a
Let a mole \(Pb \left( NO _3\right)_2\) be added

\(Pb \left( NO _3\right)_2 \rightarrow Pb ^{2+}+2 NO _3^{-}\)

a \(\quad\quad\quad\quad\quad\quad\) a \(\quad\qquad 2 a\)

\(\Delta T _{ b }=0.15=0.5[3 a ] \Rightarrow a =0.1\)

\(Pb _{( aq )}^{2+}+2 Cl _{( aq )}^{-} \rightarrow PbCl _2( s )\)

\(\begin{array}{llc} t =0 & 0.1 & 0.2 \\ t =\infty & (0.1- x ) & (0.2-2 x )\end{array}\)

In final solution

\(\Delta T _{ f }=0.8=1.8\left[\frac{0.3-3 x +0.2+0.2}{1}\right]\)

\(\Rightarrow x =\frac{2.3}{27}\)

\(\Rightarrow K _{ sp }=\left(0.1-\frac{2.3}{27}\right)\left(0.2-\frac{4.6}{27}\right)^2=13 \times 10^{-6}\)