For the thermal decomposition of $\mathrm{N}_2 \mathrm{O}_5(\mathrm{~g})$ at constant volume, the following…

For the thermal decomposition of $\mathrm{N}_2 \mathrm{O}_5(\mathrm{~g})$ at constant volume, the following table can be formed, for the reaction mentioned below.
$2 \mathrm{~N}_2 \mathrm{O}_5(\mathrm{~g}) \rightarrow 2 \mathrm{~N}_2 \mathrm{O}_4(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g})$

$\mathrm{x}=\ldots \times 10^{-3} \mathrm{~atm} \text { [nearest integer] }$
Given : Rate constant for the reaction is $4.606 \times 10^{-2} \mathrm{~s}^{-1}$.

Solution

$2 \mathrm{~N}_2 \mathrm{O}_5(\mathrm{~g}) \rightarrow 2 \mathrm{~N}_2 \mathrm{O}_4(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g})$
$\begin{aligned} & k=\frac{2.303}{t} \log \frac{0.9-0.6}{(0.9-x)} \\ & 2 \times 10^{-2} \times 100=\log \frac{0.3}{(0.9-x)} \\ & 100=\frac{0.3}{(0.9-x)} \\ & =\frac{0.9-x}{0.3}=0.01 \\ & 0.9-X=0.003 \\ & =897 \times 10^{-3}\end{aligned}$

Asked in: JEE Main 2025 (23 Jan Shift 1)

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