Colligative Properties

Colligative: from Latin. = Co mean ‘together’; ligare means ‘to bind’.

Colligative properties are those properties which depend only upon the number of solute particles in a solution irrespective of their nature.

Relative Lowering of Vapour Pressure:

It is the ratio of lowering in the vapour to vapour pressure of the pure solvent. The relative lowering of the vapour pressure of the solution containing a nonvolatile solute is equal to the mole fraction of solute in the solution.

For dilute solution, n_B << n_A . Hence,

Above expression is used to find the molecular weight of an unknown solute dissolved in a given solvent. Where, W_B and W_A = mass of solute and solvent respectively. M_B and M_A = molecular weight of solute and solvent respectively.

Ostwald and walker method is used to determine the relative lowering of vapour pressure.

Elevation in Boiling Point (∆T_b)

Boiling point of a liquid is the temperature at which its vapour pressure is equal to the atmospheric pressure. As the vapour pressure of a solution containing a nonvolatile solute is lower than that of the pure solvent, it boiling point will be higher than that of the pure solvent as shown in figure. The increase in boiling point is known as elevation in boiling point, ∆T_b

K_b is molal elevation constant or ebullioscopic constant. Molecular mass of solute can be calculated as

Thus, in order to determine M₂, molar mass of the solute, known mass of solute in a known mass of the solvent is taken and ΔT_b is determined experimentally for a known solvent whose K_b value is known.

∆T_b = K_b × m = 0.52 K kg mol^-1 × 0.1 mol kg^-1 = 0.052 K

Since water boils at 373.15 K at 1.013 bar pressure, therefore, the boiling point of solution will be 373.15 + 0.052 = 373.202 K.

The boiling point elevation of a solution is determined by

1. Landsberger’s method
2. Cottrell’s method

Depression in Freezing Point (ΔT_f)

The freezing point of a liquid is the temperature at which its vapour pressure of the solvent in its liquid and solid phase become equal. As we know that vapour pressure of a solution containing nonvolatile solute is lower than that of the pure solvent, the solid form gets separated out at a lower temperature as shown in the figure.

The decrease in freezing point of a liquid is known as depression in freezing point

Depression in freezing point (∆T_f) = T⁰_f – T_f

Thus, for determining the molar mass of the solute we should know the quantities w₁, w₂, ΔT_f, along with the molal freezing point depression constant.
The values of K_f and K_b, which depend upon the nature of the solvent, can be ascertained from the following relations.

Here the symbols R and M₁ stand for the gas constant and molar mass of the solvent, respectively and T_f and T_b denote the freezing point and the boiling point of the pure solvent respectively in kelvin. Further, Δ_FusH and Δ_VapH represent the enthalpies for the fusion and vaporization of the solvent, respectively.