Chemistry Question from JEE Main 2025 · 8 April, Shift 2

The equilibrium constant for decomposition of $H_2O$ $\text{(g)}$

$$H_2O(g) \rightleftharpoons H_2(g) + \frac{1}{2} O_2(g) \quad (\Delta G^\circ = 92.34 \, kJ \ mol^{-1})$$

is $8.0 \times 10^{-3}$ at $2300 \, \text{K}$ and total pressure at equilibrium is $1 \, \text{bar}$. Under this condition, the degree of dissociation ($\alpha$) of water is _____ $\times 10^{-2}$ (nearest integer value).

[Assume $\alpha$ is negligible with respect to $1$]