Half-life of first order reaction X \longrightarrow $\mathrm{Y}+\mathrm{Z}$ is 3 minutes. What is the time…
Half-life of first order reaction X \longrightarrow $\mathrm{Y}+\mathrm{Z}$ is 3 minutes. What is the time required to reduce the concentration of ${ }^{\prime} \mathrm{X}^{\prime}$ by $90 \%$ of it's initial concentration?
$4 \cdot 12$ minutes
$9.969$ minutes
$9 \cdot 105$ minutes
$12 \cdot 05$ minutes
Solution
$\begin{array}{l}
\mathrm{t}_{1 / 2}=3 \mathrm{~min} \\
\therefore \mathrm{k}=\frac{0.693}{\mathrm{t}_{1 / 2}}=\frac{0.693}{3}=0.231 \mathrm{~min}^{-1}
\end{array}$
$\begin{array}{l}
{[\mathrm{A}]_{0}=\text { Original amount of reactant }=100} \\
{[\mathrm{~A}]_{t}=\text { Reactant remaining unreacted }=100-90=10}
\end{array}$
For first order reaction,
$t=\frac{2.303}{k} \log _{10} \frac{[A]_{0}}{[A]_{t}}=\frac{2.303}{0.231 \mathrm{~min}^{-1}} \log _{10} \frac{100}{10}=9.969 \mathrm{~min}$