An organic compound undergoes first order decomposition. If the time taken for the 60% decomposition is 540 s, then the time required for 90% decomposition will be is ______ s. (Nearest integer). (Given: ln 10 = 2.3; log 2 = 0.3)

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Solution

Q.
An organic compound undergoes first order decomposition. If the time taken for the 60% decomposition is 540 s, then the time required for 90% decomposition will be is ______ s. (Nearest integer).

(Given: ln 10 = 2.3; log 2 = 0.3) [2023]

Ans.
(1350)

First order reaction

$t = \frac{1}{k} \ln \frac{C_{0}}{C_{t}}$

$540 = \frac{1}{k} \ln \frac{100}{40}$ $. . . (1)$

$t = \frac{1}{k} \ln \frac{100}{10}$ $. . . (2)$

$From (1) and (2)$

$\frac{540}{t} = \frac{\ln \frac{100}{40}}{\ln \frac{100}{10}} = \frac{\log 100 - \log 40}{\log 100 - \log 10}$

$\frac{540}{t} = \frac{2 - 1.6}{2 - 1} = 0.4$

$t = \frac{540}{0.4} = 1350 s$

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