The ideal solubility of gases in liquids

Let it be supposed that a solution of a gas in a liquid obeys Baoult s law over the whole range of comx osition and in particular up to the mole fraction of unity which corresponds to the liquefied gas at the particular temperature. Under such conditions the solubility of the gas can be calculated from a knowledge of its vapour pressure. This may be illustrated by means of an example. 

At 20 liquid carbon dioxide has a vapour pressure of 56.3 atm. If carbon dioxide dissolves in a solvent and obeys Baoult s law its mole fraction in the solution at 20 will be given by 

This value may be called the ideal solvbility at atmospheric pressure and is evidently independent of the nature of the solvent when it is expressed in the above form as a mole fraction. The tablet shows some of the observed solubilities, and it is seen that the ideal solubility is of the right order of magnitude in most of the solvents. 

In some cases, in order to apply the theory, it is necessary to extrapolate the vapour pressure of the liquefied gas beyond the critical point. For example, suppose that it is desired to estimate the ideal solubility of methane at a temperature of 25 C, which is far above critical. If the observed vapour pressures are extrapolated by means of the Clausius-Clapeyron equation, the estimated value of p at 25 is found to be 289 atm— but of course this does not correspond to a stable state of gas-liquid ecjuUibrium. The ideal solubility of methane at 25 is therefore 1/289=0.0035. Some of the observed solubilities, as quoted by Hildebrand and Scott, are given in the table. 

According to the theory, the solubility of a gas may be expected to decrease with rising temperature, since this causes an increase in this is in general agreement with experience. The most soluble gases may also be expected to be those which are the most condensible, corresponding to low values of p.  

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For the ideal solubilities of gases in liquids, a similar approach to that taken in Section 3.1 for the ideal solubilities of solids in liquids can be used and thus, Equation (3.69), analogous to Equation (3.8), is obtained ... 

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