Question

A first order reaction is 90% completed in 25 seconds. Find the rate constant and half-life period.

Answer 1

(A)

Rate constant

Formula for rate constant

$K=\frac{2.303}{t}{\log }_{10}\left(\frac{a_o}{a_o-x}\right)$

Given $t=25sec$

let, $a_o=100$ (since initial value not given)

$x=90$ ($90\%$ reaction completed)

$a_o-x=100-90=10$

Substituting the values

$K=\frac{2.303}{25}{\log }_{10}\left(\frac{100}{10}\right)$

$K=\frac{2.303}{25}\times 1\{{\log }_{10}10=1\}$

$k=0.09212se{c}^{-1}$

(B)

Half life period

Formula for $t1/2=\frac{0.693}{k}$

Substituting value of $k$ from above

$t1/2=\frac{0.693}{0.09212}$

$t1/2=7.5228sec$