Solubility with Temperature

The procedure for deriving the temperature coefficient of the solubility of a solute in an ideal solution parallels that just used for the pressure coefficient. The condition for maintenance of equilibrium with a change in temperature is still Equation (14.48). 

As at constant pressure the chemical potential of the pure sohd is a function only of the temperature, and the chemical potential of the solute is a function of the temperature and mole fraction, we can express Equation (14.48) as 

As T is the temperature at which a liquid solution is in equilibrium with a pure, solid solute, one also can interpret Equation (14.63) as describing the way in 

As we pointed out in Chapter 13, each of the two-phase regions has one degree of freedom, and the equilibrium relationship between T and X is given by curves AB or BC when component 2 or component 1, respectively, is in higher concentration. In the region below the horizontal line, only the temperamre can vary because both phases are pure solids. 

The equation of curve AB can be obtained by integrating Equation (14.64), and the equation of curve BC can be obtained by integrating the corresponding equation  

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Where substances vary little in solubility with temperature, isothermal crystallisation may sometimes be employed. This usually takes the form of a partial evaporation of a saturated solution at room temperature by leaving it under reduced pressure in a desiccator. 

Zinc Molten zinc is reported to attack niobium at a significant rate at temperatures above 450°C . It is attacked by zinc at 600°C and shows increasing solubility with temperature up to 850°C. 

The Number of Dipoles per Unit Volume. The Entropy Change Accompanying Proton Transfers. The Equilibrium between a Solid and Its Saturated Solution. Examples of Values of L and AF°. The Change of Solubility with Temperature. Uni-divalent and Other Solutes. Lithium Carbonate in Aqueous Solution. H2COj in Aqueous Solution. Comparison between HjCOj and Li2C03 in Aqueous Solution. Heats of Solution and the Conventional Free Energies and Entropies of Solution. 

The Change of Solubility with Temperature. The solubilities of various salts have been measured in aqueous solution at various temperatures. But from these measurements we cannot derive values of L as a function of temperature, until the activity coefficients in the various saturated solutions have been accurately measured. In dilute solutions... 

There seem to be no direct calorimetric determinations of enthalpies of solution of rare-earth tribromides in nonaqueous solvents,3 and very few reports on the temperature variation of solubilities whence solution enthalpies might be roughly estimated. The most detailed set of data concerns cerium tribromide in pyridine (257). In this system there exists a series of solvates (cf. Section IH,C,2), but sufficient solubilities were determined for the estimation of enthalpies of solution of each solvate. These enthalpies are included in Fig. 3, which shows an extraordinary zig-zag variation of solubility with temperature. The actual values of enthalpies of solution cannot be accurate, but at least it is clear that they change sign and magnitude in an eccentric manner. 

Where substances vary little in solubility with temperature, isothermal crystallisation may sometimes be employed. 

Variations of solubility with temperature are illustrated in Fig. 4 for 10 gases in cyclohexane. The slopes of the lines times the gas constant R give values for the entropy of solution. In decending from C2H > to He the... 

Solubility variation with pressure Low-pressure solubility High-pressure solubility Heat of solution—related to variation of solubility with temperature at fixed pressure Relatively linear Low Continues to increase Relatively low and approximately constant with loading Highly nonlinear High Levels off Relatively high and decreases somewhat with increased solute loading... 

Figure 15.2 Variation of Solubility with Temperature of Various Solutes in Water...

Because SH°a n refers to dissolving a small amount of solute in a large amount of a 1.0 M ideal solution, it is not necessarily relevant to the process of dissolving a solid in a saturated solution. Thus AH° n is of limited use in predicting the variation of solubility with temperature. 

Predicting the temperature dependence of solubility is very difficult. For example, although there is some correlation between the sign of AH°0 and the variation of solubility with temperature, important exceptions exist. The only sure way to determine the temperature dependence of a solid s solubility is by experiment. 

The principles of thermodynamics provide a quantitative relation between the change in solubility with temperature of a substance (its temperature coefficient of solubility) and its heat of solution, the heat... 

Variation of Mutual Solubility with Temperature Second Order Transitions... 

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