Question

Two substances $R$ and $S$ decompose in solution independently, both following first order kinetics. The rate constant of $R$ is twice that of $S$. In an experiment, the solution initially contained $0.5$ millimoles of $R$ and $0.25$ of $S$. The molarities of $R$ and $S$ will be equal just at the end of time equal to

• A. twice the half life of R
• B. twice the half life of S
• C. the half life of S
• D. the half life of R

Answer 1

Answer: (A)

Substance $R$ Substance $S$
$2kk$ rate constant
$t^{1/2}{2}^{\circ }$ Half life period
$T=n\times t_{1/2}$
where $n=$ number of half life period
Amount of $R$ left $=\frac{0.5}{{\left(2\right)}^{T/t_{\frac{1}{2}}}}$
Amount of $S$ left $=\frac{0.25}{{\left(2\right)}^{T/2t_{\frac{1}{2}}}}$
Equating both $\frac{0.5}{0.25}=\frac{(2{)}^{\frac{T}{t_{1/2}}}}{(2{)}^{\frac{T}{t_{1/2}}}}$
or $2=(2{)}^{\frac{T}{t_{1/2}}}$
$\therefore T=2t_{1/2}.2t_{1/2}$ is half life of $S$ and twice the half -life of $R$