Chemistry - Chemical Equilibrium Question with Solution | TestHub

Decomposition of water gives:
${\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right) \rightleftharpoons {\mathrm{H}}_2\left(\mathrm{g}\right) + \frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)$

${\mathrm{P}}_0\left[1-\mathrm{\alpha }\right] {\mathrm{P}}_0\mathrm{\alpha } \frac{{\mathrm{P}}_0\mathrm{\alpha }}{2}$  partial pr. at eq.

Thus, ${\mathrm{P}}_0\left[1+\frac{\alpha }{2}\right]=1 \dots \left(1\right)$

${\mathrm{K}}_{\mathrm{p}}=\frac{\left({\mathrm{P}}_{{\mathrm{H}}_2}\right){\left({\mathrm{P}}_{{\mathrm{O}}_2}\right)}^{1/2}}{{\mathrm{P}}_{{\mathrm{H}}_2\mathrm{O}}}$

$\frac{\left({\mathrm{P}}_0\alpha \right){\left(\frac{{\mathrm{P}}_0\alpha }{2}\right)}^{1/2}}{{\mathrm{P}}_0\left[1-\mathrm{\alpha }\right]}=2\times {10}^{-3}$

since $\alpha$ is negligible w.r.t 1 thus, $1-\alpha \approx 1$

$\Rightarrow \frac{\alpha \sqrt{\alpha }}{\sqrt{2}}=2\times {10}^{-3}$

$\Rightarrow {\alpha }^{3/2}=2^{3/2}\times {10}^{-3}$

$\Rightarrow \alpha =2^{3/2\times 2/3}\times {10}^{-3\times 2/3}$

$\Rightarrow \alpha =2\times {10}^{-2}, \%\alpha =2\%$