Exercises

EXERCISES

1. Consider the reaction, 2HI → H2 + I2, determine the rate of disappearance of HI when the rate of I2
    formation is 1.8 x 10-6 Ms-1.
  
    Answer : 3.6 × 10-6 Ms-1


2. Because it has a nonpolluting product (water vapor), hydrogen gas is used for fuel aboard the
    space shuttle and may be used by Earth-bound engines in the near future.

   2H2(g) + O2(g) 2H2O(g)
   • Express the rate in terms of changes in [H2],
   [O2] and [H2O] with time.
   • When [O2] is decreasing at 0.23 molL-1 s-1, at
   what rate is [H2O] increasing?
  
   Answer : 0.46molL-1s-1


3. Consider the reaction,

    NO(g) + O2(g) →2NO2(g).
    Suppose that at a particular moment during the
    reaction nitric oxide (NO) is reacting at the rate
    of 0.066 Ms-1

    a) At what rate is NO2 being formed?
    b) At what rate is molecular oxygen reacting?


4. Consider the reaction,

    N2(g) + 3H2(g) → 2NH3(g)
   
    Suppose that at a particular moment during the reaction molecular hydrogen is reacting at the
    rate of 0.074 Ms-1

     a) At what rate is ammonia being formed?
     b) At what rate is molecular nitrogen reacting?

5. ClO2(aq) + 2OH- (aq) → products

    The results of the kinetic studies are given below.

    exp              [ClO2] / M                   [OH-] / M                  Initial rate / Ms-1

     1                     0.0421                         0.0185                        8.21 ×10-3
     2                     0.0522                         0.0185                        1.26 ×10-2
     3                     0.0421                         0.0285                        1.26 ×10-2

    a) Explain what is meant by the order of reaction
    b) Referring to the data determine
         (i) rate law /rate equation
         (ii) rate constant, k
         (iii) the reaction rate if the concentration of both ClO2 and OH- = 0.05 M

   Answer : rate = k [ClO2]2[OH-]
                   k = 250 M-2s-1
                   rate = 3.12 ×10-2 M/s


6. Write rate law for this equation,

     A + B → C

    i) When [A] is double, rate also double. But double the [B] has no effect on rate.

    ii) When [A] is increase 3x, rate increases 3x, and increase of [B] 3x causes the rate to increase 9x.

   iii) Reduce [A] by half has no effect on the rate, but reduce [B] by half causing the rate to be half of the
     initial rate.

   Answer : Rate = k[A]
                 Rate = k[A] [B]2
                 Rate = k[B]

7. C + D → E

    The results of the kinetic studies are given below.

     exp             Initial [ ] (M)         Time interval (Min)          The change in concentration of C (M)

            [C]      [D]

   1                0.10    1.0                        30                                       2.5 x

10-3

      2                0.10    2.0                        30                                       1.0 x 10-2      3                0.05    1.0                       120                                      5.0 x

 

    a) Calculate the rate of reaction for each experiment

    b) Determine the order of reaction with respect to C and D and write the rate law.

    

        of C remains constant.c) State the effect on the reaction rate if the concentration of D is doubled but the concentration   
    Answer : a) 8.33 ×10-5 ,3.33 × 10-4, 4.17×10-5 M min-1 
                   b) rate = k [C] [D]2                   c) rate increase by a factor of 4
 8. The reaction 2A to B is first order in A with a rate constant of 2.8 x 10-2 s-1 at 800oC.M to 0.14 M ?

    How long will it take for A to decrease from 0.88

    Answer : t = 66s

9. For the first order decomposition of H2O2(aq) given that k = 3.66 x 10-3 s-1 and [H2O2 ]o = 0.882 M,2 O2] = 0.600 M105.26 s

    determine;

    a) the time at which [H

    b) the [H2O2] after 225 s.

  Answer : a)
                  b) [H2O2] = 0.387 M

10. The decomposition of ethane, C2H6 to methyl radicals is a 1st order reaction with a rate constant-4 s-1 at 700o C.2H6(g) to 2CH3(g)

      of 5.36 x 10

      C

      Calculate the half life of the reaction in minutes.
     
      Answer :  t1/2 = 2 1 . 5 min
11. The decomposition of nitrogen pentoxide is as below;
      
      N
       time, t/min                    0      10      20      30      40      50      60     [N2O5] x 10-4 M      176   124    93      71       53      39     29

    

     The decomposition is first order reaction.

     a)Plot a linear graph to prove it.

     b)From the plot determine rate constant, k

     Answer : k = 0.0296 s-1

12. The decomposition of HI is second order, at 500oC, the halflife of HI is 2.11 min when the initial HI   concentration is 0.10 M. What will be the half-life (in minutes) when the initial HI concentration is 0.010 M? 

     Answer : 21 minutes

13. The rate constant for the first-order decomposition of  N2O5(g) at 100oC is 1.46 x10-1s-1.

      a) If the initial concentration of N2O5 in a reaction vessel is 4.5 ×10-3 mol/L, what will the concentration 

          be 20.0 s after the decomposition begins?

      b) What is the half-life (in s) of N2O5 at 100oC?

     

      Answer : a) 0.00024 M

                    b) 4.75 s

14. For the reaction A + B produce C + D, the enthalpy change of the forward reaction is + 21 kJ/mol. The activation energy of the forward reaction is  84 kJ/mol.

a) What is the activation energy of the reverse reaction ?

b) Sketch the reaction profile of this reaction.

15. In the presence of platinum as a catalyst, hydrogen iodide decomposes to form hydrogen and  iodine. The activation energy for this reaction is 58 kJ mol-1. Calculate the ratio of the rate constant at 30oC and 20oC.

Answer : 0.46

16. The results of the decomposition of N2O5 at two different temperature were recorded as;10-5       308                            6.61 x

a) Base on the unit of the rate constant, k, determine the order of the reaction.

b) Find the value of E

Answer : a) first
              b) 102 kj per mola and A for the reaction. 10-5

Temperature(K)           rate constant, k (s-1)

       298                            1.74 x 

2O5(g) to 2 NO2(g) + ½ O2(g)10-3