PHYSICAL CHEMISTRY IN BRIEF

CHAP. 2: STATE BEHAVIOUR [CONTENTS] 54

states may be also applied in such a way that the sought for compressibility factorzA of a
substance A is determined using the compressibility factorzRof a reference substance R whose
state behaviour is known
zA(Tr, pr) =zR(Tr, pr).

The compressibility factor of a reference substance for a givenTrandpris most often calculated
using an equation of state. The results of this procedure are the better the more similar is the
reference substance to the one under investigation.

Example

The compressibility factor of butane at a temperature of 523.15 K and a pressure of 13.25 MPa is

z= 0.6093. At which temperature and pressure has butadiene the same compressibility factor?

Data: the critical quantities of butane areTc= 425.14 K,pc= 3.784 MPa. The critical quantities

of butadiene areTc= 425.0 K,pc= 4.33 MPa.

Solution

We calculate the reduced quantities of butane using equations (2.6) and (2.7)

Tr=

523. 15

425. 14

= 1. 2305 , pr=

13. 25

3. 748

= 3. 5016.

The reduced quantities of butadiene at the same compressibility factor are the same. The tem-

perature and pressure at which the compressibility factor of butadiene equals 0.6093 are

T=TrTc= 1. 2305 × 425 .0 = 522. 9 K, p=prpc= 3. 5016 × 4 .33 = 15. 162 MPa.

2.2.10 Application of equations of state

• The equation of state of an ideal gas(2.15)—This equation is commonly applied for
  gases at low reduced pressures and high reduced temperatures. Its strengths consist
  in its simplicity and universal character (no constants characterizing the substance are
  needed). The accuracy of the equation depends on the kind of substance, temperature
  and pressure. For gases at a normal boiling point (pressure 101 kPa), e.g., the error in
  volume determination is about 5 percent.