Thermodynamics of Ideally Dilute Solutions

Just as was done previously, one develops the thermodynamic description of an ideally dilute solution by considering the equilibrium between the dilute solute component in the liquid solution and in the vapor phase. If the minority component is designated B, then one may write its chemical potential as 

Since Henry s law holds when the solution is ideally dilute, this can be rewritten as 

It should be noted that gives the standard chemical potential for the ideally dilute solute in a hypothetical system in which the mole fraction of B is unity. This is obviously a fictitious state which is impossible in reality but whose properties are obtained by extrapolating the Henry s law line to Xb = 1 (see fig. 1.12). When Henry s law is not obeyed, an activity coefficient 73 introduced so that the product Yb h b is equal to the vapor pressure Pb- The activity of the dilute component Ub is defined to be 73 3- Thus, the general expression for the concentration dependence of pb becomes 

Because of the inconvenient nature of the standard state defined above, the concentration units used to describe the concentration dependence of the chemical potential are usually different. More convenient choices for concentration are molality and molarity. When the solution is dilute the relationship between mole fraction and molality is quite simple (see equation (1.2.3)). In terms of molality, the expression for the concentration dependence of the chemical potential of component B becomes 

When the dilute system does not obey Henry s law, one introduces an activity coefficient as above to correct to the experimentally observed value. Thus, in general, one may write 

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