# Why don't P graphs contradict Raoult's law graphs?

Our teacher gave us the following question:

1 mole each of liquids A, B are mixed in a piston-type vessel and piston is moved slowly and isothermally. (PA0 = 75 torr and PB0 = 25 Torr)
Find:
(a) Find pressure when first bubble is formed. And its composition.
(b) Find pressure when last drop of the liquid is remaining.
Ans: (a) 37.5 Torr (b) 50 Torr

Subsequently, he drew a graph to introduce us to bubble-point and dew-point curves:

And made us write, "At a given temperature, a pure liquid has a fixed/definite vapor pressure, but an ideal solution doesn't have a fixed vapor pressure."

Now the doubt which irks me is that

(i) When Raoul's law's straight-line graphs were drawn, each composition corresponded to only one value of vapor pressure. But here (through the attached graph) we can see multiple values of vapor pressure at a particular composition, (since I'm assuming that external pressure and vapor pressure would be the in this case). Don't these 2 graphs contradict each other? Since one shows a single value of vapor-pressure while the other (the attached one) shows no-fixed value?

(ii) How do the terms "pure liquid" and "ideal solution" differ in this context?

• The same compositions of liquid and gaseous phase belong to different pressures and temperatures. OTOH, horizontal isobaric lines determines composition of both phases at the given pressure. Sep 10, 2023 at 18:45
• At $x_B=1/2$ (1:1 mixture , fixed ) and at v. low pressure, only vapour is present, then increasing pressure at $37.5$ torr the vapour first condenses, then at $50$ torr it is all liquid. You can calculate the total pressure $P=(1-x_B)p_A^* + x_Bp_B^*$ where* indicates pure A or B, and the dew point (lower) curve as $x_B(g) = x_Bp_B^*/P$ where $x$ is a mole fraction. Sep 11, 2023 at 12:15

There is important to consider that the gaseous phase will have at equilibrium always higher relative content of the more volatile liquid $$\ce{A}$$, compared to the equilibrium composition of the liquid phase.

For the $$1:1$$ molar mixture of liquids:

• The higher pressure $$\ce{50 torr}$$ on the straight line crossing 1:1 ratio belongs to the equilibrium pressure for the liquid phase mixture 1:1. The gaseous phase has at that point roughly $$80\ \%$$ of liquid A vapor (a horizontal line crossing the curve).

• The lower pressure $$\ce{37.5 torr}$$ on the curve, crossing 1:1 ratio belongs to the equilibrium pressure for the gaseous phase mixture 1:1. The liquid phase mixture has at that point roughly $$15\ \%$$ of liquid A.(a horizontal line crossing the straight line)

• For pure liquids, both the straight line and the curve converge to the same point. Composition of both gaseous and liquid phases is identical and there is single pressure value for both bubble and dew point.

The two curves in your diagram have different meanings. More specifically, the x-axis means different things for the two curves.

The curve labeled "bubble point" shows the relationship between pressure and composition of the liquid. According to Raoult's law, this curve should be a straight line. (Raoult's law is often not true, or even close to true, but an ideal solution is a mixture where it is true, and that curve actually is a straight line.)

The curve labeled "dew point" shows the relationship between pressure and composition of the gas. Raoult's law has nothing to say about this curve, because Raoult's law only talks about the pressure of a vapor above a liquid of known composition.

That is why there is no contradiction.