Differential heat of dilution

The quantities H/m and (3A AH/mx) are known as integral and differential heats of dilution, since they relate to the solvent. 

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... 

If the relative partial molar heat content Iri of the solvent (i.e., the differential heat of dilution) is small, as it is for dilute solutions, the activity coefficient of the... 

It is important that the distinction between the similar equations (38.5) and (38.13) sliould be clearly understood. The former gives the variation with temperature of the activity of the solvent in a solution at its freezing point, which varies with the composition. The latter applies to the activity of the solvent in a solution of constant composition, t It is also the differential heat of dilution of the given solution (cf. 44b.)... 

Problem The integral heat of solution at infinite dilution per mole of KCl was found by extrapolation to be 4,120 cal. at 25 C. The integral heat of solution of 1 mole of KCl in 55.5 moles of water, to make a 1 molal solution, is 4,012 cal. From the slope of the plot of the heat of solution per mole of solute against the number of moles of solvent, the differential heat of dilution of 1 molal KCl solution is found to be 3.57 cal. mole What is the differential heat of solution of KCl in this solution ... 

Show that for a solution condsting of nt moles of solvent and n% moles of solute the following relationship holds tit (integral heat of solution — differential heat of solution) ni (differential heat of dilution). 

To determine the differential heat of dilution of aqueous sucrose at mole fraction 0.1. 

If denotes the partial enthalpy of the solvent water in the solution and H the value of in the pure solvent, the differential heat of dilution J is given by... 

Roughly speaking, we may also state that the differential heat of dilution of a salt for the concentrations at which its lyotropic effect is considered, becomes... 

The partial or differential heat of dilution AH differs fix)m AH2 in that it is a consequence of adding solvent, rather than solute, to a solution and is almost always expressed as the heat per mol of added solvent. Accordingly,... 

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