Question

If the rate constant for a first order reaction is k, the time(t) required for the completion of $99\%$ of the reaction is given by :

• A. t = 4.606/k
• B. t = 2.303/k
• C. t = 0.693/k
• D. t = 6.909/k

Answer 1

Answer: (A)

First order rate constant is given as,
$k=\frac{2.303}{t}\log \frac{\left[A_0\right]}{{\left[A\right]}_t}$
99% completed reaction,
$k=\frac{2.303}{t}\log \frac{100}{1}$
$=\frac{2.303}{t}\log 10^2$
$k=\frac{2.303}{t}\times 2\log 10$
$t=\frac{2.303}{k}\times 2=\frac{4.606}{k}$
$t=\frac{4.606}{k}$