Chemistry Question from JEE Main 2025 · 24 January, Shift 1

$37.8 \, \text{g}$ $N_2O_5$ was taken in a $1 \, \text{L}$ reaction vessel and allowed to undergo the following reaction at $500 \, \text{K}$:

$$2N_2O_5(g) \rightarrow 2N_2O_4(g) + O_2(g)$$

The total pressure at equilibrium was found to be $18.65 \, \text{bar}$. Then, $K_p$ is _____ $\times 10^{-2}$ (nearest integer). Assume $N_2O_5$ behaves ideally under these conditions. Given:

$$R = 0.082 \, \text{bar L mol}^{-1} \text{K}^{-1}$$