Pressure, volume and temperature relationship for oxygen at
20 degrees Centigrade is reported as a function of pressure. Calculate the fugacity coefficient at 100
atmospheres.
PV is equal to ‘a’ plus ‘b’ P plus ‘c’ P2.
Solution:
As pressure tends to zero, PV is equal to ‘a’. By definition, the compressibility factor is
equal to 1 as pressure becomes zero. It
implies that the compressibility factor, Z, that is, PV over RT is equal to 1,
or RT is equal to ‘a’. A generic
expression for Z would then by 1 plus b/a P plus c/a P2. It is equivalent of normalizing the PV
relationship as given. This results in Z
as 1 plus b’P plus cP2.
The fugacity coefficient is defined by the following
equation: log of phi is equal to
integral from zero to P of (Z minus one) over P dP. If we plug
in the expression for Z, then this integral can be integrated as aP plus b/2P2. At 100 atmospheres, log of phi is calculated
to be minus 0.0631. So, fugacity
coefficient is equal to 0.9388. If you
are interested in finding the value of fugacity, then it is 0.9388 times 100 or
93.88 atmospheres.