In this problem, we have partially immiscible liquids, and we start out with the system
- so one mole of a liquid mixture is heated at constant pressure until 0.05 moles of vapor
are present. So we start out total one mole, and we end up vapor is 0.05 moles. And liquid
mixture - so we're along this dashed line, 0.75, and the whole diagram is at constant
pressure - so we start here, for example. And this point corresponds to this composition
in one liquid phase in equilibrium with this other liquid phase. And as we increase the
temperature, we get to this point. So at this point, we have liquid 1 with mole fraction
of component B equal to about 0.27, and we have liquid 2 with a mole fraction of about
0.83. And now once we get to this temperature we start getting evaporation until all of
liquid 1 disappears. The vapor that's in equilibrium with the two liquids has a mole fraction of
B equal to 0.6. So now we need to determine the amounts of these phases. We've determined
the compositions. So I'm going to call this xB in phase 1 and in phase 2. And then yB
is in the vapor and there's only one vapor phase. So I can do a mass balance on component
B, and essentially I'm saying the number of moles of B in liquid 1 - so that's the mole
fraction of B in liquid 1 times the amount of liquid 1 - plus the number of B moles in
liquid 2 - mole fraction B in liquid 2 times the amount - plus the number of moles of B in
the vapor phase - which is mole fraction times the number of moles - and for a basis of one
mole, this should add up to 0.75. Right, that's our initial and our overall mole fraction
of B. So we have these numbers that we read. The mole fraction here is 0.27. The amount
of liquid 1 we don't know. This mole fraction is 0.83. This mole fraction is 0.60. And we
do know, we're given this. Well the other thing we have to do to solve this is to say
0.27 liquid 1 plus 0.83 - amount of liquid 2 - so liquid 1 plus liquid 2 must add
up to 0.95 moles because 0.05 moles is vapor. And six tenths of 0.05 is 0.03. And we can
solve this algebraic equation for liquid 1. Liquid 1's 0.13 moles. Liquid 2, 0.82 moles.
And the composition in liquid 1, 0.27 mole fraction of B. And in liquid 2, the mole fraction's
0.83. And then of course we have vapor as given in the problem statement, and it's mole
fraction is 0.60.