In this screencast I am going to describe the Pxy diagram which we use to represent
the vapor liquid equilibrium behavior for a binary system. This is assuming an ideal
solution which means Raoult's law and Raoult's law is that the mole fraction in the liquid
phase times the saturation pressure for a given component i is equal to the mole fraction
in the vapor phase times the total pressure. What we want to observe is how the relative
amounts of liquid and vapor change and also how the mole fractions of the liquid and vapor
change: 1 as we change the pressure and keeping the overall mole fraction constant and 2 as
we keep the pressure constant and change the overall mole fraction. The lever rule can
be used to determine the amounts of liquid and vapor and that is described in another
screencast. Let's look at the diagram. I am presenting the diagram from a online interactive
simulation that was prepared by someone else and the details are on the Wolfram demonstration
project website and here is the link. We have modified it slightly to make it a little easier
to see in the screencast. What we are showing is the pressure vs the mole fraction for benzene
and toluene equilibrium. Where on this plot on the left at high pressures of course, we have liquid and
at low pressures, vapor. This is vapor and liquid equilibrium in the
region between these two graphs. The red line which is a straight line in Raoult's law corresponds
to the bubble point and the blue line corresponds to the dew point. On the right we are showing
the relative amounts of liquid and vapor. When we are at this pressure a purple dot
here represents our overall composition but that is composed of some liquid and some vapor.
From the lever rule because we are closer to the dew point line, closer to the vapor, you notice on the bar graph we have
more vapor than liquid. The lever rule will allow us to calculate
how much of each. Then we are given the compositions of the vapor and the liquid here. As we change
the location of this purple dot we would change the relative amounts or as we change the pressure.
Now we are going to go to this interactive simulation just to observe the behavior as
we change these. You can certainly on your own play around with this interactive simulation.
Here is the interactive version where now, for example, I can change the overall mole fraction by
moving this slider. Notice as I move it to the left the amount of liquid increases and
the amount of vapor decreases in the bar graph. Something again the lever rule would allow
us to determine. If we move it far enough to the left of course, this region is all liquid. If we move it to
the right this is more vapor and less liquid. The overall composition above 0.67 or so then
we have all vapor. As we fix the composition and we increase the pressure we go from all
vapor to liquid. As we continue to increase the pressure the amount of liquid increases.
Notice the mole fractions of both the liquid and the vapor are increasing. Eventually we
are going to reach the point where we have all liquid. So right there. Right when we're at the red line, of course.
That is the bubble point. At higher pressure, we have all liquid. The simulation allows
you to look at different conditions, different mole fractions and determine for that pressure
do we have all liquid or all vapor or what is the composition of the mixture.