# Under what circumstances would azeotrope exist in non ideal solutions? (when would the dew point curve and the bubble point curve meet?)

[solved. For anyone who's interested in this topic, please view MaxW's comment under his/her answer. A thousand thanks to Poutnik and MaxW.]

I looked up several books on thermodynamics, and they all states that for non ideal solutions, the dew point curve and the boiling point curve sometimes meet at some point. Azeotropes forms there.

What I couldn't figure out was, under what circumstances would the two curves meet? Do they always meet if both of them have a local minimum? What is the logic under this phenomenon?

• Edited: I corrected the wrong statement. The books just mentioned the meeting of the curve, but they didn't say "always".
– Wang
Apr 20, 2020 at 15:50

Azeotropes do not exist for all non-ideal solvent solutions. All solvent solutions are more or less non-ideal, but not all solvent combinations form azeotropes.

E.g. ethanol and isopropanol form azeotropes with water, but methanol does not.

Azeotropes exist if there is large enough deviation from the Raoult law. It means if the azeotrope point of the diagram is pushed enough away from the endpoint connections.

For near ideal solutions, like n-pentane + n-hexane. there is no bottleneck and onle one convex/concave chart segment.

Back to the meeting of boiling and condensation curves, they meet at the pure solvent points and eventually at the azeotrope point, if it exists.

Existance of such minimums ( or maximums ) ob the vapour diagram means there is an azeotrope. An azeotrope behaves like if it were the 3rd substance, with the same composition of liquid and vapour above it, so the curves meet there.

Minimums meet if and only if liquid and vapour compositions are the same. That happens if and only if either the liquid is pure solvent either it has the composition of the azeotrope ( if it exists ).

You can create simulations yourself by defining nonideal vapour pressure equations as $$p_i(T)<>p_{i,0}(T) \cdot x_i$$. It cannot be exactly calculated, as neither the mixture of pure solvent and azeotropic mixture has the ideas behaviour.

• Is there any picture with minimum in dew point curve and bubble point curve, and those minimum does not meet? Also I can't find out if the Txy diagram of ethanol-water solution is calculable by some equation, or is it pure experiment results?
– Wang
Apr 20, 2020 at 14:01
• So how does the picture change, when the deviation from Raoult law is small to large enough to form an azeotrope? I mean why would the minimum always meet when they exist?
– Wang
Apr 20, 2020 at 14:08
• @Wang Non-ideal vapor-liquid equilibrium curves can be generated using Wilson's Equation of State and Antoine's Equation. Dec 5, 2021 at 1:49

Binary Mixture Which is an Ideal Liquid

Well let's start with what an ideal liquid binary mixture would be. An ideal liquid binary mixture would obey Raoult's law as shown in the figure below from the Wikipedia article.

A ideal liquid is a special cases of Raoult's law where the mole fraction of both phases form a straight line from the boiling point of A to the boiling point of B. Thus for an ideal liquid the dew point curve and the boiling point curve have exactly the same mole fraction at any temperature. Thus, by definition, an ideal liquid can not have an azeotrope.

Binary Mixture Which is an Non-Ideal Liquid

Now in the following figure there is a region bounded by drawing a horizontal line from A across the diagram, and a horizontal line from B across the diagram. Consider this the bounded region.

So the correct statement is that if the dew point curve goes outside the bounded region, then there must be an azeotrope.

The statement:

For non ideal solutions, the dew point curve and the boiling point curve must meet at some point.

is just wrong. A lot of ideal behavior can occur with the dew point curve and the boiling point curve in the bounded region.

In chemistry there is usually some weird outlier for any general statement. I can't think of a binary system which has an azetrope where the dew point curve and the boiling point curve stay the bounded region but I'd bet that there is at least one known.

Edit - I realize now that if the dew point curve crosses the ideal line then there must be an azeotrope at the crossing point.

• Why must azeotrope exist if the dew point curve goes outside the bounded region?(I think this equals to "if the dew point curve goes outside the bounded region, then it must meet the bubble point curve". I hope this equivalence isn't wrong.)
– Wang
Apr 20, 2020 at 15:47
• @Wang - yes that statement would be equivalent to mine.
– MaxW
Apr 20, 2020 at 15:49
• @Wang - My calculus is too rusty to work it out, but I'm sure that it is the calculus rather than the chemistry. If the dew curve goes outside the bounded region, then it must form a maxima or a minima. Remember if the vapor phase is changing composition, so must the liquid phase.
– MaxW
Apr 20, 2020 at 16:38
• The math seems to have been worked out in "New Trends in Statistical Physics" by Alfredo Maacias and Leonardo Dagdug, Chapter 6 - Thermodynamic Properties and Model for Vapor-Liquid Azeotropic Binary mixtures
– MaxW
Apr 20, 2020 at 17:59
• @BuckThorn - OK, I broke the post into sections and explicitly stated that an ideal liquid is a special case of Raoult's Law. // An ideal liquid has no azeotrope of course. // Think that the changes made the article better.
– MaxW
Apr 21, 2020 at 17:09

According to statistical mechanics and algebraic analysis (10.26434/chemrxiv-2021-xsj92-v2), the bounded region is related to $$|ln(p_A^*/p_B^*)|$$ $$k_B T$$. Only if the intermolecular interaction between A and B components is stronger than this amount, the binary mixtures can form azeotropes.