To help understand fugacity we will look at three questions that compare f of different
components or the same component at different concentrations.
So first go ahead and read through these questions and on your own, answer them, and then one
by one we will go through the explanations for the answers.
So for this vapor liquid mixture of a binary component we want to know which component
has the higher f in the liquid phase.
First thing we are going to take advantage of, say for component a in the liquid phase,
equals f of a in the vapor phase.
And then I'm going to use notation that is often used, the hat indicating that component
a and mixture.
And in the vapor phase at these low pressures, f is really close to the partial pressure.If
it's an ideal gas it is indeed the partial pressure, and so the f of a is just the partial
pressure of a, just 0.2 bar.
And of course that means that the f of b in the liquid phase, is its partial pressure
in the gas phase that is in equilibrium with it, so 0.8.
So the f of b in the liquid phase is greater than f of a in the liquid phase, even though
the mole fraction, or the composition of b is lower than that of a.
So in this problem we are adding salt to water, we add enough Na to saturate the H20 and we
continue adding Na and we have Na sitting on the bottom of the container.
And the question is, does the salt or the water have the higher f.
So again we can look at what is in equilibrium with the vapor phase.
So in the vapor phase, the f of water in the liquid phase is going to be approximately
the mole fraction of water in the liquid phase times the saturation P of water.
We all know, let's make an estimate, let's say, it's mole fraction is half, probably
higher than that.
And then the saturation P of water at 25 degrees, about 0.03 bar.
So we say f of water is approximately 0.015 bar.
Well the f of Na then, in the liquid phase, right, so this is the liquid phase, would
be again, a guess, it's mole fraction times it's saturation P, the mole fraction of Na
in the liquid phase times the saturation pressure of Na.
Well let's say this was 0.5, the saturation P of salt we don't know off hand but our experience
would say that Na doesn't evaporate in our lifetime, so let's make it 10^-10 bar as a
guess, maybe it's 10^-15.
All that matters is that the fugacity of water is much much greater than the f of salt in
the liquid phase.
And that is what the question is asking.
So in this case we have pure water at 75 degrees and we have two concentrations, so they are
in different phases, and the question is which of these has the higher f.
Well we need more information, we can't tell from concentrations which has a higher f.
So if we go to steam tables and look up what is usually listed as specific volume and we
take that inverse, and again steam tables are usually in g or kg and we converted to
moles, then we find out that this happens to be the density of the vapor at 75 degrees,
saturated vapor.
And this happens to be the density of saturated liquid at 75 degrees C. So we can say the
f of the liquid is equal to the f of the vapor in equilibrium and so these two concentrations
actually have the same f because they are in equilibrium.