# Dalton’s law of partial pressure

This may be stated as follows:

If a mixture of gases occupies a given volume at a given temperature, the total pressure exerted by the mixture equals the sum of the pressures of the constituents, each being considered at the same volume and temperature.

It is possible to show that if Dalton’s law holds, each component of the mixture obeys the general gas law. As a consequence, it is sometimes more convenient to re-express the law in two parts:

(i) the pressure exerted by each gas in a mixture of gases is independent of the presence of the other gases, and

(ii) the total pressure exerted by a mixture of gases equals the sum of the partial pressures.

Figure 2.4 illustrates this. It shows an air-tight container under three different conditions, from which it can be seen that the partial pressures exerted by the water vapour in (b) and (c) are equal, as are those exerted by the dry air in (a) and (c) and, that in (a), (b) and (c), the total pressure equals the sum of the partial pressures.

As in the two gas laws already considered, Dalton’s law agrees with the results achieved by the kinetic theory of gases and, to some extent, finds substantiation in experiment.

 Dry air plus water vapour

 Water Vapour Only

 Dry Air Only

 (a) : 20°C ma = 1 kg ms = 0 kg pa = 100143 Pa Ps = 0 Pat = 100143 Pa

 F =

T = 20°C ma = 0 kg ms = 0.007 376 kg

Pa = 0

Ps = 1182 Pa Pa, = 1182 Pa

(c)

T = 20°C ma = 1 kg ms = 0.007 376 kg pa = 100143 Pa ps = 1182 Pa pa, = 101 325 Pa

Fig. 2.4 Dalton’s law of partial pressure referred to a mixture of dry air and water vapour.

It is now necessary to turn attention to the behaviour of water vapour at the state of saturation and to consider its partial pressure when it is in the superheated state and mixed with dry air.

Posted in Engineering Fifth Edition