Chemistry: Chemical Kinetics: Important Questions with Answers, Solution and Explanation

**Answer
the following questions:**

1.
Define average rate and instantaneous rate.

2.
Define rate law and rate constant.

3.
Derive integrated rate law for a zero order reaction A → product .

4.
Define half life of a reaction. Show that for a first order
reaction half life is independent of initial concentration.

5.
What is an elementary reaction? Give the differences between order
and molecularity of a reaction.

6.
Explain the rate determining step with an example.

7.
Describe the graphical representation of first order reaction.

8.
Write the rate law for the following reactions.

a.
A reaction that is 3/2 order in x and zero order in y.

b.
A reaction that is second order in NO and first order in Br_{2}.

9.
Explain the effect of catalyst on reaction rate with an example.

10. The rate law for a
reaction of A, B and C hasbeenfoundtobe rate = k [
A]^{2} [B][L]^{3/2}

How would the rate of
reaction change when

(i) Concentration of [L] is quadrupled

**Solution**

(ii) Concentration of both [A] and [B] are doubled

**Solution**

(iii) Concentration of
[A] is halved

**Solution**

(iv) Concentration of [A] is reduced to(1/3)
and concentration of [L] is quadrupled.

**Solution**

11. The rate of formation of
a dimer in a second order reaction is 7.5 ×
10^{−}^{3} mol L^{−}^{1}*s*^{−}^{1} at 0.05 mol L^{−}^{1} monomer concentration.
Calculate the rate constant.

**Solution**

Let us consider the dimerisation of a monomer M

2M → (M)_{2}

Rate= k [M]^{n}

Given that n=2 and [M] = 0.05 mol L^{-1}

Rate = 7.5 X 10^{-3} mol L^{-1}s^{-1}

k = Rate/[M]^{n}

k = 7.5x10^{-3}/(0.05)^{2} = 3mol^{-1}Ls^{-1}

12. For a reaction *x* + *y* + *z* →products the rate law is
given by rate = k [ *x* ]^{3/2} [ *y* ]^{1/2} what is the overall
order of the reaction and what is the order of the reaction with respect to z.

**Solution**

i.e., second order reaction.

Since the rate expression does not contain the concentration of z
, the reaction is zero order with respect to z.

13. Explain briefly the
collision theory of bimolecular reactions.

14. Write Arrhenius equation
and explains the terms involved.

15. The decomposition of Cl_{2}O_{7}
at 500K in the gas phase to Cl_{2} and O_{2} is a first order
reaction. After 1 minute at 500K, the pressure of Cl_{2}O_{7}
falls from 0.08 to 0.04 atm. Calculate the rate constant in s^{-1}.

**Solution**

16. Hydrolysis of methyl
acetate in aqueous solution has been studied by titrating the liberated acetic
acid against sodium hydroxide. The concentration of an ester at different
temperatures is given below.

17. Explain pseudo first
order reaction with an example.

18. Identify the order for
the following reactions

(i) Rusting of Iron

(ii) Radioactive disintegration of _{92} U^{238}

(iii) 2 A +
3B → products ; rate = k [ A]^{1/2} [B ]^{2}

19.
A gas phase reaction has energy of activation 200 kJ mol^{-1}.
If the frequency factor of the reaction is 1.6 × 10^{13} *s*^{−}^{1 }Calculate the rate
constant at 600 K.
(* e ^{ }*

**Solution**

20.
For the reaction 2*x* +
*y* → L find the rate law from
the following data.

**Solution**

21. How do concentrations of
the reactant influence the rate of reaction?

22. How do nature of the
reactant influence rate of reaction.

23. The rate constant for a
first order reaction is 1.54 × 10^{-3} s^{-1}. Calculate its
half life time.

**Solution**

We know that, t_{1/2} = 0.693/ k

t_{1/2} = 0.693/1.54 x 10^{-3} s^{-1} =
450 s

24. The half life of the
homogeneous gaseous reaction SO_{2}Cl_{2} → SO_{2} + Cl_{2}
which obeys first order kinetics is 8.0 minutes. How long will it take for the
concentration of SO_{2}Cl_{2} to be reduced to 1% of the
initial value?

**Solution**

We know that, k = 0.693/ t_{1/2}

k = 0.693/ 8.0 minutes= 0.087 minutes^{-1}

For a first order reaction,

25. The time for half change
in a first order decomposition of a substance A is 60 seconds. Calculate the
rate constant. How much of A will be left after 180 seconds?

**Solution**

26. A zero order reaction is
20% complete in 20 minutes. Calculate the value of the rate constant. In what
time will the reaction be 80% complete?

**Solution**

i) Let A = 100M, [A_{0}]–[A] = 20M,

For the zero order reaction

k=([A_{0}]-[A] / t)

k=(20M / 20min) = 1 Mmin^{-1}

Rate constant for a reaction = 1Mmin^{-1}

ii) To calculate the time for 80% of completion

k = 1Mmin^{-1}, [A_{0}] = 100M, [A_{0}]-[A]
= 80M, t = ?

Therefore

t=([A_{0}]-[A] / k) = (80M / 1Mmin^{-1}) = 80min

27. The activation energy of
a reaction is 225 k Cal mol^{-1} and the value of rate constant at 40°C
is 1.8 ×10^{−}^{5} s^{−}^{1} . Calculate the
frequency factor, A.

**Solution**

Here, we
are given that

E_{a}
= 22.5 kcal mol^{-1} = 22500 cal mol^{-1}

T = 40°C = 40 + 273 = 313 K

k = 1.8 × 10^{-5} sec^{-1}

Substituting the values in the equation

log A = log (1.8) −5 + (15.7089)

log A = 10.9642

A = antilog (10.9642)

A = 9.208 × 10^{10} collisions s^{−1}

28.
Benzene diazonium chloride in aqueous solution decomposes
according to the equation C_{6}H_{5}N_{2}Cl → C_{6}H_{5}Cl
+ N_{2} . Starting with an initial concentration of 10 g L^{−}^{1} , the volume of N_{2}
gas obtained at 50 °C at different intervals of time was found to be as under:

Show that the above
reaction follows the first order kinetics. What is the value of the rate
constant?

**Solution**

For a first order
reaction

In the present case, V∞
= 58.3 ml.

The value of k at
different time can be calculated as follows:

Since the value of k comes out to be
nearly constant, the given reaction is of the first order. The mean value of k
= 0.0676 min^{-1}

29.
From the following data, show that the decomposition of hydrogen
peroxide is a reaction of the first order:

Where t is the time in minutes and V is the volume of standard KMnO4 solution required for titrating the same volume of the reaction mixture.

**Solution**

In the present case, V_{o} =
46.1 ml.

The value of k at each instant can
be calculated as follows:

Thus, the value of k comes out to be
nearly constant. Hence it is a reaction of the first order.

30.
Where *t* is the time in minutes and V is the volume of
standard KMnO_{4} solution required for titrating the same volume of
the reaction mixture.

**Solution**

i) For the first order reaction k = 2.303/t log [A_{0}]/[A]

Assume, [A_{0}] = 100 %, t =
50 minutes

Therefore, [A] = 100 – 40 = 60

k = (2.303 / 50) log (100 / 60)

k = 0.010216 min^{-1}

Hence the value of the rate constant
is 0.010216 min^{-1}

ii) t = ?, when the reaction is 80%
completed,

[A] = 100 – 80 = 20%

From above, k = 0.010216 min^{-1}

t = (2.303 / 0.010216) log (100 / 20)

t = 157.58 min

The time at which the reaction will
be 80% complete is 157.58 min.

31.
A first order reaction is 40% complete in 50 minutes. Calculate
the value of the rate constant. In what time will the reaction be 80% complete?

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