Question

A first order reaction is 50% completed in 1.26 * 10^{14} s. How much time
would it take for 100% completion?
(i) 1.26 * 10^{15} s
(ii) 2.52 * 10^{14} s
(iii) 2.52 * 10^{28} s
(iv) infinite


NCERT Class XII
Chemistry - Exemplar Problems

Chapter 4. Chemical Kinetics

Answer 1

infinite as completion

Answer 2

Given:

$t_\frac{1}{2}$ of the reaction = 1.26 ×$10^{14}$

Order of the reaction = 1st

To find:

t = ?

Solution:

For first order reaction the value of $t_\frac{1}{2}$ is

$t_\frac{1}{2} = \frac{0.693}{K}$

∴ K =$\frac{0.693}{t_\frac{1}{2}} = \frac{0.693}{1.26\times10^{14}}$

For 100% completion it gives

$K = \frac{2.303}{t}log\frac{R_0}{R}$

At 100% of completion of the reaction R value is 0

∴ t = $\frac{2.303}{k}log\frac{R_0}{R}$ = ∞

Conclusion:

The reaction would take ∞ time for 100% calculation. Thus option iv is correct answer.

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