Question

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

Answer 1

$ 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 \%$