PHYSICAL CHEMISTRY IN BRIEF

CHAP. 2: STATE BEHAVIOUR [CONTENTS] 61

2.4.5 Equations of state for mixtures

The state behaviour of mixtures can be described using the same equations of state as those
applied when describing the behaviour of pure fluids. In this case, the constants in the equations
depend on composition. These constants are usually estimated using the constants of pure
substances. This procedure is called themethod of constants combination.
The following estimates are used for the constantsaandbin the Van der Waals (2.23) and
the Redlich-Kwong (2.27) equations:

a=





∑k

j=1

xja

1 / 2

j





2

, b=

∑k

j=1

xjbj, (2.42)

whereajandbjare the respective constants of pure substances.

Example

Let the constants in the van der Waals equation for a pure substance A be:

aA= 0. 36 Pa m^6 mol−^2 ,bA= 40× 10 −^6 m^3 mol−^1 , and for a pure substance B

aB= 0. 64 Pa m^6 mol−^2 ,bB= 70× 10 −^6 m^3 mol−^1.

Calculate the constants of an equation for an equimolar mixture of substances A and B.

Solution

An equimolar mixture contains the same amount of substance A and B. Hence, the mole fractions

of the mixture arexA=^12 ,xB=^12. The constants of the mixture are calculated using equations

(2.42)

a=

(

1

2

0. 361 /^2 +

1

2

0. 641 /^2

) 2

= 0, 49 Pa m^6 mol−^2

b=

1

2

40. 10 × 10 −^6 +

1

2

70. 10 × 10 −^6 = 55. 10 × 10 −^6 m^3 mol−^1.