Solid Lead nitrate is dissolved in \(1\,litre\) of water. The solution was found to boil at \(100.15^{\circ}\,C\). When \(0.2\,mol\) of \(NaCl\) is added to the resulting solution, it was observed that the solution froze at \(-0.8^{\circ}\,C\). The solutbility product of \(PbCl _2\) formed is \(...........\times 10^{-6}\) at \(298\,K\). (Nearest integer) Given : \(K _{ b }=0.5\,K\,kg\,mol ^{-1}\) and \(K _{ f }=1.8\,kg\,mol ^{-1}\). Assume molality to be equal to molarity in all cases.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.