Dyakiw,Matoian, Mitri 1
Background
:
Equations of state are used to describe physical properties for a substance or a mixture of
substances, and relate these properties, such as temperature, pressure, and volume, in a particular
state.
The ideal gas law (PV=nRT) is one of the simplest equations of state.
However, it cannot
predict the formation of a liquid and becomes less accurate at higher pressures and lower
temperatures (Equations n.p.).
Cubic equations of state, on the other hand, are more accurate.
Such equations are
RhedlichKwong, SoaveRedlichKwong, and PengRobinson.
These equations are cubic in
volume and have one or more real roots, also known as solutions.
If the solution to the equation
has one real root, it refers to the volume of a vapor phase and indicates there is no liquid phase
present.
When the solution to the equation has three real roots, one root indicates a liquid phase
and another root indicates that a vapor state is present. Typically, the smallest root indicates a
liquid phase and the largest root corresponds to a vapor phase.
The PengRobinson equations,
however, does not necessarily follow this concept that the two phases are coexisting in the data
range. “Vapor and liquid phases coexist only at the vapor pressureabove the vapor pressure, the
liquid root is most stablebelow the vapor pressure, the vapor root is more stable” (Elliott 208).
The intermediate root has no real meaning simply because it is considered thermodynamically
unstable.
The PengRobinson equation of state, which was chosen for the calculations, was
introduced in 1976 and is successful at deriving vapor pressure values for a pure compound near
the critical point. (Equation n.p.) The equation taken from Introductory Chemical Engineering
Thermodynamics
consists of the following:
P=
RT
ρ

a(T)*
ρ
2
(1b
ρ
)
(1+2b
ρ
b
2
p
2
)
where, V refers to the molar volume of pure oxygen, T to temperature in degree Kelvin, and R
is