PHYSICAL CHEMISTRY IN BRIEF

CHAP. 2: STATE BEHAVIOUR [CONTENTS] 57

Note:This equation is suitable for estimating the temperature dependence of the molar

volume of a saturated liquid. Saturated liquid is such that at a given temperature is in

equilibrium with its vapour (i.e. at boiling, for more information see7.1.4). The pressure

of a saturated liquid (see7.1.7) is the lowest pressure at which a substance may be in the

liquid (equilibrium) state at a given temperature. If we want to find the molar volume of

a liquid at a pressure higher than that of a saturated liquid, we may use the isothermal

compressibility coefficientβTfor the conversion (see (2.35)).

Example

Using the Rackett equation estimate the molar volume and density of liquid methane when boiling

at a temperature of 150 K. Data:Tc= 190.55 K,pc= 4.604 MPa,Vc= 99 cm^3 mol−^1.

Solution

Substituting into (2.36) yields

Vm(l)= 99× 10 −^6

(

4. 604 × 106 × 99 × 10 −^6

8. 314 × 190. 55

)(1− 150 / 190 .55) 2 / 7

= 44. 45 × 10 −^6 m^3 mol−^1.

The density is calculated from (2.3) and (2.1)

ρ=

M

Vm

=

16 × 10 −^3

44. 45 × 10 −^6

= 360kg m−^3.

2.3.3 Solids

The volume of a solid substance is little dependent on temperature and pressure. This depen-
dence is usually ignored, or the volume is calculated using equations (2.34) and (2.35).