JEE MAIN - Chemistry (2023 - 29th January Morning Shift - No. 18)
Water decomposes at 2300 K
$$\mathrm{H_2O(g)\to H_2(g)+\frac{1}{2}O_2(g)}$$
The percent of water decomposing at 2300 K and 1 bar is ___________ (Nearest integer).
Equilibrium constant for the reaction is $$2\times10^{-3}$$ at 2300 K.
Answer
2
Explanation
$\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2}$
$$ \begin{aligned} & \mathrm{K}_{\mathrm{p}}=\frac{\mathrm{P}_{\mathrm{T}}^{\frac{3}{2}}\left(1+\frac{\alpha}{2}\right) \alpha^{\frac{3}{2}}}{2^{\frac{1}{2}} \mathrm{P}_{\mathrm{T}}\left(1+\frac{\alpha}{2}\right)^{\frac{3}{2}}(1-\alpha)} \\\\ & 2 \times 10^{-3}=\frac{\alpha^{\frac{3}{2}}}{2^{\frac{1}{2}}}\left[\text { as } \alpha<<1 \text { and let } \mathrm{P}_{\mathrm{T}}=1\right] \end{aligned} $$
$$ \begin{aligned} & \alpha^{\frac{3}{2}}=2^{\frac{3}{2}} \times 10^{-3} \\\\ & \approx 2 \times 10^{-2} \end{aligned} $$
$\therefore \%$ of water decomposition $=2 \%$
$$ \begin{aligned} & \mathrm{K}_{\mathrm{p}}=\frac{\mathrm{P}_{\mathrm{T}}^{\frac{3}{2}}\left(1+\frac{\alpha}{2}\right) \alpha^{\frac{3}{2}}}{2^{\frac{1}{2}} \mathrm{P}_{\mathrm{T}}\left(1+\frac{\alpha}{2}\right)^{\frac{3}{2}}(1-\alpha)} \\\\ & 2 \times 10^{-3}=\frac{\alpha^{\frac{3}{2}}}{2^{\frac{1}{2}}}\left[\text { as } \alpha<<1 \text { and let } \mathrm{P}_{\mathrm{T}}=1\right] \end{aligned} $$
$$ \begin{aligned} & \alpha^{\frac{3}{2}}=2^{\frac{3}{2}} \times 10^{-3} \\\\ & \approx 2 \times 10^{-2} \end{aligned} $$
$\therefore \%$ of water decomposition $=2 \%$
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