PHYSICAL CHEMISTRY IN BRIEF

CHAP. 6: THERMODYNAMICS OF HOMOGENEOUS MIXTURES [CONTENTS] 144

Example

A mixture containing 40 mole percent acetone(1) and 60 mole percent benzene(2) has a molar

volumeVm= 83. 179 cm^3 mol−^1 at temperature 25◦C and normal pressure. Calculate the mixing

volume of this mixture if the molar volumes of the pure substances areVm, 1 = 73. 936 cm^3 mol−^1

andVm, 2 = 89. 412 cm^3 mol−^1.

Solution

Substituting for volume into (6.18) gives

∆VM= 83. 179 − 0. 4 × 73. 936 − 0. 6 × 89 .412 =− 0. 0426 cm^3 mol−^1.

Note: Note that although the values of the enthalpy, internal energy, Helmholtz energy

and Gibbs energy of a mixture cannot be determined absolutely, it is possible to determine

absolutely their mixing quantities.

6.2.2 Excess quantities

In addition to mixing quantities,excess quantitiesare also used. In this case the properties a
mixture are related to the properties of an ideal mixture [see6.1]. The molar excess quantities
are defined by the relation
∆YE=Ym−Ym,id.mix, (6.27)

whereYm,id.mixis the corresponding molar thermodynamic quantity determined based on the
relation valid for an ideal mixture, (6.2) to (6.9).
The following relations apply between mixing and excess quantities:

∆VE = ∆VM, (6.28)

∆HE = ∆HM, (6.29)

∆UE = ∆UM, (6.30)

∆CVE = ∆CVM, (6.31)

∆CpE = ∆CpM, (6.32)

∆SE = ∆SM+R

∑k

i=1

xilnxi, (6.33)