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PROFESSOR CIMA: Now, if I go back here, you'll see that I could vary the
composition. So I did this for equal amounts of A and B.
I can change the ratio. And of course, the points at which it starts
to freeze are going to be different, and where it's finished freezing
is going to be different, as I vary the composition.
So I could do a whole set of experiments where I just vary the
composition, do these cooling curves, and record where the freezing starts
and where the freezing ends. And I could then plot them up.
So if this is 100% B and this is 100% A, that's the mole fraction.
Or you'll see today, you can do it in weight fraction, too.
It's not too hard to convert between them. Well, I know that pure B melts, let's say,
here. And pure A melts at a higher temperature,
at least the way I've defined it.
And of course, if I'm at the 50-50 mixture that I had, it started melting
here, and it finished melting somewhere here. So it was all liquid above that and all solid
below. So there's two of my points at one composition.
I could go to, let's say, this one, and I would record two new points, or
this one here, two new points. Again, these are just from the cooling curves,
just from where it stops that slope and goes to a new slope.
And you can see, what I'm going to create is a locus of points that look
like that, where it's all liquid above this line, all solid below this line.
And in between, it's mixtures of liquid plus solid at equilibrium.
So at any temperature-- if I'm at, let's say, this composition, if
I'm at this temperature, I know I can read across it that
I actually have this solid and this liquid in contact with one another.
So just like the extensive variable of volume that we showed last time, at
the last of the lecture, the extensive variable here is composition.
And so what happens in the phase diagram is you open up these gaps.
And the lines that describe equilibrium are called tie lines.
And you can see, there's a tie line at any temperature.
If I go to this temperature, there's a tie line here.
Of course, if I'm below the melting point, there are no tie lines--
melting point of the lowest melting material, there's no tie line.
If I'm above the melting point of the highest melting material,
there's no tie lines. It's only in this freezing range that you
have tie lines. Another way to think about this is that, if
I take a liquid at this temperature--
it's all molten-- and I cool it down, what it does, the first solid that
it's in equilibrium with is richer in A than the liquid was.
If it's 50/50, the solid in equilibrium with that liquid has got
more A in it than the liquid did. So how did I form it?
If this is richer than this one, where did I get the A from?
Anybody know? STUDENT: From the liquid.
PROFESSOR CIMA: Well, the only place it could come from is the liquid.
Now, of course, if I did that, then I would actually have to be at a lower
temperature, because I took some A from the liquid.
So the reason why, when I reach this point, there's no solid, even though
there's a solid that would be in equilibrium with it, I haven't formed
any solid yet. The volume fraction of solid at this point
is zero. As soon as I form some volume of solid, I
have to change the composition of the liquid.
And in order to do that, I have to lower the temperature.
See what's happened? I get the richer A from the liquid.
And of course, that moves this composition this way.
It makes it depleted in A. And we call this process disproportionation.
So it's mass-balanced, right? I can't create something that's richer in
A without taking it from the liquid.
And if I take it from the liquid, the liquid gets lean in A.