The reaction $2 \mathrm{X} \rightarrow \mathrm{B}$ is a zeroth order reaction. If the initial concentration…
The reaction $2 \mathrm{X} \rightarrow \mathrm{B}$ is a zeroth order reaction. If the
initial concentration of $\mathrm{X}$ is $0.2 \mathrm{M}$, the half-life is $6 \mathrm{~h}$. When the initial concentration of $X$ is $0.5 \mathrm{M}$, the time required to reach its final concentration of $0.2 \mathrm{M}$ will be
$9.0 \mathrm{~h}$
$12.0 \mathrm{~h}$
$18.0 \mathrm{~h}$
$7.2 \mathrm{~h}$
Solution
For the reaction $2 \mathrm{X} \rightarrow \mathrm{B}$, follow zeroth order Rate equation is $\mathrm{Kt}=[\mathrm{A}]_{0}-[\mathrm{A}]$
For the half-life; $t=t_{1 / 2}$ and $[A]=0.1$ $\mathrm{Kt}_{12}=0.2-0.1$
$\frac{0.2-0.1}{6}=\frac{0.1}{6} \mathrm{Mhr}^{-1}$
$\therefore$ Time required to reach from $0.5 \mathrm{M}$ to $0.2 \mathrm{M}$ $\mathrm{Kt}=[\mathrm{A}]_{0}-[\mathrm{A}]$
$\frac{0.1}{6} \times \mathrm{t}=(0.5-0.2) ; \mathrm{t}=18$ hour