This interactive simulation demonstrates relatively complicated behavior, how fugacity changes
with temperature.
So if you look at a snapshot of fugacity as a function of temperature for a given, overall
mole fraction.
This is ideal solution, benzene and toluene, and the idea is the point here represents
the condition that we can see on the Txy diagram.
So when we move the temperature, it will move the point on this diagram, but it will also
move the point on the Txy diagram.
But we have the option of serving both of them at the same time, but just in a compressed
format.
'the thing to note is that for example when we look at component B here, benzene, as we
raise the temperature, this is in the liquid phase, then the fugacity is increasing exponentially
because the fugacity is the liquid phase mole fraction, which in this case is 0.65 times
the saturation pressure, and the saturation pressure is increasing exponentially with
pressure.
We then get into the two phase region, and now notice that the fugacity is decreasing.
Whereas the fugacity of the toluene is increasing.
This is because the mole fraction in the liquid phase of benzene is decreasing, because it
has a higher saturation pressure.
And then eventually we get to this region which is the vapor phase.
And in the vapor phase, the fugacity, since we are assuming ideal gases, the fugacity
is just the mole fraction, 0.65 times the total pressure, 1 bar.
The idea of this simulation is to better understand fugacities of individual components, keeping
in mind that when we have vapor liquid equilibrium, the fugacity of benzene in the liquid phase
is equal to the fugacity of benzene in the vapor phase, and likewise for toluene.
So we now look at the interactive simulation we can see the other curves and better understand
this behavior.
So we are here in the interactive simulation we are looking at how the fugacity of the
two components change as you raise the temperature.
We can move the overall mole fraction, and those are rather dramatic differences as I
change the overall mole fraction.
But in all cases the fugacity of B increases as the lower temperature when it is a liquid.
In the two phase region the fugacity of B decreases.
And the fugacity of T, toluene, increases in this two phase region as we raise the temperature.
And we can see what is happening a little easier, and I also can show you first just
to pick the temperature we can see the behavior of the dot, and this dot corresponds to where
we are here as we change the temperature we are in the liquid region.
Now as we change the temperature notice that the mole fraction of B is decreasing in both
the gas and the liquid.
And as a result the fugacity is decreasing.
And then once I get in the gas phase, raising the temperature I am not changing the pressure,
the fugacity is the total pressure times the mole fraction, I am not chaining the mole
fraction, so fugacity doesn't change.
So when I look at this, fugacity isn't changing as I raise the temperature in the gas phase
region.
I can look at both of these graphs together although things are a little bit more squeezed
together.
But hopefully looking at both helps you understand the behavior that we are seeing.
And particularly as we change the mole fractions, you can see rather significant differences
between the benzene and the toluene fugacitites as a function of temperature.
So the idea here is to give you a better understanding of fugacity, and what it corresponds to, of
course for an ideal gas fugacity it's just partial pressures.
For a liquid it is the saturation pressure times the liquid mole fraction for an ideal
solution.