Page 70 - Separation process principles 2

2.3 Ideal-Gas, Ideal-Liquid-Solution Model 35

temperature on the zero-pressure vapor heat capacity of a empirical vapor-pressure equations are tabulated for hun-
pure component is the following fourth-degree polynomial dreds of compounds by Poling et al. [Ill. At low pressures,
the enthalpy of vaporization is given in terms of vapor pres-
equation:
sure by classical thermodynamics:

where the constants nk depend on the species. Values of the
constants for hundreds of compounds, with Tin K, are tabu-
lated by Poling, Prausnitz, and O'Connell [ll]. Because If (2-39) is used for the vapor pressure, (2-40) becomes
cp = dh/dT, (2-35) can be integrated for each species to
give the ideal-gas species molar enthalpy:

The vapor molar entropy is computed from (3) in Table 2.4 The enthalpy of an ideal-liquid mixture is obtained by
by integrating C;v / T from To to T for each species, sum- subtracting the molar enthalpy of vaporization from the ideal
ming on a mole-fraction basis, adding a term for the effect of vapor molar enthalpy for each species, as given by (2-36),
pressure referenced to a datum pressure, Po, which is gener- and summing these, as shown by (5) in Table 2.4. The en-
ally taken to be 1 atm (101.3 kPa), and adding a term for the tropy of the ideal-liquid mixture, given by (6), is obtained in
entropy change of mixing. Unlike the ideal vapor enthalpy, a similar manner from the ideal-gas entropy by subtracting
the ideal vapor entropy includes terms for the effects of pres- the molar entropy of vaporization, given by A HvaP/ T.
sure and mixing. The reference pressure is not taken to be The final equation in Table 2.4 gives the expression for
zero, because the entropy is infinity at zero pressure. If the ideal K-value, previously included in Table 2.3. Al-
(2-35) is used for the heat capacity, though it is usually referred to as the Raoult's law K-value,
where Raoult's law is given by

the assumption of Dalton's law is also required:
The liquid molar volume and mass density are computed
from the pure species molar volumes using (4) in Table 2.4
and the assumption of additive volumes (not densities). The
effect of temperature on pure-component liquid density from
Combination of (2-42) and (2-43) gives the Raoult's law
the freezing point to the critical region at saturation pressure
K-value:
is correlated well by the empirical two-constant equation of
Rackett [12]:

where values of the constants A, B, and the critical tempera- The extended Antoine equation, (2-39) (or some other
ture, T,, are tabulated for approximately 700 organic com- suitable expression), can be used to estimate vapor pressure.
pounds by Yaws et al. [13]. Note that the ideal K-value is independent of phase compo-
The vapor pressure of a pure liquid species is well repre- sitions, but is exponentially dependent on temperature, be-
sented over a wide range of temperature from below the cause of the vapor pressure, and inversely proportional to
normal boiling point to the critical region by an empirical pressure. From (2-21), the relative volatility using (2-44) is
extended Antoine equation: independent of pressure.

EXAMPLE 2.3
Styrene is manufactured by catalytic dehydrogenation of ethyl-
where the constants kk depend on the species. Values of the benzene, followed by vacuum distillation to separate styrene
constants for hundreds of conlpounds are built into the from unreacted ethylbenzene [14]. Typical conditions for the
physical-property libraries of all computer-aided process feed to an industrial distillation unit are 77S°C (350.6 K) and
simulation and design programs. Constants for other 100 torr (13.33 kPa) with the following vapor and liquid flows