Discussion Forum



1)

The rate constant and half-life of a first order reaction are related to each other as


A) $ t_{1/2}=\frac{0.693}{k}$

B) $t_{1/2}=0.693 k$

C) k=$0.693 t_{1/2}$

D) $k t_{1/2}=\frac{1}{0.693}$

Answer:

Option A

Explanation:

For first order reaction,    $k=\frac{2.303}{t}\log\frac{[A_{0}]}{[A]}$

At   $t= t_{1/2}$,[A]=$[A_{0}]$/2

$k=\frac{2.303}{t_{1/2}}\log\frac{[A_{}]}{[A_{0}]/2};k=\frac{2.303}{t_{1/2}}\log 2$

$k=\frac{2.303}{t_{1/2}} $    or $t_{1/2}=\frac{0.693}{k}$