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  4. For a first order reaction at 27°C, the ratio of time required for 75% completion to 25% completion of reaction is

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Q. For a first order reaction at 27$^{\circ}$C, the ratio of time required for 75% completion to 25% completion of reaction is

EAMCETEAMCET 2009Chemical Kinetics

Solution:

For a first order reaction,
$ t =\frac{2.303}{k} \, log_{10} \, \frac{a}{a-x}$
Let initial amount of reactant is 100.
$ \frac{t_1}{t_2} = \frac{log \frac{100}{100-75}}{log \frac{100}{100-25}} \, [\therefore \, k \, remains \, constant]$
$ =\frac{log \frac{100}{25}}{log \frac{100}{75}} = \frac{log \, 4}{log \, 4/3}$
$ =\frac{log \, 4}{log \, 4 - log \, 3}$
$ =\frac{2 \times 0.3010}{2 \times 0.3010-0.4771}$
$ = \frac{0.6020}{0.1249} = 4.81$