\( = \,\frac{{\Delta {T_f}}}{{{K_f}}}\, = \,\frac{{3.82}}{{1.86}}\, = \,2.054\,mol/1000\,g\) solvent

Molality (theoretical)

\( = \,\frac{{mole\,\,of\,solute}}{{wt.\,of\,solventing\,(g)}} \times 1000\)

\( = \,\frac{{5\,g\,/\,142\,g\,/\,mole}}{x} \times 1000\)

                                            \(N{a_2}S{O_4}\, \to \,2N{a^ + }\, + \,SO_4^{2 - }\)

Moles before dissociation              \(1\)              \(0\)              \(0\)

Moles after dissociation              \(1-x\)              \(2x\)              \(x\)

Von't Hoff Factor \((i) = \,\frac{{Moles\,after\,\,dissociation}}{{Moles\,before\,\,dissociation}}\)

                               \( = \frac{{(1 - x)\, + \,2x\, + \,x}}{1}\)

\(Na_2SO_4\) is ionised \(81.5\%\) means \(x\,=\,0.815\)

                             \( = \frac{{(1 - 0.815)\, + \,2 \times 0.815\, + \,0.815}}{1}\)

                              \(=\,2.63\)

\(i\, = \,\frac{{Observed\,\,molarrity}}{{Calculated\,\,molarity}}\)

\( \Rightarrow \,2.63\, = \,\frac{{2.054}}{{\frac{{0.0352}}{x} \times 1000}}\, = \,45.07\,g\)