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Consider the following single step reaction in gas phase at constant temperature.
\(2 \mathrm{~A}_{(\mathrm{g})}+\mathrm{B}_{(\mathrm{g})} \rightarrow \mathrm{C}_{(\mathrm{g})}\)
The initial rate of the reaction is recorded as \(\mathrm{r}_1\) when the reaction starts with \(1.5 \mathrm{~atm}\) pressure of \(\mathrm{A}\) and \(0.7 \mathrm{~atm}\) pressure of \(\mathrm{B}\). After some time, the rate \(\mathrm{r}_2\) is recorded when the pressure of \(\mathrm{C}\) becomes \(0.5 \mathrm{~atm}\). The ratio \(\mathrm{r}_1: \mathrm{r}_2\) is ______ \(\times 10^{-1}\). (Nearest integer)
\(2 \mathrm{~A}_{(\mathrm{g})}+\mathrm{B}_{(\mathrm{g})} \rightarrow \mathrm{C}_{(\mathrm{g})}\)
The initial rate of the reaction is recorded as \(\mathrm{r}_1\) when the reaction starts with \(1.5 \mathrm{~atm}\) pressure of \(\mathrm{A}\) and \(0.7 \mathrm{~atm}\) pressure of \(\mathrm{B}\). After some time, the rate \(\mathrm{r}_2\) is recorded when the pressure of \(\mathrm{C}\) becomes \(0.5 \mathrm{~atm}\). The ratio \(\mathrm{r}_1: \mathrm{r}_2\) is ______ \(\times 10^{-1}\). (Nearest integer)
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The correct answer is:
315
$2 \mathrm{~A}(\mathrm{~g})+\mathrm{B}(\mathrm{g}) \longrightarrow \mathrm{C}(\mathrm{g})$
$\begin{array}{ll}
\mathrm{r}_1 & 1.5 \mathrm{~atm} \quad 0.7 \mathrm{~atm} \\
\mathrm{r}_2 & 0.5 \mathrm{~atm} \quad 0.2 \mathrm{~atm} \quad 0.5 \mathrm{~atm} \\
& \because \mathrm{r}=\mathrm{K}\left[\mathrm{P}_{\mathrm{A}}\right]^2\left[\mathrm{P}_{\mathrm{B}}\right] \\
& \mathrm{r}_1=\mathrm{K}[1.5]^2[0.7] \\
& \mathrm{r}_2=\mathrm{K}[0.5]^2[0.2] \\
& \frac{\mathrm{r}_1}{\mathrm{r}_2}=9 \times \frac{7}{2}=31.5=315 \times 10^{-1}
\end{array}$
Ans. 315
$\begin{array}{ll}
\mathrm{r}_1 & 1.5 \mathrm{~atm} \quad 0.7 \mathrm{~atm} \\
\mathrm{r}_2 & 0.5 \mathrm{~atm} \quad 0.2 \mathrm{~atm} \quad 0.5 \mathrm{~atm} \\
& \because \mathrm{r}=\mathrm{K}\left[\mathrm{P}_{\mathrm{A}}\right]^2\left[\mathrm{P}_{\mathrm{B}}\right] \\
& \mathrm{r}_1=\mathrm{K}[1.5]^2[0.7] \\
& \mathrm{r}_2=\mathrm{K}[0.5]^2[0.2] \\
& \frac{\mathrm{r}_1}{\mathrm{r}_2}=9 \times \frac{7}{2}=31.5=315 \times 10^{-1}
\end{array}$
Ans. 315
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