Chapter 4 : Chemical Kinetics

Q. The decomposition of dimethyl ether leads to the formation of

C H_{4}, H_{2}

and

C O

and the reaction rate is given by:

R a t e = k [C H_{3} O C H_{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.,

R a t e = k [P_{C H_{3} O C H_{3}}]^{3 / 2}

If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constants?

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Q. For a first order reaction, show that time required for

99

% completion is twice the time required for the completion of

90

% of reaction.

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Q. During nuclear explosion, one of the products is

^{90} S r

with half life of

28.1 y r

. If

1 μ g

^{90} S r

was absorbed in the bones of a newly born baby instead of calcium, how much of it will remain after

10

year and

60

year if it is not lost metabolically.

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Q. Mention the factors that affect the rate of a chemical reaction.

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Q. In a pseudo first order hydrolysis of ester in water the following results were obtained:

$t / s$	$0$	$30$	$60$	$90$
$[E s t e r] / M .$	$0.55$	$0.31$	$0.17$	$0.085$

(i) Calculate the average rate of reaction between the time interval

30

60

seconds.
(ii) Calculate the pseudo first order rate constant for the hydrolysis of ester.

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Q. A first order reaction takes

40

min for

30

% decomposition. Calculate

t_{1 / 2}

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Q. The experimental data for decomposition of

N_{2} O_{5}

[2 N_{2} O_{5} \to 4 N O_{2} + O_{2}]

in gas phase at

318 K

are given below:

t/s	$0$	$400$	$800$	$1200$	$1600$	$2000$	$2400$	$2800$	$3200$
$10^{2} \times [N_{2} O_{5}] / m o l L^{- 1}$	$1.63$	$1.36$	$1.14$	$0.93$	$0.78$	$0.64$	$0.53$	$0.43$	$0.35$

(i) Plot

[N_{2} O_{5}]

against t.
(ii) Find the half-life period for the reaction.
(iii) Draw a graph between

log [N_{2} O_{5}]

and t.
(iv) What is the rate law?
(v) Calculate the rate constant.
(vi) Calculate the half-life period from k and compare it with (ii)

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Q. In a reaction between

A

and

B

, the initial rate of reaction

(r_{0})

was measured for different initial concentrations of

A

and

B

as given below:

$A / m o l L^{- 1}$	$0.20$	$0.20$	$0.40$
$B / m o l L^{- 1}$	$0.30$	$0.10$	$0.05$
$r_{0} / m o l L^{- 1} s^{- 1}$	$5.07 \times 10^{- 5}$	$5.07 \times 10^{- 5}$	$1.43 \times 10^{- 4}$

What is the order of the reaction with respect to

A

and

B

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Q. For the decomposition of azo-isopropane to hexane and nitrogen at

543 K

, the following data are obtained.

$t (s e c)$	$P$ (mm of $H g$ )
$0$	$35.0$
$360$	$54.0$
$720$	$63.0$

Calculate the rate constant.

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Q. Calculate the half life of a first order reaction from their rate constants given below:
(a)

200 s^{- 1}

; (b)

2 m i n^{- 1}

; (c)

4 y e a r^{- 1}

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Q. 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 / 16^{t h}

value?

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Q. 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	$[A] / m o l L^{- 1}$	$B] / m o l L^{- 1}$	Initial rate/ $m o l L^{- 1} m i n^{- 1}$
I	$0.1$	$0.1$	$2.0 \times 10^{- 2}$
II	-	$0.2$	$4.0 \times 10^{- 2}$
III	$0.4$	$0.4$	-
IV	-	$0.2$	$2.0 \times 10^{- 2}$

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Q. A reaction is second order with respect to a reaction. How is the rate of reaction affected if the concentration of the reactant is : (a) doubled, (b) reduced to

1 / 2

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Q. From the rate expression for the following reactions, determine their order of reaction and the dimensions of the rate constants.
(i)

2 N O (g) \to N_{2} O (g); R a t e = k [N O]^{2}

(ii)

H_{2} O_{2} (a q) + 3 I^{-} (a q) + 2 H^{+} \to 2 H 2 O (I) + 3 I; R a t e = k [H_{2} O_{2}] [I^{-}]

(iii)

C H_{3} C H O (g) \to C H_{4} (g) + C O (g); R a t e = k [C H_{3} C H O]^{3 / 2}

(iv)

C_{2} H_{5} C l (g) \to C_{2} H_{4} (g) + H C l (g); R a t e = k [C_{2} H_{5} C l]

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Q. The rate for the decomposition of

N H_{3}

on platinum surface is zero order. What are the rate of production of

N_{2}

and

H_{2}

K = 2.5 \times 10^{- 4} m o l l i t r e^{- 1} s^{- 1}

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Q. A reaction is first order in

A

and second order in

B

:
(i) Write differential rate equation.
(ii) How is the rate affected when the concentration of

B

is tripled?
(iii) How is the rate affected when the concentration of both

A

and

B

is doubled?

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Q. The half-life for radioactive decay of

^{14} C

5730

years. An archaeological artifact containing wood had only

80 %

of the

^{14} C

found in a living tree. Estimate the age of the sample.

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Q. The following results have been obtained during the kinetic studies of the reaction:

2 A + B \to C + D

Experiment	$[A] / m o l L^{- 1}$	$[B] / m o l L^{- 1}$	Initial rate of formation of $D / m o l L^{- 1} m i n^{- 1}$
I	$0.1$	$0.1$	$6.0 \times 10^{- 3}$
II	$0.3$	$0.2$	$7.2 \times 10^{- 2}$
III	$0.3$	$0.4$	$2.88 \times 10^{- 1}$
IV	$0.4$	$0.1$	$2.40 \times 10^{- 2}$

Determine the rate law and the rate constant for the reaction.

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Q. 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?

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Q. For the reaction:

2 A + B \to A_{2} B

, the rate

= k [A] [B]^{2}

with

k = 2.0 \times 10^{- 6} m o l^{- 2} L^{2} s^{- 1}

Calculate the initial rate of the reaction when

[A] = 0.1 m o l L^{- 1}, [B] = 0.2 m o l L^{- 1}

. Calculate the rate of reaction after

[A]

is reduced to

0.06 m o l L^{- 1}

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