fractional crystallization
temperature. In fact, the magnitudes of the changes in both enthalpy and entropy for dissolution are temperature dependent. Because the solubility of a compound is ultimately determined by relatively small differences between large numbers, there is generally no good way to predict how the solubility will vary with temperature. The variation of solubility with temperature has been measured for a wide range of compounds, and the results are published in many standard reference books. Chemists are often able to use this information to separate the components of a mixture byfractional crystallization, the separation of compounds on the basis of their solubilities in a given solvent. For example, if we have a mixture of 150 g of sodium acetate CH3CO2Na and 50 g of KBr, we can separate the two compounds by dissolving the mixture in 100 g of water at 80C and then cooling the solution slowly to 0C. According to the temperature curves in Figure 13.9 "Solubilities of Several Inorganic and Organic Solids in Water as a Function of Temperature", both compounds dissolve in water at 80C, and all 50 g of KBr remains in solution at 0C. Only about 36 g of CH3CO2Na are soluble in 100 g of water at 0C, however, so approximately 114 g 150 g 36 g of CH3CO2Na crystallizes out on cooling. The crystals can then be separated by filtration. Thus fractional crystallization allows us to recover about 75% of the original CH3CO2Na in essentially pure form in only one step. Fractional crystallization is a common technique for purifying compounds as diverse as those shown in Figure 13.9 "Solubilities of Several Inorganic and Organic Solids in Water as a Function of Temperature" and from antibiotics to enzymes. For the technique to work properly, the compound of interest must be more soluble at high temperature than at low temperature, so that lowering the temperature causes it to crystallize out of solution. In addition, the impurities must be more soluble than the compound of interest as was KBr in this example and preferably present in relatively small amounts.