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:

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> NEET (UG)-2019

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

Answer 1

The correct option is A $t=4.606/k$

First order rate constant is given as,
$k=\frac{2.303}{t}log\frac{\left[A_0\right]}{\left[A_t\right]}$
$\left[A_0\right]$ is initial concentration of reactant
$\left[A_t\right]$ is concentration of reactant at time 't'

99% completed reaction,

$k=\frac{2.303}{t}log\frac{100}{1}=\frac{2.303}{t}log{10}^{2}k=\frac{2.303}{t}\times 2log10t=\frac{2.303}{k}\times 2=\frac{4.606}{k}t=\frac{4.606}{k}$

Hence, option (a) is correct.