A) \[Nearly\text{ }240\text{ }min\]
B) \[Nearly\text{ }480\text{ }min\]
C) \[Nearly\text{ }450\text{ }min\]
D) \[Nearly\text{ }400\text{ }min\]
Correct Answer: D
Solution :
The first order reaction is \[\Rightarrow \] \[k=\frac{2.303}{t}{{\log }_{10}}\left( \frac{a}{a-x} \right)\] For \[50%\] decomposition, \[t=120\text{ }min\]\[a=100\] \[(a-x)=100-50=50\] \[k=\frac{2.303}{120}{{\log }_{10}}\frac{100}{50}\] or \[k=\frac{2.303}{120}{{\log }_{10}}2\] \[k=\frac{2.303\times 0.3010}{120}\] or \[k=\frac{0.6931}{120}\] For \[90%\]decomposition \[t=?\] s\[a=100\] \[(a-x)=100-90=10\] \[k=\frac{2.303}{t}{{\log }_{10}}\frac{a}{(a-x)}\] \[\frac{0.6931}{120}=\frac{2.303}{t}{{\log }_{10}}\frac{100}{10}\] \[t=\frac{2.303\times 120}{0.6931}\] \[t=398.76\min \]
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