What is the specific volume of isopropanol
vapor at 250 degrees Centigrade and 106 atmospheres? Critical temperature is 508.15 Kelvin and
critical pressure is 53 atmospheres?
Solution:
The nonideality of a gas is conveniently expressed by the
compressibility factor, Z: that is equal to PV/RT where V is equal to molar
volume, P is absolute pressure, T is absolute temperature, and R is universal
gas constant. The gas constant R assumes
different values for different sets of units.
Values of
the Gas constants R are 83.144 bar cm3 per mole per Kelvin; 8.314
Joules per mole per Kelvin; 82.057 atmosphere cm3 per mole per
Kelvin; 0.08206 atmospheres liters per mole per Kelvin.
For an
ideal gas Z is equal to 1.0. For real
gases, Z is normally less than 1 except at high reduced temperatures and
pressure. The compressibility factor is
often correlated with the reduced temperature Tr and pressure Pr as Z is
equal to function of Tr and Pr. In this function Tr is equal to T over Tc
and Pr is equal to P over Pc. The function f( )
has been obtained from experimental PVT data and the final curves given in the
literature as figures.
Except as
noted below, the use of these figures to obtain Z at given Tr
and Pr should lead to errors
of less than to 4 to 6 percent except near the saturation curve or near
the critical point, where Z is very sensitive to both Tr
and Pr. These figures should
not be used for strongly polar fluids, nor are the recommended for helium,
hydrogen, or neon unless special, modified constants are used.
For ideal gases, pV
is equal to RT where p is total pressure, V is the volume and T is
temperature. R is the universal gas
constant. Pay attention to the numeric
values of this constant. If we consider
that pV is equal to ZRT where Z is the
compressibility factor and is given by two parameters, reduced pressure, Pr,
and reduced temperature, Tr, then the
value of this compressibility factor could be found by any compressibility
factor chart, like the one provided by Hougen &
Watson.
These reduced values are defined as ratio of absolute value
to the critical value. For the present
situation, reduced pressure is 106 over 53 and is equal to 2. Reduced temperature is 523.15 over 508.15 and
is equal to 1.03. Now we can get the
value of Z from the chart as a function of reduced pressure with reduced
temperature as a parameter. It is found
to be equal to 0.33.
The value of R is equal to 0.08206 atmospheres liters per
mole per Kelvin. Volume of the vapors is
equal to ZRT over P and is calculated to be 0.142 liters per mole.