}
    4. D.
      ClO⊖\mathrm{ClO^{\ominus}}
  8. Ex Q.1 (viii)
    The elementary reaction O3(g)+O(g)⟶2 O2(g)\mathrm{O_3(g) + O(g) \longrightarrow 2\,O_2(g)} is
    1. A.
      unimolecular and second order
    2. B.
      bimolecular and first order
    3. C.
      bimolecular and second order
    4. D.
      unimolecular and first order
  9. Ex Q.1 (ix)
    Rate law for the reaction, 2 NO+Cl2⟶2 NOCl\mathrm{2\,NO + Cl_2 \longrightarrow 2\,NOCl} is rate =k[NO2]2[Cl2]= k[\mathrm{NO_2}]^2[\mathrm{Cl_2}]. Thus kk would increase with
    1. A.
      increase of temperature
    2. B.
      increase of concentration of NO\mathrm{NO}
    3. C.
      increase of concentration of Cl2\mathrm{Cl_2}
    4. D.
      increase of concentrations of both Cl2\mathrm{Cl_2} and NO\mathrm{NO}
  10. Ex Q.1 (x)
    For an endothermic reaction, X⇌Y\mathrm{X \rightleftharpoons Y}. If EfE_f is activation energy of the forward reaction and ErE_r that for reverse reaction, which of the following is correct?
    1. A.
      Ef=ErE_f = E_r
    2. B.
      Ef<ErE_f < E_r
    3. C.
      Ef>ErE_f > E_r
    4. D.
      ΔH=Ef−Er\Delta H = E_f - E_r is negative

2. Answer the following in one or two sentences.

Practice · 10
  1. Answer the following in one or two sentences.
    Ex Q.2 (i)
    For the reaction, N2(g)+3 H2(g)⟶2 NH3(g)\mathrm{N_2(g) + 3\,H_2(g) \longrightarrow 2\,NH_3(g)}, what is the relationship among d[N2]dt\dfrac{d[\mathrm{N_2}]}{dt}, d[H2]dt\dfrac{d[\mathrm{H_2}]}{dt} and d[NH3]dt\dfrac{d[\mathrm{NH_3}]}{dt}?
  2. Ex Q.2 (ii)
    For the reaction, CH3Br(aq)+OH−(aq)⟶CH3OH⊖(aq)+Br⊖(aq)\mathrm{CH_3Br(aq) + OH^{-}(aq) \longrightarrow CH_3OH^{\ominus}(aq) + Br^{\ominus}(aq)}, rate law is rate =k[CH3Br][OH⊖]= k[\mathrm{CH_3Br}][\mathrm{OH^{\ominus}}] a. How does reaction rate changes if [OH⊖][\mathrm{OH^{\ominus}}] is decreased by a factor of 55 ? b. What is change in rate if concentrations of both reactants are doubled?
  3. Ex Q.2 (iii)
    What is the relationship between coefficients of reactants in a balanced equation for an overall reaction and exponents in rate law. In what case the coefficients are the exponents?
  4. Ex Q.2 (iv)
    Why all collisions between reactant molecules do not lead to a chemical reaction?
  5. Ex Q.2 (v)
    What is the activation energy of a reaction?
  6. Ex Q.2 (vi)
    What are the units for rate constants for zero order and second order reactions if time is expressed in seconds and concentration of reactants in mol/L\mathrm{mol/L}?
  7. Ex Q.2 (vii)
    Write Arrhenius equation and explain the terms involved in it.
  8. Ex Q.2 (viii)
    What is the rate determining step?
  9. Ex Q.2 (ix)
    Write the relationships between rate constant and half life of first order and zeroth order reactions.
  10. Ex Q.2 (x)
    How do half lives of the first order and zero order reactions change with initial concentration of reactants?

3. Answer the following in brief.

Practice · 17
  1. Answer the following in brief.
    Ex Q.3 (i)
    How instantaneous rate of reaction is determined?
  2. Ex Q.3 (ii)
    Distinguish between order and molecularity of a reaction.
  3. Ex Q.3 (iii)
    A reaction takes place in two steps, 1. NO(g)+Cl2(g)⟶NOCl2(g)\mathrm{NO(g) + Cl_2(g) \longrightarrow NOCl_2(g)} 2. NOCl2(g)+NO(g)⟶2 NOCl(g)\mathrm{NOCl_2(g) + NO(g) \longrightarrow 2\,NOCl(g)} a. Write the overall reaction. b. Identify reaction intermediate. c. What is the molecularity of each step?
  4. Ex Q.3 (iv)
    Obtain the relationship between the rate constant and half life of a first order reaction.
  5. Ex Q.3 (v)
    How will you represent zeroth order reaction graphically?
  6. Ex Q.3 (vi)
    What are pseudo-first order reactions? Give one example and explain why it is pseudo-first order.
  7. Ex Q.3 (vii)
    What are requirements for the colliding reactant molecules to lead to products?
  8. Ex Q.3 (viii)
    How catalyst increases the rate of reaction? Explain with the help of potential energy diagram for catalyzed and uncatalyzed reactions.
  9. Ex Q.3 (ix)
    Explain with the help of Arrhenius equation, how does the rate of reaction changes with (a) temperature and (b) activation energy.
  10. Ex Q.3 (x)
    Derive the integrated rate law for first order reaction.
  11. Ex Q.3 (xi)
    How will you represent first order reactions graphically.
  12. Ex Q.3 (xii)
    Derive the integrated rate law for the first order reaction, A(g)⟶B(g)+C(g)\mathrm{A(g) \longrightarrow B(g) + C(g)} in terms of pressure.
  13. Ex Q.3 (xiii)
    What is zeroth order reaction? Derive its integrated rate law. What are the units of rate constant?
  14. Ex Q.3 (xiv)
    How will you determine activation energy: (a) graphically using Arrhenius equation (b) from rate constants at two different temperatures?
  15. Ex Q.3 (xv)
    Explain graphically the effect of temperature on the rate of reaction.
  16. Ex Q.3 (xvi)
    Explain graphically the effect of catalyst on the rate of reaction.
  17. Ex Q.3 (xvii)
    For the reaction 2A+B⟶\mathrm{2A + B \longrightarrow} products, find the rate law from the following data.
    [A]/M[B]/Mrate/M s−1^{-1}
    0.30.050.15
    0.60.050.30
    0.60.21.20

4. Solve

Practice · 9
  1. Solve
    Ex Q.4 (i)
    In a first order reaction, the concentration of reactant decreases from 20 mmol dm−320\ \mathrm{mmol\ dm^{-3}} to 8 mmol dm−38\ \mathrm{mmol\ dm^{-3}} in 3838 minutes. What is the half life of reaction?
  2. Ex Q.4 (ii)
    The half life of a first order reaction is 1.71.7 hours. How long will it take for 20%20\% of the reactant to react?
  3. Ex Q.4 (iii)
    The energy of activation for a first order reaction is 104 kJ/mol104\ \mathrm{kJ/mol}. The rate constant at 25 ∘C25\ ^\circ\mathrm{C} is 3.7×10−5 s−13.7 \times 10^{-5}\ \mathrm{s^{-1}}. What is the rate constant at 30 ∘C30\ ^\circ\mathrm{C}? (R=8.314 J/K mol)(R = 8.314\ \mathrm{J/K\ mol})
  4. Ex Q.4 (iv)
    What is the energy of activation of a reaction whose rate constant doubles when the temperature changes from 303 K303\ \mathrm{K} to 313 K313\ \mathrm{K}?
  5. Ex Q.4 (v)
    The rate constant of a reaction at 500 ∘C500\ ^\circ\mathrm{C} is 1.6×103 M−1s−11.6 \times 10^{3}\ \mathrm{M^{-1}s^{-1}}. What is the frequency factor of the reaction if its activation energy is 56 kJ/mol56\ \mathrm{kJ/mol}.
  6. Ex Q.4 (vi)
    Show that time required for 99.9%99.9\% completion of a first order reaction is three times the time required for 90%90\% completion.
  7. Ex Q.4 (vii)
    A first order reaction takes 4040 minutes for 30%30\% decomposition. Calculate its half life.
  8. Ex Q.4 (viii)
    The rate constant for the first order reaction is given by log⁡10k=14.34−1.25×104 T\log_{10} k = 14.34 - 1.25 \times 10^{4}\ T. Calculate activation energy of the reaction.
  9. Ex Q.4 (ix)
    What fraction of molecules in a gas at 300 K300\ \mathrm{K} collide with an energy equal to activation energy of 50 kJ/mol50\ \mathrm{kJ/mol} ?