Obtain the relationship between freezing point depression of a solution containing nonvolatile-nonelectrolyte solute and its molar mass. - Chemistry

Exercise | Q 6 | Page 46

Obtain the relationship between freezing point depression of a solution containing nonvolatile-nonelectrolyte solute and its molar mass.

Solution:

1. The freezing point depression (ΔT_f) is directly proportional to the molality of solution.

Thus, ΔT_f = K_f m         ….(1)

2. Suppose we prepare a solution by dissolving W₂ g of solute in W₁ g of solvent.

Moles of solute in W₁ g of solvent = ${\displaystyle \frac{{\text{W}}_2}{{\text{M}}_2}}$

where, M₂ is the molar mass of solute.

Mass of solvent = W₁ g = ${\displaystyle \frac{{\text{W}}_{1}g}{100\text{g}/\text{kg}}=\frac{{\text{W}}_1}{1000}}$ kg

3. The molality is expressed as,

m = ${\displaystyle \frac{\text{Moles of solute}}{\text{Mass of solvent in kg}}}$

m = ${\displaystyle \frac{{\text{W}}_2/{\text{M}}_2 \text{mol}}{{\text{W}}_1/1000\text{kg}}}$

m = ${\displaystyle \frac{1000{\text{W}}_2}{{\text{M}}_2{\text{W}}_1}{\text{mol kg}}^{-1}}$    ....(2)

4. Substituting equation (2) in equation (1), we get,

${\displaystyle △{\text{T}}_{\text{f}}=\frac{1000{\text{K}}_{\text{f}}{\text{W}}_2}{{\text{M}}_2{\text{W}}_1}}$

Hence,

${\displaystyle {\text{M}}_2=\frac{1000{\text{K}}_{\text{f}}{\text{W}}_2}{△{\text{T}}_{\text{f}}{\text{W}}_1}}$