Question

Water decomposes at $2300K$
$H_{2}O(g)\to H_2(g)+\frac{1}{2}{O}_2(g)$
The percent of water decomposing at $2300K$ and 1 bar is______ (Nearest integer).
Equilibrium constant for the reaction is $2\times 10^{-3}$ at $2300K$.

Answer 1

Answer: 2

$P_0\left[1+\frac{\alpha }{2}\right]=1$...(i)
$K_p=\frac{\left(P_{H_2}\right){\left(P_{O_2}\right)}^{1/2}}{P_{H_{2}O}}$
$\frac{\left(P_0\alpha \right){\left(\frac{P_0\alpha }{2}\right)}^{1/2}}{P_0[1-\alpha ]}=2\times 10^{-3}$
since $\alpha$ is negligible w.r.t $1\text{ so }{P}_0=1\text{ and }1-\alpha \approx 1$
$\frac{\alpha \sqrt{\alpha }}{\sqrt{2}}=2\times 10^{-3}$
${\alpha }^{3/2}=2^{3/2}\times 10^{-3}$
$\alpha =2^{3/2\times 2/3}\times 10^{-3\times 2/3}$
$\alpha =2\times 10^{-2}\%\alpha =2\%$