Question

For a first order reaction the rate constant is 6.909 $min^{-1}$. The time taken for 75% conversion in minutes is

• A. $\frac{3}{2} \, log \, 2$
• B. $\frac{2}{3} \, log \, 3$
• C. $\frac{2}{3} \, log \, 2$
• D. $\frac{3}{2} \, log \, \frac{3}{4}$
• E. $\frac{2}{3} \, log \, \frac{4}{3}$

Answer 1

Answer: (C)

For first order reaction,
$ k = \frac{2.303}{t} \, log \, \frac{a}{a-x}$
$ 6.909 = \frac{2.303}{t} \, log \, \frac{100}{100-75}$
$t = \frac{2.303}{6.909} \, log \, 4$
$ = \frac{1}{3} \, log \, 2^2$
$ = \frac{2}{3} \, log \, 2$