##### 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 W_{2} g of solute in W_{1} g of solvent.

Moles of solute in W_{1} g of solvent = $\frac{{\text{W}}_{2}}{{\text{M}}_{2}}$

where, M_{2} is the molar mass of solute.

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

3. The molality is expressed as,

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

m = $\frac{{\text{W}}_{2}/{\text{M}}_{2}\text{mol}}{{\text{W}}_{1}/1000\text{kg}}$

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

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

$\u25b3{\text{T}}_{\text{f}}=\frac{1000{\text{K}}_{\text{f}}{\text{W}}_{2}}{{\text{M}}_{2}{\text{W}}_{1}}$

Hence,

$\text{M}}_{2}=\frac{1000{\text{K}}_{\text{f}}{\text{W}}_{2}}{\u25b3{\text{T}}_{\text{f}}{\text{W}}_{1}$

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 W_{2} g of solute in W_{1} g of solvent.

Moles of solute in W_{1} g of solvent =

where, M_{2} is the molar mass of solute.

Mass of solvent = W_{1} g =

3. The molality is expressed as,

m =

m =

m =

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

Hence,