Thermodynamic Concepts and Ideal Solubility

As we have shown previously, the condition for equilibrium between a solid solute and a solvent is given by the relation 

Comparing Eq. (1.10) with Eq. (1.37) shows us that the activity a, = Through a series of manipulations it can be shown (Prausnitz et al. 1999) that for phases in equilibrium 

38) will be more convenient for us to use in describing the solubility of organic solids in various solvents. The fugacity is often thought of as a corrected pressure and reduces to pressure when the solution is ideal. Eq. (1.38) can be rewritten as 

40) is a general equation for the solubility of any solute in any solvent. We can see from this equation that the solubility depends on the activity coefficient and on the fugacity ratio filft- The standard state fugacity normally used for solid-liquid equilibrium is the fugacity of the pure solute in a subcooled liquid state below its melting point. We can simplify Eq. (1.40) further by assuming that our solid and subcooled liquid have small vapor pressures. We can then substitute vapor pressure for fugacity. If we further assume that the solute and solvent are chemically similar so that 72 = 1, then we can write 

AHip = enthalpy change for the liquid solute transformation at the triple point Tip = triple point temperature 

---