PHYSICAL CHEMISTRY IN BRIEF

CHAP. 6: THERMODYNAMICS OF HOMOGENEOUS MIXTURES [CONTENTS] 153

6.3.5 Differential heat of solution and dilution

If we denote the solvent in ak−component mixture as component 1, we can define

• thedifferential heat of solutionof solutei(i >1) using the relation

H

⊗

i =Hi−H

⊗

m,i. (6.56)

Note:If a pure solute is in the same phase as the mixture, i.e.Hm⊗,i=H•m,i, the differential

heat of solution of the substance equals its excess partial molar enthalpyH⊗i =HEi

• thedifferential heat of dilution, which is a term used for the excess partial molar
  enthalpy of a solvent, using the relation

H

E

1 =H^1 −H

• m, 1. (6.57)

Note:The differential heats of solution depend on the concentration of the solution. Dur-

ing dissolving a first portion of the substance in a pure solvent, this heat is usually termed

thefirst differential heat of solution; during dissolving a last portion of the substance

in an almost saturated solution the corresponding heat is termed thelast differential

heat of solution.

• Conversions between integral and differential heats:
  If we know ∆HM(x 1 ) or ∆solH 2 (nrel), we can derive the following relations for a binary
  mixture from relations (6.36) to (6.40):

H

E

1 = ∆H

M+x

2

(

∂∆HM

∂x 1

)

T,p

=

(

∂∆solH 2

∂nrel

)

T,p

, (6.58)

H

⊗

2 = ∆H

M−x

1

(

∂∆HM

∂x 1

)

T,p

= (6.59)

= ∆solH 2 −nrel

(

∂∆solH 2

∂nrel

)

T,p

. (6.60)

Note:HEi is (see the preceding example) a partial molar quantity relating to ∆HE. How-

ever, for quantities defined by the first law of thermodynamics, ∆YE= ∆YM[see6.2.2].