The molar mass of calcium nitrate as determined from the colligative properties is found to be $65.6 \mathrm{g}{ \mathrm{mol}}^{-1}$, The degree of dissociation of the salt is

We have

$\begin{array}{ll}{\mathrm{Ca}}_3{\left({\mathrm{NO}}_3\right)}_2\rightleftharpoons & {\mathrm{Ca}}^{2+}+2{\mathrm{NO}}_3^{-}\\ c(1-\alpha )& \mathrm{c}\alpha c\left(2\alpha \right)\end{array}$

Total concentration $=c(1-\alpha )+c\alpha +c\left(2\alpha \right)=c(1+2\alpha )$

$\frac{\text{ Theoretical molecular mass }}{\text{ Observed molecular mass }}=\frac{(1+2\alpha )}{1}\Rightarrow \frac{164}{65.6}=\frac{1+2\alpha }{1}\Rightarrow \alpha =0.75$