Question

A first order reaction takes 40 min for $30\%$ decomposition. Calculate $t_{\frac{1}{2}}$

Answer 1

a = 100; a - x = 100 - 30 = 70; t = 40 min
$k=\frac{2.303}{t}log\frac{a}{(a-x)}=\frac{2.303}{40min}log\frac{100}{70}=\frac{2.303}{40}log\frac{10}{7}=\frac{2.303}{40}log1.428=\frac{2.303}{40}\times 0.1548k=8.91\times {10}^{-3}mi{n}^{-1}{t}_{\frac{1}{2}}=\frac{0.693}{k}=\frac{0.693}{8.91\times {10}^{-3}mi{n}^{-1}}=77.78min{t}_{\frac{1}{2}}=77.78min$