A) 2 min
B) 4 min
C) 12 min
D) 1 min
Correct Answer: B
Solution :
First order kinetic equation is: \[k=\frac{2.303}{t}\log \frac{a}{(a-x)}\] or \[t=\frac{2.303}{k}\log \frac{a}{(a-x)}\] According to question \[8=\frac{2.303}{k}\log \frac{100}{100-75}\] \[8=\frac{2.303}{k}\log \frac{100}{25}\] \[8=\frac{2.303}{k}\log 4\] ?(i) And \[t=\frac{2.303}{k}\log \frac{100}{100-50}\] \[\frac{2.303}{k}\log 2\] ?(ii) By dividing Eq. (ii) by Eq. (i), we get \[\frac{t}{8}=\frac{\frac{2.303}{k}\log 2}{\frac{2.303}{k}\times 2\log 2}\] \[\frac{t}{8}=\frac{\log 2}{2\log 2}\] \[\frac{t}{8}=\frac{1}{2}\] \[2t=8\] \[t=\frac{8}{2}=4\,\min \]
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