Integral heat of dilution

The heat absorbed when unit mass of solute is dissolved in an infinite amount of solvent is the differential heat of solution for zero concentration, Lo, and this is evidently equal to the integral heat of solution for concentration s plus the integral heat of dilution for concentration s ... 

FIG. 29 Integral heats of dilution for a solution of ammonium dodecane 1-sulfonate in water. 

Henry s law is obeyed by a solute in a certain temperamre range. Prove that An2. Ani. and the integral heat of dilution are zero within this range. Do not assume that Heiuy s-law constant is independent of temperamre generally, it is not. 

One consequence of the variation of the heat of solution with the composition of the solution is that dilution of a solution from one concentration to another is also accompanied by a heat change. Consideration of the change of heat content per mole at any instant in the course of the dilution process, known as the differential heat of dilution, will be left to a subsequent chapter. The net change per mole of solvie associated with the dilution of a solution from one concentration to another is the integral heat of dilution. For example, using the data for hydrochloric acid given above, it is possible to write... 

The dilution of the HCKSOHjO), i.e., 1.11 molal, to the HC1(400H20), i.e., 0.139 molal, solution is thus accompanied by the evolution of a total amount of 0.30 kcal. per mole of hydrogen chloride, at 25 C. By utilizing the extrapolated heat of solution at infinite dilution, the integral heat of dilution of any solution to infinite dilution can be calculated in an analogous manner. Thus,... 

The integral heat of dilution is the change of heat content per mole of solute, when a solution is diluted from one specified concentration to another. By Hess s law, i.e., by the fiist law of thermodynamics, the integral heat of dilution must be equal to the difference of the integral heats of solution in the initial and final states. If the dilution is carried out by means of an infinite amount of solvent, so that the final solution is infinitely dilute, the heat change is referred to as the integral heat of dilution to infinite dilution. 

It can also be obtained from the variation with concentration of the integral heat of dilution. Or it may be determined from the temperature dependence of the activity a [ of solvent according to the Gibbs-Helmholtz equation... 

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