Question

Identify the value of $\mathrm{X}$, if $\mathrm{X}$ molal solution of a compound in benzene has mole fraction of solute equal to $0.2$

Answer 1

Step 1: Given data

Mole fraction of $\mathrm{X}$ solute$=0.2$

Step 2: Calculating molality

Mole fraction$=\frac{\mathrm{number}\mathrm{of}\mathrm{moles}\mathrm{of}\mathrm{solute}}{\mathrm{number}\mathrm{of}\mathrm{moles}\mathrm{of}\mathrm{solvent}}$

$=\frac{{\mathrm{n}}_{\mathrm{B}}}{{\mathrm{n}}_{\mathrm{A}}+{\mathrm{n}}_{\mathrm{B}}}$

Let the total moles$=1$

Mole fraction of Benzene$=1-0.2\Rightarrow 0.8$

Molar mass of benzene$=78\mathrm{g}{\mathrm{mol}}^{-1}$

Molality$=\frac{1000\times {\mathrm{x}}_2}{{\mathrm{x}}_1\times {\mathrm{m}}_1}$

where ${\mathrm{x}}_2=$mole fraction of solute, ${\mathrm{x}}_1=$the mole fraction of benzene, and ${\mathrm{m}}_1=$the molar mass of benzene.

Molality$=\frac{1000\times 0.2}{0.8\times 78}\Rightarrow \frac{200}{57.4}\Rightarrow 3.205\mathrm{moles}{\mathrm{Kg}}^{-1}$

Therefore, molality or $\mathrm{X}$$=3.2\mathrm{moles}{\mathrm{Kg}}^{-1}$