# Differential and Integral Heat of Solution

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The change in enthalpy accompanying this reaction depends upon the final solution concentration. Two measures of enthalpy have proved useful in determining the heat of solution: the integral heat of solution and the differential heat of solution. The integral heat of solution 1

per mole of solute dissolved Δ Hint is defined as the heat absorbed when one mole of solute is dissolved isothermally in solvent to form a solution of concentration m. Δ Hint does depend upon the final concentration m, and as m approaches zero (infinite dilution) Δ Hint asymptotically approaches a constant value, Δ H∞ , a characteristic of the solute-solvent couple. Δ H∞ is the enthalpy change per mole solute as one mole of solute is added to an infinite amount of solvent. In some thermodynamic calculations it is necessary to know the enthalpy change when pure solute A dissolves in a solution of A at some concentration, m, at a known pressure and temperature. This enthalpy change is the differential heat of solution and is defined as the enthalpy change for one mole of solute dissolved in an infinite amount of solution of concentration m. (Notice that Δ H∞ , the integral heat of solution at infinite dilution, is the differential heat of solution at m = 0.) Experimentally it is difficult to measure the heat absorbed per mole when a very small amount of solute is dissolved in a finite amount of solution at concentration m. In practice it is easier to measure the integral heat of solution Δ Hint as a function of concentration and then derive the differential heat of solution in the following way. The enthalpy change, ΔH, for the process (at constant T and p): n1 moles of S + n2 moles of A → Solution (n1 S + n2 A) is given by: Δ H = H soln - n1 H1 - n 2 H 2

where H1 and H 2 are the standard molal enthalpies of pure S and pure A. The differential heat of solution Δ H 2 is the change in ΔH as a result of a small change in n2 . Δ H2 = and ∂Δ Hsolution |P,T,n1 ≡ H 2 ∂ n2 ∂ΔH ∂ Δ Hsoln - Δ H2 |P,T,n1 = | ∂ n2 ∂ n 2 P,T,n1

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Therefore, the differential heat of solution, Δ H 2 = H 2 - H 2 , is the enthalpy of solution of one mole of pure A going to form a large volume of solution with a specific concentration. (II) Effect of concentration. If the solute is an ionic substance, the activity of all...

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