\(P _0[1-\alpha] \quad P _0 \alpha \quad \frac{ P _0 \alpha}{2} \quad \text { partial pr. at eq }\)

\(P _0\left[1+\frac{\alpha}{2}\right]=1\)

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

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

since \(\alpha\) is negligible w.r.t 1 so \(P _0=1\) and \(1-\alpha \approx 1\)

\(\frac{\alpha \sqrt{\alpha}}{\sqrt{2}}=2 \times 10^{-3}\)

\(\alpha^{3 / 2}=2^{3 / 2} \times 10^{-3}\)

\(\alpha=2^{3 / 2 \times 2 / 3} \times 10^{-3 \times 2 / 3}\)

\(\alpha=2 \times 10^{-2} \quad \% \alpha=2 \%\)