Estimate density of liquid benzene at 290 Kelvin and 100
atmospheres. The following data are
given:
Critical temperature 561.65 Kelvin, Critical pressure 47.7
atmospheres, critical density 304 kilogram per cubic meter, liquid density at
saturated conditions 888.2 kilogram per cubic meter, saturation vapor pressure
0.0849 atmospheres.
Molecular weight of nitrogen is 0.078 kilogram per mole, Gas
constant, R, has a value of 8.32 Pascal cubic meters per mole per Kelvin.
Solution:
Liquid density at elevated pressure and temperature is given
by a correlation provided as Equation 3.62 from Perry’s Chemical Engineers’
Handbook. This complicated function of
temperature is calculated for different values of reduced temperature and is
tabulated. One of the parameter used in
this equation is given by Cheuh as N, that is a
function of reduced temperature and acentric factor
and is given as Equation 3-63 in the Perry’s Handbook.
It uses acentric factor, which is defined as minus log of reduced vapor
pressure (at reduced temperature of 0.7) minus 1.00. To obtain values of omega, the reduced vapor
pressure (Pr equal to pressure over critical pressure) at Tr (equal to T over critical temperature) equal to 0.7 is
required. Omega represents the acentricity or nonsphericity of a
molecule. For monoatomic
gases, omega is, therefore, essentially zero.
For higher-molecular weight hydrocarbons, omega increases. It also rises with polarity. These acentric
factors are given in the literature. If acentric factors are needed, the usual technique is to
locate (estimate) the critical constants Tc
and Pc and then determine the vapor pressure at Tr
equal to 0.7. This estimation is
normally made by using one of the reduced vapor pressure correlations.
If the
vapor pressure correlation chosen were log P is equal to A plus B over T, with
A and B found, say, from the sets (Tc, Pc;
Tb, P equal to 1 atmosphere), then omega is given by 3 over 7 (theta
over (one minus theta) time log Pc minus 1.
In many
instances in the literature, one finds omega related to Zc
by 0.291 minus 0.08 time omega.
For benzene, Pitzer’s temperature
is 0.7 time 561.65 or 393.2 Kelvin.
Vapor pressure at this temperature is given as 2.974 atmospheres.
Plugging in these values, we obtain omega as 0.205.
Second parameter that is used in Equation 3-62 of Perry’s
Handbook, is Zc, critical compressibility
factor.
It is equal to Pc M over RTc
dc. In this equation dc
is the mass density at critical conditions.
Critical compressibility factor can be found to be 0.266.
For situation at hand, reduced temperature is 290 over 561.65
or 0.516. For Tr equal to 0.516, Table provided
value of the function Chueh as 0.0282. Now parameter N can be found from Equation
3-63 as 0.0168.
Finally, liquid density can be calculated as 890.6 kilogram
per cubic meter.