Question

The rate constant for a first order reaction is 60/s. How much time will it take to reduce the initial concentration of the reactant to its 1/10 th value ?

Answer 1

Let the initial concentration of reactant be $a_o$ M.

So, the one-tenth value of the initial value will be $0.1a_o$ M.

Given, Rate constant (k) of reaction = $60se{c}^{-1}$

For first-order reaction:

$t=\frac{2.303}{k}log\frac{a_o}{a_t}$

$⟹t=\frac{2.303}{60}log\frac{a_o}{0.1a_0}$

$⟹t=\frac{2.303}{60}log10$

$⟹t=\frac{2.303}{60}$

$⟹t=0.38sec$

So, the time taken to reduce the initial concentration of the reactant to its one-tenth value is 0.38 sec.