Question

The first order decomposition reaction takes 40 minutes for 50% decomposition.Calculate its half life period

Answer 1

Answer:

$\Large \bf{Given} -$

t = 40min

50% of the reactants undergoes decomposition that means out of 100 particles in reactant 50 particles has been used

Now,50 particles will undergo out of 100 particles

$\Large \bf{To\:find} -$

$\Large \sf{t_\frac{1}{2}} = \Large{?}$

$\Large \bf{Answer}$

$\text{You know for a first order reaction}$ $\text{half life is -}$

$\Large \sf{t_\frac{1}{2}}$ = $\Large \frac{0.693}{k}$

$\text{You can directly put half life formula }$ $\text{but k is missing}$

$\text{So,now you have to bring k in order to }$ $\text{solve}$

$\text{Now you can use,}$

$\Large \sf{k} = \frac{2.303}{t} \log\frac{[R]_o}{[R]}$

$\Large \sf{k} = \frac{2.303}{40} \log\frac{100}{50}$

$\Large \sf{k} = \frac{2.303}{40} \log2$

$\Large \sf{k} = \frac{2.303}{40}× 0.3010$

$\Large \sf{k} = \frac{0.6932}{40}$

$\large \sf{k} = 0.01733$

$\text{Now put k in half-life formula}$

$\Large \sf{t_\frac{1}{2}} = \frac{0.693}{0.01733}$

$\Large \sf{t_\frac{1}{2}} = 39.98min$