PHYSICAL CHEMISTRY IN BRIEF

CHAP. 6: THERMODYNAMICS OF HOMOGENEOUS MIXTURES [CONTENTS] 154

c α

(

∂∆HsolI, 2

∂nrel

)

=H

E

1 =H^1 −H

• m, 1

H

⊗

2 =H^2 −H

⊗

m, 2

∆Hsol, 2

nrel

Obr.6.2:Dependence of the integral heat of solution on the relative amount of a solvent. The slope
of the tangent shows the differential heat of dilution. The intercept on the vertical axis equals the
differential heat of solution.

Relations between the integral heat of solution and the differential heats of solution are

illustrated in Figure6.2.

Example

Dependence of the enthalpy of mixing of ethanol(1) and water(2) on composition at temperature

298 K has the minimal value− 783 J mol−^1 atx 1 = 0. 17 (mole fraction of ethanol). Calculate

the differential heat of solution of ethanol given this composition.

Solution

Since in the minimum (∂∆HM/∂x 1 ) = 0,we obtain from relation (6.58)H

E

1 =−783 + (1−

0 .17)×(0) =− 783 J mol−^1.