Chemistry Question from JEE Main 2023 · 29 January, Shift 1

Solid lead nitrate is dissolved in $1 \, \text{litre}$ of water. The solution was found to boil at $100.15^\circ \text{C}$. When $0.2 \, \text{mol}$ of NaCl is added to the resulting solution, it was observed that the solution froze at $-0.8^\circ \text{C}$. The solubility product of $\text{PbCl}_2$ formed is _____ $\times 10^{-6}$ at $298 \, \text{K}$ (Nearest integer).

Given: $K_b = 0.5 \, \text{K kg mol}^{-1}$, $K_f = 1.8 \, \text{kg mol}^{-1}$