Question

In a first order reaction, $x$ is converted into $y$. $40\%$ of the sample decomposes in $112$ min. What is the half life of this reaction?

Answer 1

After 112 mins, reactant left$=a_t=0.6a_0$

where $a_0=$ initial reactant concentration

For 1st order reaction , $K=\frac{1}{t}\ln \frac{a_0}{a_t}$ & $K=\frac{\ln 2}{t_{\frac{1}{2}}}$

$\therefore \frac{\ln 2}{t_{\frac{1}{2}}}=\frac{1}{112}\times \ln \frac{a_0}{0.6a_0}$

$\therefore t_{\frac{1}{2}}=151.9mins$