In Chapter 16 we discussed how the partial pressure of a gas is defined as the mole fraction of the gas multiplied by the total pressure. If a gas with partial pressure Ps is in contact with a liquid, the steady-state concentration U of gas in the liquid is given by
where a is the solubility of the gas in the liquid. Because of this, we can define the partial pressure of a dissolved gas with concentration U to be U/a.
Now suppose that a gas with partial pressure Pg is brought into contact with a liquid within which that same gas is dissolved with concentration U, and thus partial pressure U/a. If U/a is not equal to Pg, then there will be a net flow of gas across the interface. The simplest model (but not necessarily the most accurate) assumes that the flow is linearly proportional to the difference in partial pressures across the interface,
where q is the net flux per unit area of the gas (positive when gas is flowing from the gaseous phase to the dissolved phase), and Ds is the surface diffusion constant.
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