PHYSICAL CHEMISTRY IN BRIEF

CHAP. 1: BASIC TERMS [CONTENTS] 39

whereVi•andVm,i• are the volume and the molar volume of a pure substanceiin the same
state of matter as the mixture.
U Main unit:dimensionless quantity.
S Symbols:The symbolXj•will be used to denote thermodynamic quantityXof a pure substance
jat the temperature and pressure of the mixture, with the pure substance being in the same
state of matter as the mixture (i.e. if the mixture is liquid,Xj•will be a thermodynamic quantity
of a pure liquid substance). If the mixture is in the solid state, the symbol•will denote a pure
substance in the same crystalline form as the mixture.
The sum of the volume fractions of all components equals one.

∑k

i=1

φi= 1. (1.12)

Note:For a mixture of ideal gases, the volume fraction equals the mole fraction

φi=xi.

Example

Calculate the volume fractions in a solution prepared by mixing 40 cm^3 of ethanol and 160 cm^3

of water. Is it possible to calculate the volume of the solution based on this data?

Solution

From (1.11) we obtain

φwater=

160

160 + 40

= 0. 8 , φethanol=

40

160 + 40

= 0. 2.

The volume of a solution cannot be calculated using the volumes of pure substances, but it has

to be measured. In the considered mixture of ethanol and water it will be smaller than 160 + 40

= 200 cm^3.