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)

t = 4.606/k

Answer 2

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,
$k = \frac{2.303}{t} \log \frac{100}{1}$
$= \frac{2.303}{t} \log10^{2}$
$k = \frac{2.303}{t} \times2 \log 10$
$t = \frac{2.303}{k} \times2 = \frac{4.606}{k}$
$t = \frac{4.606}{k}$