Influence of Temperature on Solubility

For ideal solutions, the van't Hoff relation of equation (17), and the Hildebrand relation of equation (24), state that the ln(XB) term is linearly dependent on 1/T and on ln( T). The enthalpy of solution is equal to the enthalpy of melting

(i.e., AH = AHT), since the enthalpy of mixing is zero for an ideal solutions. Since A H for ideal solutions is always endothermic and positive, the solubility of an ideal solution would increase with increasing temperature.

In non-ideal solutions, however, the enthalpy of solution does not equal the enthalpy of melting because the enthalpy of mixing does not equal zero. Moreover, because the heat capacity of the solid is different from the heat capacity of the supercooled liquid, the ACp term does not equal zero, and:

The strong solute-solvent interactions in solution may significantly reduce the free energy of the final solution compared to that of the pure solute and solvent. Despite the positive entropy of mixing, the enthalpy of mixing term may be negative, especially when the molecules in solution are oriented by the strong polar-polar, polar-induced-polar, and/or hydrogen-bonding interactions. Moreover, the second term in equation (42) may yield a negative contribution to the total enthalpy of solution. Therefore, the dissolution of a solute in a non-ideal solution might turn out to be an exothermic process, characterized by a negative A Hs. For those systems where A Hs is negative, it follows that the solubility would decrease with increasing temperature. The dissolution of carbon dioxide in water is characterized by a negative enthalpy ofsolution, and therefore carbonated waters go flat when their temperature is raised.

Grant et al. (1984) proposed an equation that better represents the temperature dependence of the molar solubility of polar organic compounds in water:

In equation (43), a, b, and c are adjustable parameters, and this equation enables one to simulate the solubility of most solute-solvent combinations over a wide temperature range.

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