In this screencast I'm going to use an interactive simulation to demonstrate what equilibrium
phases are present.
This is for a binary system- we are going to represent it on a Txy diagram.
And two components are only partially miscible in the liquid phase.
And so what I am showing here first is what the diagram is going to look like in the interactive
simulation.
I'm plotting temperature versus mole fraction on the left side.
On the right side I plotted the relative amounts of the phases, so the alpha phase corresponds
to this region that is enriched in component A, so component B is partially miscible in
component A.
The beta liquid corresponds to this region where now A is partially miscible in component
B. And then we have a very large region where the two phases coexist as two distinct phases.
And the dot here corresponds to mixture of the two phases.
And then we have vapor liquid equilibrium the same way we have normally seen vapor liquid
equilibrium.
The kind of question that you should be able to answer if you understand this Txy diagram
is, What happens if I start at this point and I add heat to the system so I raise the
temperature, what phases do I see as I move up until I'm all in the vapor phase?
And if we look at the phase rule, number of degrees of freedom that we have, 2 plus the
number of components minus the number of phases.
So 2+2 say we could have three phases, that would tell us we have one degree of freedom.
And we have already picked that because the pressure is fixed.
So we have no degrees of freedom for three phases.
And the three phases exist then at just one temperature and that is along this line.
So what we want to do now is look at this simulation to understand how we go from two
immiscible liquid phases to one phase all vapor in a closed container so a fixed composition.
So the simulation I am going to use is available online on the Wolfram Demonstration Website.
Go to that site and then we will look at the simulation.
So we are starting where we have two liquids.
Slightly more alpha liquid than beta liquid.
Then I'm going to add heat so I'm going to move this slider to the right.
And we see some slight changes in the amount of phases.
And then we reach this temperature of about 77 or 78 degrees.
And now notice we have three phases present.
So we start to see some vapor forming.
Vapor in equilibrium with these two liquid phases.
As I continue to add heat, so I'll move the slider slightly further.
Well notice I still have three phases, the point on the diagram doesn't move, but I'm
getting more vapor.
Again the point hasn't moved, so one point on the diagram represents a large number of
conditions, like different amounts of alpha liquid, beta liquid and vapor.
And so essentially we are getting evaporation at constant temperature.
And notice that the beta liquid is preferentially disappearing.
So as I continue to add heat, when you get to the point where essentially all the beta
is going to disappear, now we are going to move above that temperature because now we
just have normal vapor liquid equilibrium between the alpha phase and vapor and then
as we raise the temperature we of course get more vapor and less liquid but the temperature,
where boiling curve is evaporation, keeps changing as the composition changes.
And then eventually we get to all vapor so as we add more heat we are just raising the
temperature of the vapor.
So an important thing to notice is that we have a condition where we have three phases
which we can indicate determine from the phase rule, that is possible, and therefore one
point represents multiple conditions on this diagram.
Let's look at just one other case.
Let's say I start with an overall composition that is a much higher mole fraction of component
B. And then I'm going to do the same thing, starting with two liquids, lever rule tells
us we have majority beta liquid.
But then as I raise the temperature we are going to get to, again, about 77 or 78 degrees
and again we have three phases.
But now notice that in addition to the vapor, and maybe I can take some heat away, the alpha
liquid is preferentially disappearing.
If we go back we can see the alpha liquid is preferentially disappearing compared to
the beta liquid for making vapor.
And as we continue to add heat we are going to get to the point where all the alpha liquid
disappears and then we are going to move off this constant temperature 77 or 78 degrees.
Now we are going to have just vapor liquid equilibrium and the dashed line indicates
the compositions of vapor and liquid.
In this case it's the beta liquid enriched in component B and vapor and now the temperature
evaporation changes as we add heat until we add enough heat where we are all in the vapor
phase.