CHAP. 2: STATE BEHAVIOUR [CONTENTS] 52
Solution
We first estimate the constantsaandbfrom the specified critical quantities, using equations
(2.24)a=27
64
(8. 314 ×800)^2
8. 314 × 106
= 2. 2448 Pa m^6 mol−^2 , b=8. 314 × 800
8 × 8. 314 × 106
= 1× 10 −^4 m^3 mol−^1.The pressure is calculated from the first of equations (2.23)p=8. 314 × 800
1. 1 × 10 −^3 − 1 × 10 −^4
−
2. 2448
(1. 1 × 10 −^3 )^2
= 6. 4588 × 106 Pa.The compressibility factor can be calculated from the second of equations (2.23), or from the
definition (2.4). The result isz= 0. 8545.2.2.7 Redlich-Kwong equation of state
p =nRT
V−nb−
an^2
T^1 /^2 V(V+nb)=
RT
Vm−b−
a
T^1 /^2 Vm(Vm+b),
z =Vm
Vm−b−
a
RT^3 /^2 (Vm+b). (2.27)
Parametersaandbare the constants of the Redlich-Kwong equation of state. Their values are
different for every substance. They can be obtained from experimental data on state behaviour,
or they can be estimated from the critical quantities of substances using the relations
a =1
9(2^1 /^3 −1)
R^2 Tc^5 /^2
pc= 0. 42748
R^2 Tc^5 /^2
pc, (2.28)
b =21 /^3 − 1
3
RTc
pc= 0. 08664
RTc
pc, (2.29)
which follow from equations (2.5) and (2.27).