Answer

Applying equation (2.17) at the two partial pressures, noting that k is the same at both:

Wl/Pl = W 2 Ip2 where p1 = 25 torr and w1 = 8.31 mg dm-3 p2 = 100 torr and w2 = ? gives w2 = 100 x 8.31/25 = 33.2 mg dm-3

The solubility of oxygen at a partial pressure of 100 torr is 33.2 mg dm 3.

Rather than considering equation (2.17) as a means of expressing the solubility of a gas in terms of vapour pressure, we could also view it as a way of expressing the vapour pressure developed by a given concentration of dissolved gas, as explained in Box 2.2.

Box 2.2 Relationship between Henry's law and Raoult's law

By expressing the solubility of a gas in terms of vapour pressure, we invoke an analogy with Raoult's law which gives the vapour pressure p^ of the solvent in equilibrium with a solution in which the solvent mole fraction is Xy, as pi = xi pe

where pf is the vapour pressure of pure solvent. Assuming the solute rather than the solvent to be the volatile component, we may write p2 = x2pe

For a dilute solution of a gas we may express the concentration of gas in terms of the mole fraction and thus Henry's law may be written x2 = k ' p2

Comparing equations (2.19) and (2.20), it is clear that the Henry's law and Raoult's law expressions would become identical if k' could be equated with 1 /pf. Such an equating of terms is valid in the case of ideal solutions only, and in most solutions of gases in liquids, although k' is constant, it is not equal to 1/pf.

Figure 2.9 shows the plot of the partial pressure of chloroform in an oleyl alcohol-chloroform mixture as a function of the percentage of chloroform in the gas phase. Significant departures from Raoult's law are apparent when the amount of dissolved chloroform exceeds about 20%.

Figure 2.9 Plot of the partial pressure of chloroform in the gas phase over an oleyl alcohol-chloroform mixture at 20°C as a function of the percentage of chloroform in the mixture; solid circles represent experimental results; full curve is the Raoult's law plot.

Reproduced from J. F. Nunn, Br. J. Anaesth., 32, 346 (1960) with permission.

Figure 2.9 Plot of the partial pressure of chloroform in the gas phase over an oleyl alcohol-chloroform mixture at 20°C as a function of the percentage of chloroform in the mixture; solid circles represent experimental results; full curve is the Raoult's law plot.

Reproduced from J. F. Nunn, Br. J. Anaesth., 32, 346 (1960) with permission.

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