A first order reaction takes 40 min for 30% ...

NCERT Class XII Chemistry
Chapter - Chemical Kinetics
Questions with Solutions

Question : 19 of 39

Marks: +1, -0

A first order reaction takes 40 min for 30% decomposition. Calculate

t_{\frac{1}{2}}

Solution:

30% decomposition means that x = 30% of

[R_0]

or,

[R] = [R_0] - 0.3 [R_0]

= 0.7 [R_0]

For reaction of

1^{\text{st}}

order,

k = \frac{2.303}{t} \log \frac{[R]_0}{[R]}

= \frac{2.303}{40} \log \frac{[R_0]}{0.70 [R_0]}

= \frac{2.303}{40} \log \frac{10}{7} \mathrm{min}^{-1}

= \frac{2.303}{40} \times 0.1549 \mathrm{min}^{-1}

= 8.918 \times 10^{-3} \mathrm{min}^{-1}

For a

1^{\text{st}}

order reaction,

t_{\frac{1}{2}} = \frac{0.693}{k}

= \frac{0.693}{8.918 \times 10^{-3} \mathrm{min}^{-1}}

= 77.7 \mathrm{min}

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