PHYSICAL CHEMISTRY IN BRIEF

CHAP. 2: STATE BEHAVIOUR [CONTENTS] 56

2.3 State behaviour of liquids and solids

The above equations of state offer little accuracy in describing the state behaviour of liquids.

Equations of state with a large number of constants (20 and more) are used to describe the

behaviour of fluids in a broad range of temperatures and pressures. When we are interested

only in a liquid at not very high pressures, it is easier to use the following procedures.

2.3.1 Description of state behaviour using the coefficients of

thermal expansionαp and isothermal compressibilityβT.

For not very great differences in temperature and pressure, we may considerαpandβT for

liquids and solids to be constant, and by integrating the definitions (2.9) and (2.10) we obtain

ln

Vm, 2

Vm, 1

= αp(T 2 −T 1 ), (2.34)

ln

Vm, 1

Vm, 2

= βT(p 2 −p 1 ). (2.35)

Example

The molar volume of liquid heptane at a temperature of 20◦C and a pressure of 101 325 Pa is

Vm= 146. 6 cm^3 mol−^1 , and its isothermal compressibility isβT= 1. 4 × 10 −^9 Pa−^1. What is the

molar volume of heptane at the same temperature and a pressure of 2 MPa?

Solution

Substituting into equation (2.35) gives Vm, 2 = 146.6 exp[− 1. 4 × 10 −^9 (2× 106 −101325)] =

146. 2 cm^3 mol−^1.

2.3.2 Rackett equation of state.

Vm(l)=Vcz(1−T /Tc)

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c [saturated liquid] (2.36)
wherezcis the compressibility factor at the critical point.
S Symbols:The superscript (l) denotes the liquid phase.