In the last problem (Problem 10.43) within the problem section of Chapter 10 in "Introduction to Chemical Engineering Thermodynamics" (J.M. Smith, H.C. Van Ness, M.M. Abbott, McGraw-Hill, 7th edition, 2004), the last exercise states the following:

Vapour/liquid equilibrium azeotropy is impossible for binary systems rigorously descripted by Raoult's law (Pb. 10.5). For real systems (those with $\gamma_i \neq 1$), azeotropy is inevitable at temperatures where the $P_i^\mathrm{sat}$ are equal. Such a temperature is called a Bancroft point. Not all binary systems exhibit such a point. (...)"

In other words, if the vapour-liquid equilibrium curves of two different compounds intersect, they will inevitably present an azeotrope once mixed. This claim seems to be very general and unexpected. I tried it on many compounds, just for curiosity, and surprisingly it holds. I exemplify with water+2-butanol below:

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This system has a Bancroft point at $\approx \pu{87.7 °C}$, and indeed shows an azeotrope. A reference is found here. I am unable to find any information about this topic.


Is there any way to prove this very general statement? Is it a mistake? Any hint?


When the authors claim that "not all binary systems exhibit such a point", they refer to the next idea. Suppose $\ce{A}$ presentes VLE equilibrium in the range $\pu{50-150 °C}$, and compound $\ce{B}$ in $\pu{160-250 °C}$, then both curves can't intersect and thus the Bancroft's point can't exist. However, if the ranges overlap and the VLE curves do intersect, then azeotropy is a fact.



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