5 g of Na_2 SO_4 was dissolved in x g of H_2 O. The change in freezing point was found to be 3.82°C. If Na_2 SO_4 is 81.5% ionised, the value of x (…

$\displaystyle 5$ g of $\displaystyle \mathrm{Na}_2 \mathrm{SO}_4$ was dissolved in $\displaystyle x \mathrm{~g}$ of $\displaystyle \mathrm{H}_2 \mathrm{O}$. The change in freezing point was found to be $\displaystyle 3.82$°C. If $\displaystyle \mathrm{Na}_2 \mathrm{SO}_4$ is $\displaystyle 81.5$% ionised, the value of $\displaystyle x$ ( $\displaystyle K_f$ for water $\displaystyle =1.86^{\circ} \mathrm{C} \mathrm{kg} \mathrm{mol}^{-1}$ ) is approximately : (molar mass of $\displaystyle \mathrm{S}=32 \mathrm{~g} \mathrm{~mol}^{-1}$ and that of $\displaystyle \mathrm{Na}=23 \mathrm{~g} \mathrm{~mol}^{-1}$ )