Question

A first order reaction completes $50$% in $69.3$ minute. How much time it will take for $90$% completion?

Answer 1

For a first order reaction,
rate constant, $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{69.3}=0.01mi{n}^{-1}$
$k=\frac{2.303}{t}lo{g}_{10}\frac{a}{a-x}$
where, $a=$ initial amount of reactant
$(a-x)=$amount of reactant remaining after time t
${}^{\prime }{t}^{\prime }=0.1a$ for $90\%$ completion
$0.01=\frac{2.303}{t}lo{g}_{10}\frac{a}{0.1a}$
$t=\frac{2.303}{0.01}=230.3min$
Hence, (a) option is correct.