1. Tardigrade
  2. Question
  3. Chemistry
  4. 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

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Q. 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

BITSATBITSAT 2014

Solution:

Substance $R\,\,\,$ Substance $S$
$2k\,\,\, k$ 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 $R$