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  • An Organic compound undergoes first order decomposition. If the time taken is 680 s for the 60% decomposition then the time required for 90% decomposition will be<s

An Organic compound undergoes first order decomposition. If the time taken is 680 s for the 60% decomposition then the time required for 90% decomposition will be

Option: 1

2000\, \mathrm{sec}


Option: 2

1500 \, \mathrm{sec}


Option: 3

1200\, \mathrm{sec}


Option: 4

1700\, \mathrm{sec}


Answers (1)

best_answer

\mathrm{\begin{aligned} & t=\frac{1}{k} \ln \frac{a_0}{d t} \\ & \frac{t_1}{t_2}=\frac{\frac{1}{k} \ln \frac{a_0}{0.4 a_0}}{\frac{1}{k} \ln \frac{a_0}{0.1 a_0}} \\ & \frac{680}{t_2}=\frac{\ln \frac{10}{4}}{\ln 10} \\ & \frac{680}{t_2}=\frac{\log 10-\log 4}{\log 10} \end{aligned} }
\mathrm{\begin{aligned} \frac{680}{t_2} & =\frac{1-0.6}{1} \\ \frac{680}{t_2} & =0.4 \\ t_2 & =\frac{680}{0.4}=1700\, \mathrm{sec} \end{aligned} }

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