## T0r

Mole fraction may be replaced by molality, m, using the relationship x2 = m^/1000

Therefore,

where Kb is the molal elevation constant, which has the value 0.511 K mol-1 kg for water, and My is the molecular weight of the solvent.

point lowering can be derived in a similar manner to that for boiling point elevation, giving

RT0M1m

1QQQ AH,

fus where AHfus is the molal heat of fusion. Therefore,

where Kf is the molal freezing point constant, which is 1.86 K mol 1 kg for water.

2.4 Solubility of gases in liquids

The amount of gas which can be dissolved by a particular liquid depends on the temperature, the pressure and the nature of both the gas and the liquid solvent. The solubility may be expressed by Bunsen's absorption coefficient, a, which is the volume of gas reduced to 273 K and a pressure of 1 bar which dissolves in a unit volume of the liquid at the given temperature when the partial pressure of the gas is 1 bar.

EXAMPLE 2.4 Calculation of the Bunsen absorption coefficient

If the solubility of N2 in water at 25°C and a nitrogen pressure of 450 torr is 0.378 mol m-3, calculate the Bunsen coefficient.

The volume, V, of dissolved nitrogen at 0°C and a pressure of 760 torr (1.013 x 105 N m-2), assuming ideality, is given by equation (2.1) as

The volume of N2 that would dissolve at a nitrogen pressure of 760 torr is

That is, the Bunsen absorption coefficient for N2 at 25°C is 0.0143.

In anaesthetic practice, an alternative solubility coefficient, the Ostwald solubility coefficient, is preferred. This coefficient is defined as the volume of gas which dissolves in a unit volume of the liquid at the given temperature. The volume of gas is not corrected to standard temperature and pressure but instead is measured at the temperature and pressure concerned. The important difference between these two coefficients is that the Ostwald coefficient is independent of pressure, as we can see from the following example.

Consider a closed vessel containing 1 dm3 (1 litre) of water above which is nitrogen at a pressure of 1 bar at room temperature. The volume of nitrogen dissolved at equilibrium is 0.016 dm3. If the pressure is increased to 2 bar at the same temperature, then the amount of nitrogen which dissolves is doubled, according to Henry's law (see section 2.4.2). The resultant volume of nitrogen dissolved is 0.032 dm3 when measured at 1 bar but 0.016 dm3 when measured at the ambient pressure of 2 bar (according to the ideal gas law). Consequently, the volume of nitrogen dissolved measured at ambient pressure, and hence the Ostwald coefficient, remains unchanged even though the partial pressure of the nitrogen and also the number of dissolved molecules are doubled.

### 2.4.1 Effect of temperature on solubility

When gases dissolve in water without chemical reaction there is generally an evolution of heat. Hence by Le Chatelier's principle an increase in temperature usually leads to a decreased solubility. The effect of temperature on the absorption coefficient may be determined from an equation analogous to the van't Hoff equation:

0 0