Question

Time required for 99.9% completion of a first order reaction is _____ time the time required for completion of 90% reaction.(nearest integer).

Answer 1

Correct Answer: 3

The rate constant $K$ for a first-order reaction is given by: \[ K = \frac{1}{t} \ln\left(\frac{100}{100 - \text{completion percentage}}\right) \]
For 99.9% completion:
\[ t_{99.9\%} = \frac{\ln(1000)}{K} \]
For 90% completion:
\[ t_{90\%} = \frac{\ln(10)}{K} \]
Ratio of times:
\[ \frac{t_{99.9\%}}{t_{90\%}} = \frac{\ln(1000)}{\ln(10)} = \frac{3 \ln(10)}{\ln(10)} = 3 \]