The equilibrium constant for decomposition of H_2 O ( g ) H_2 O ( g ) ⇌ H_2( g )+1/2 O_2( g )(Δ G^°=92.34 kJ mol^-1) is 8.0 × 10^-3 at 2300 K and…

The equilibrium constant for decomposition of $\displaystyle \mathrm{H}_2 \mathrm{O}(\mathrm{g})$ $$\mathrm{H}_2 \mathrm{O}(\mathrm{~g}) \rightleftharpoons \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g})\left(\Delta \mathrm{G}^{\circ}=92.34 \mathrm{~kJ} \mathrm{~mol}^{-1}\right) $$ is $\displaystyle 8.0 \times 10^{-3}$ at $\displaystyle 2300$ K and total pressure at equilibrium is $\displaystyle 1$ bar. Under this condition, the degree of dissociation ( $\displaystyle \alpha$ ) of water is $\displaystyle \_\_\_\_$ $\displaystyle \times 10^{-2}$ (nearest integer value). [Assume $\displaystyle \alpha$ is negligible with respect to $\displaystyle 1$]