CHAPTER 9
CONTACT EQUILIBRIUM PROCESSES - THEORY (cont'd)

GAS/LIQUID EQUILIBRIA

Molecules of the components in a liquid mixture or solution have a tendency to escape from the liquid surface into the gas above the solution. The escaping tendency sets up a pressure above the surface of the liquid owing to the resultant concentration of the escaped molecules. This pressure is called the vapour pressure of the liquid.

The magnitude of the vapour pressure depends upon the liquid composition and upon the temperature. For pure liquids, vapour-pressure relationships have been tabulated and may be found in reference works such as Perry (1997) or the International Critical Tables. For a solution or a mixture, the various components in the liquid each exert their own partial vapour pressures.

When the liquid contains various components it has been found that, in many cases, the partial vapour pressure of any component is proportional to the mole fraction of that component in the liquid. That is,

p_A = H_Ax_A                                                               (9.4)

where p_A is the partial vapour pressure of component A, H_A is a constant for component A at a given temperature and x_A is the mole fraction of component A in the liquid.

This relationship is approximately true for most systems and it is known as Henry's Law. The coefficient of proportionality H_A is known as the Henry's Law constant for component A, and has units of kPa (mole fraction)^-1. In reverse, Henry's Law can be used to predict the solubility of a gas in a liquid. If a gas exerts a given partial pressure above a liquid, then it will dissolve in the liquid until Henry's Law is satisfied and the mole fraction of the dissolved gas in the liquid is equal to the value appropriate to the partial pressure of that gas above the liquid. The reverse prediction can be useful for predicting the gas solubility in equilibrium below imposed gaseous atmospheres of various compositions and pressures.

EXAMPLE 9.3. Solubility of carbon dioxide in water
Given that the Henry's Law constant for carbon dioxide in water at 25°C is 1.6 x 10⁵ kPa (mole fraction)^-1, calculate the percentage solubility by weight of carbon dioxide in water under these conditions and at a partial pressure of carbon dioxide of 200 kPa above the water.

From Henry's Law p = Hx
                        200 = 1.6 x 10⁵x

                           x = 0.00125

                                     =  (w_CO2) /(   w_H20 +   w_CO2)
                                         44           18           44

But since ( w_H20/18) » (w_CO2/44)

                     1.25 x 10^-3 » (w_CO2/44) / ( w_H20/18)

and so (w_CO2/ w_H20) » 1.25 x 10^-3 / (44/18)
                                = 3.1 x 10^-3
                                = 3.1 x 10^-1 %
                                =  0.31%

Contact-Equilibrium Processes - THEORY > SOLID-LIQUID EQUILIBRIA

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