A solution of 1.25 g of P in 50 g of water lowers the freezing point of water by 0.3^oC. Molar mass of P is $94.{\mathrm{K}}_{\mathrm{f}\left(\mathrm{water}\right)}=1.86 \mathrm{K} \mathrm{kg} {\mathrm{mol}}^{-1}$.' The degree of association of P in water is

Step I Calculation of van't Hoff factor for P
             $\begin{array}{r}{\mathrm{\Delta T}}_{\mathrm{f}}=\mathrm{i}\times {\mathrm{K}}_{\mathrm{f}}\times \mathrm{m}=\mathrm{i}\times {\mathrm{K}}_{\mathrm{f}}\times \frac{{\mathrm{w}}_2\times 1000}{{\mathrm{w}}_1\times {\mathrm{M}}_2}\\ 0.3=\mathrm{i}\times 1.86\times \frac{1.25\times 1000}{50\times 94}\\ \Rightarrow \mathrm{i}=\frac{0.3\times 50\times 94}{1.86\times 1.25\times 1000}=0.6064\end{array}$
Step II Calculation of degree of association of P Degree of association,$\mathrm{\alpha }$
            $\begin{array}{r}=\frac{\mathrm{i}-1}{\frac{1}{\mathrm{n}}-1}=\frac{0.6064-1}{\frac{1}{2}-1}=\frac{-0.3936}{-0.5}\\ =0.7872=78.72\mathrm{\%}\approx 80\mathrm{\%}\end{array}$