Example of fugacity calculations, we're going to calculate first the fugacity of a pure
gas at 30 bar and 500 K, then we're going to assume that this happens to be the saturation
pressure at 500 K, and we want to calculate the fugacity of liquid in equilibrium with
that gas.
And then we want to increase the pressure on the liquid to 60 bar and calculate its
fugacity.
So we're given the volume of the liquid and we're assuming it's constant over this pressure
range, and we're assuming that we're using a compressibility factor that's a simplified
form, basically to make the calculations easier to demonstrate what we're trying to show.
So what we're going to do is use the relation between the fugacity coefficient, which is
ln(f/p) and it relates to the compressibility factor at constant temperature by this simple
relation.
And just a reminder, where this relation came from: the change in Gibbs free energy at constant
temperature is VdP and then the way we've defined fugacity is RTdlnf.
So we'll work with this relation, ln(f/p) is the integral from 0 to 30 bar or (Z-1)
which we can see up here is just -0.01P. So -0.01P divided by P, and so we're just integrating
-0.01, which is -0.01 times 30 minus 0.
Which just is equal to -0.30.
If we take the exponent of both sides, fugacity over pressure is just e to the minus 0.30.
Remember we're evaluating this fugacity at 30, so this is really 30 times this exponential,
and if we do that calculation, the fugacity at 30 bar is 22.2 bar.
That's part A, now part B says the liquid is in equilibrium so this is the fugacity
of the vapor, fugacity of liquid is the identical value because they're at equilibrium, the
fugacities are the same, and now for part C, we want the fugacity of the liquid at 60
bar.
So what I've written down here is the Poynting correction that relates the fugacity of a
liquid at some pressure to the fugacity at saturation pressure which is of course what
we have already, this is the volume of the liquid, (molar volume), pressure difference
over RT.
So the fugacity at 60 bar is going to be 22.2 and then the exponent and I'll substitute
the numbers in.
So now we can calculate the fugacity at 60 bar.
The units cancel, here 25, 30, 83.14, and 500.
We determine the exponent is quite small, so that the correction isn't significant at
this pressure, so the fugacity at 60 bar pressure.
It takes a large increase in pressure to create a significant increase in fugacity for a liquid.