A) 5.3 min
B) 10.6 min
C) 43.3mm
D) 99.7 min
Correct Answer: A
Solution :
For a first order reaction \[k=\frac{2.303}{t}\log \frac{a}{a-x}\] At half-time, \[x=\frac{a}{2}\] \[\therefore \] \[k=\frac{2.303}{1.6}\times \log \frac{a}{a-\frac{a}{2}}\] \[=\frac{2.303}{1.6}\times \log 2\] \[=\frac{2.303}{1.6}\times 0.3010\] \[=0.4332\] For 90% completion, \[x=0.9a\] \[\therefore \] \[k=\frac{2.303}{t}\log \frac{a}{a-0.9a}\] \[0.4332=\frac{2.303}{t}\log \frac{a}{0.1a}\] \[=\frac{2.303}{t}\log 10\] \[=\frac{2.303}{t}\times 1\] \[t=\frac{2.303}{0.4332}\] \[=5.3\,\,\min \]
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