Q. The reaction $A_{\left(\right. g \left.\right)}+2B_{\left(\right. g \left.\right)} \rightarrow C_{\left(\right. g \left.\right)}+D_{\left(\right. g \left.\right)}$ is an elementary process. In an experiment, the initial partial pressure of $A\&B$ are $P_{A}=0.6\&P_{B}=0.8atm$ , when $P_{C}=0.2atm$ the rate of reaction relative to the intial rate is:

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$\frac{1}{48}$

$\frac{1}{24}$

$\frac{9}{16}$

$\frac{1}{6}$

Solution:

$ & A+ & 2B \rightarrow & C+ & D & \\ & \left(\right.g\left.\right) & \left(\right.g\left.\right) & \left(\right.g\left.\right) & \left(\right.g\left.\right) & \\ t=0 & 0.6 & 0.8 & 0 & 0 & \ldots \left(\right.1\left.\right) \\ t=t & 0.6-0.2 & 0.8-2\times 0.2 & 0.2 & 0.2 & \\ = & 0.4 & 0.4 & 0.2 & 0.2 & ..\left(\right.2\left.\right)$
from Equation $\left(\right.1\left.\right)$
$r_{i}=K\left[\right.0.6\left]\right.\left[\right.0.8\left]\right.^{2}$
From Equation $\left(\right.2\left.\right)$
$r_{f}=K\left[\right.0.4\left]\right.\left[\right.0.4\left]\right.^{2}$
$\frac{r_{f}}{r_{i}}=\frac{K \left[\right. 0 . 4 \left]\right. \left[\right. 0 . 4 \left]\right.^{2}}{K \left[\right. 0 . 6 \left]\right. \left[\right. 0 . 8 \left]\right.^{2}}$
$=\frac{0 . 4 \times 0 . 4 \times 0 . 4}{0 . 6 \times 0 . 8 \times 0 . 8}=\frac{1}{6}$

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