Calculate the rate constant of the first order reaction if $80 \%$ of the reactant reacted in 15 minute.

Question

Aicharya · Accepted Answer

$80 \%$ of the reactant has reacted. So, if $[A]_0=100$, then $[A]_{\mathrm{t}}=100-80=20$ $\begin{aligned} \mathrm{k} & =\frac{2.303}{\mathrm{t}} \log _{10} \frac{[\mathrm{A}]_0}{[\mathrm{~A}]_{\mathrm{t}}} \ & =\frac{2.303}{15} \log _{10} \frac{100}{20} \ & =\frac{2.303}{15} \log _{10}(5) \ & =\frac{2.303}{15} 	imes 0.699 \ & =0.1073 \ & \approx 0.11 	ext { minute }^{-1} \end{aligned}$

Calculate the rate constant of the first order reaction if $80 \%$ of the reactant reacted in 15 minute.

Solution