PHYSICAL CHEMISTRY IN BRIEF

CHAP. 2: STATE BEHAVIOUR [CONTENTS] 50

2.2.5 Pressure virial expansion

The pressure virial expansion is an equation of state in which the compressibility factor is
expressed in the form of a powers series ofp

z= 1 +

p

RT

[B′(T) +C′(T)p+···]. (2.20)

QuantitiesB′, C′,... are termed the pressure virial coefficients, and they are functions of
temperature. The relation between the virial and pressure virial coefficients is given by

B′ = B , (2.21)

C′ = (C−B^2 )/(RT), (2.22)

..

.

Example

The second virial coefficient of ammonia at 298.15 K is− 261 cm^3 mol−^1. Calculate the molar

volume and the compressibility factor of ammonia at this temperature and a pressure of 0.5 MPa.

Assume that at the given temperature and pressure, the terms with higher virial coefficients in

equation (2.20) are negligible.

Solution

According to the specification, equation (2.20) rearranges to

z= 1 +B′

p

RT

.

Substituting the specified values (according to (2.21),B’ equals the second virial coefficient)

yields

z= 1 + 261× 10 −^6

0. 5 × 106

8. 314 × 298. 15

= 0. 9473.

The molar volume of ammonia is then calculated using equations (2.1) and (2.4)

Vm=

zRT

p

=

0. 9473 × 8. 314 × 298. 15

0. 5 × 106

= 4. 6966 × 10 −^3 m^3 mol−^1.