a) The rate of a particular reaction doubles when the temperature changes from 300 K to 310 K. Calculate the energy of activation of the reaction.
[Given : $R = 8.314 J K^{- 1} {m o l}^{- 1}$ ].
b) Show that the half-life period of a first order reaction is independent of initial concentration of reacting species.

Open in App

Solution

a)
$l n \frac{k^{'}}{k} = \frac{E_{a}}{R} [\frac{T^{'} - T}{T T^{'}}]$
$l n \frac{2 k}{k} = \frac{E_{a}}{8.314 J / m o / K} [\frac{310 - 300}{300 \times 310}]$
$E_{a} = 53594 J / m o l$
$E_{a} = 53.594 k J / m o l$
b) The half-life period of a first order reaction is independent of initial concentration of reacting species.
For first order reaction, the integrated rate equation is
$t = \frac{2.303}{k} l o g \frac{a}{a - x}$ ......(1)
When $t = t_{1 / 2} =$ half life period,
$a - x = a / 2$
Substitute in equation (1)
$t_{1 / 2} = \frac{2.303}{k} l o g \frac{a}{a / 2}$
$t_{1 / 2} = \frac{2.303}{k} l o g 2$
$t_{1 / 2} = \frac{0.693}{k}$
Hence, the half-life period of a first order reaction is independent of initial concentration of reacting species.

Suggest Corrections

Similar questions

Q. The rate of a reaction doubles when its temperature changes from 300 K to 310 K. Activation energy of such a reaction will be:

(R = 8.314 J K^{- 1} m o l^{- 1}

and

l o g_{10} 2 = 0.301)

Q. The rate of a particular reaction doubles when temperature changes from

27^{o} C

37^{o} C

. Calculate the energy of activation for such reaction.

[R = 8.314 J K^{- 1} m o l e]

Q. The rate of a reaction doubles when its temperature changes from

300 K

310 K

. Activation energy of such a reaction will be:

[R = 8.314 J K^{- 1} m o l^{- 1}

and

log 2 = 0.301]

Q. The rate of a reaction quadruples when the temperature changes from 300 to 310 K. The activation energy of this reaction is :
(Assume activation energy and pre-exponential factor are independent of temperature;

l n 2

=0.693; R = 8.314 J

m o l^{- 1} K^{- 1}

)

The rate of reaction doubles when its temperature changes from 300K to 310 K .activation energy of such a reaction will be (R=8.314 kj/ mol and WG2= 0.031 )

Join BYJU'S Learning Program

a) The rate of a particular reaction doubles when the temperature changes from 300 K to 310 K. Calculate the energy of activation of the reaction.[Given : R=8.314JK−1mol−1].b) Show that the half-life period of a first order reaction is independent of initial concentration of reacting species.