I'm going to describe the phase behavior that can occur
when we have two components that are only partially miscible
in the liquid phase with each other.
So, the idea is if we had a pure component A,
the green circles, and a pure component B,
the blue circles, and we mix them together,
we'd actually get two distinct phases.
One phase, we'll call the "alpha" phase,
and those is mostly component A, mostly green.
The other phase, the "beta" phase,
is mostly component B.
And so, what we're interested in
is what's the behavior as a function of the relative amounts
of A and B that we mix together
and as a function of temperature.
And one of the things that we'll want to keep in mind
when we look at these phase diagrams,
is the phase rule, which says the number of degrees
of freedom is two plus the number components,
minus the number of phases.
So, we're talking about a binary system,
so, four minus the number of phases.
And the phase diagram that we're gonna look at
is one where we fix the pressure.
So let's look at that phase diagram.
So in this phase diagram,
we're plotting temperature on the y-axis
and the mole fraction of B on the x-axis.
And then the bar graph on the right
shows how much we have of each phase.
In this case, we're starting where we have the alpha liquid,
namely, we have both components, but they're miscible
in this concentration range at this temperature.
We only have one phase,
and, therefore, for relative amounts,
moles, we have one mole of the alpha phase.
If I were to add
additional B to the system,
increase the mole fraction, let's move to here.
Now this point in this white region,
this point center corresponds to two distinct phases.
The alpha phase has a mole fraction of component B of 0.11,
and the beta phase has a mole fraction of B as 0.93.
And so, the relative amounts of each of these phases,
we can calculate from the diagram using the lever rule.
And, if I increase the mole fraction,
move to the right, then we have more of the beta phase
and less of the alpha phase.
And, over here, we have one phase now.
And this is a single phase that has both components.
So the other interesting behavior
is as we raise the temperature.
Let's look at this mole fraction
and raise the temperature, so now we're on this line
at about 77 degrees Centigrade.
Now we have all three phases present.
Well, if we look at that, its phase rule
that we just mentioned, where for a binary system,
number degrees of freedom was four
minus the number of phases, so, we have three phases.
That says we have one degree of freedom
and what we've said is the pressures,
remember this diagram is at one pressure,
if we change the pressure, the diagram's going to change.
And so, we've set the pressure.
We have no degrees of freedom,
which means there's only one temperature
where we can have all three phases present.
Now the amounts of each phase
are not determined by the lever rule.
As I add heat to this system,
you'll notice, of course, we have more vapor
and less of each of the liquids.
But, we stay on this same temperature
even though we're adding heat.
If I add enough heat, the beta phase disappears.
Now I have an alpha liquid
in equilibrium with the vapor.
This behaves the way we normally are used to a binary system
in which liquids are completely miscible.
We have liquid and vapor in equilibrium
the relative amounts can be determined
from diagram by the lever rule.
And then if I move the mole fraction over to here,
then we have beta liquid in equilibrium with vapor
and again, the relative amounts you determine
by the lever rule, if I change the mole fraction,
I change the relative amounts of vapor and liquid.
And, of course, with the same amount of heat added,
the temperature is changing
because it takes energy and heat to vaporize.
So, this is just a brief overview
of a temperature composition phase diagram
for a binary system
in which liquids have limited miscibility.