The rate constant for a first order reaction ...

NCERT Class XII Chemistry
Chapter - Chemical Kinetics
Questions with Solutions

Question : 16 of 39

Marks: +1, -0

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

^{\text{th}}

value?

Solution:

Given,

k=60\,\text{s}^{-1},

[R_{0}] = [R_{0}][R] = \frac{[R_{0}]}{16}, t=?

Using formula,

t=\frac{2.303}{k} \log \frac{[R_{0}]}{[R]}

=\frac{2.303}{60} \log 16 = 4.62 \times 10^{-2} \,\text{s}

Alternatively, In general, amount of the substance left after n half lives,

R=\frac{[R_{0}]}{2^{n}}=\frac{[R_{0}]}{16}

\therefore\; n=4

and

t=n\times t_{1/2};

t=n\times \frac{0.693}{k}

=4\times \frac{0.693}{60}=0.0462 \,\text{s}

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