Question

A first order reaction has a specific reaction rate of ${10}^{-2}{s}^{-1}$. How much time will it take for $20g$ of the reactant to reduce to $5g$ ?

• A. 138.6 s
• B. 238.6 s
• C. 693.0 s
• D. 346.5 s

Answer 1

The correct option is A 138.6 s

For first order reaction,
$k=\frac{2.303}{t}log\frac{a}{(a-x)}$
​a is initial concentration
(a-x) is reactant concentration at time 't'.

Thus,
$t=\frac{2.303}{k}log\frac{20}{\left(5\right)}$
$t=\frac{2.303}{{10}^{-2}}log4$
$t=\frac{2.303}{{10}^{-2}}log{2}^2$
$t=\frac{2.303}{{10}^{-2}}\times 2log2$
$t=138.6s$

Hence, option (a) is correct.