## Vapour pressure lowering

The change of vapour pressure following the addition of a nonvolatile solute to a solvent may be determined by application of Raoult's law. Since the solute is nonvolatile, the total vapour pressure, P, above the dilute solution is

Figure 2.7 Graph of anaesthetic pressure P against the reciprocal of the reduced physiological temperature, Tr. Compounds not following the relationship (fluoromethane, perfluoromethane and perfluoroethane) are identified by the symbol □.

Reproduced from A. Cammarata, J. Pharm. Sci., 64, 2025 (1975) with permission.

Figure 2.7 Graph of anaesthetic pressure P against the reciprocal of the reduced physiological temperature, Tr. Compounds not following the relationship (fluoromethane, perfluoromethane and perfluoroethane) are identified by the symbol □.

Reproduced from A. Cammarata, J. Pharm. Sci., 64, 2025 (1975) with permission.

due entirely to the solvent and may be equated with p1, the vapour pressure of the solvent. From Raoult's law we have

where x2 is the mole fraction of the added solute. Rearranging gives Pt- Pi

That is, the relative lowering of the vapour pressure is equal to the mole fraction of the solute.

A direct consequence of the reduction of vapour pressure by the added solute is that the temperature at which the vapour pressure of the solution attains atmospheric pressure (that is, the boiling point) must be higher than that of the pure solvent.

In Fig. 2.8, points A and B represent the boiling points of pure solvent and solution respectively. The boiling point is thus raised by an amount T - T0 = A Tb. A-E represents the lowering of vapour pressure, pe - p, by the solution.

An expression for the boiling point elevation may readily be derived using the Clausius-Clapeyron equation (see Box 2.1). This expression allows the calculation of the increase of boiling point, A Tb, from the molality, m, of the solution using

ATb = Kbm where Kb is the molal elevation constant, which has the value 0.511 K mol 1 kg for water.

Another consequence of lowering of vapour pressure is that the freezing point of the solution is lower than that of the pure solvent. The freezing point of a solution is the temperature at which the solution exists in equilibrium with solid solvent. In such an equilibrium, the solvent must have the same vapour pressure in both solid and liquid states. Consequently, the freezing point is the temperature at which the vapour pressure curves of the solvent and solution intersect the sublimation curve of the solid solvent; that is, points C and D, respectively, in Fig. 2.8. The freezing point depression is T - T0 = ATf. An expression for freezing

### Box 2.1 Boiling point elevation

The vapour pressure of the solution is p at temperature T0 and pe (equal to that of pure solvent) at temperature T. According to the Clausius-Clapeyron equation we may write

 AHvap \T- 70]
0 0