Question

Find out no. of moles and weight of solute in $0.5$ molal $N{a}_{2}S{O}_4$ solution if mass of solvent is $2$Kg. Find mole fraction of solute and solvent also?

Answer 1

$0.5$ molar ${Na}_2{SO}_4$ solution.

Let the weight of ${Na}_2{SO}_4$ be $W$.

$\therefore \frac{W/142}{(W+2000)\times {10}^{-3}}=0.5$

$\Rightarrow W=0.5\times 142\times {10}^{-3}\times (W+2000)$

$\Rightarrow$ $W=143.6$gm

$\therefore$ no. of moles $=\frac{143.6}{142}\approx 1.01$ moles

$x_{{Na}_2{SO}_4}=\frac{1.01}{1.01+\frac{2000}{18}}=\frac{1.01}{112.12}=9.08\times {10}^{-3}$

$x_{H_{2}O}=\frac{2000/18}{1.01+\frac{2000}{18}}=\frac{111.111}{112.12}=0.99\approx 1$