# Re: Has anyone a reference to the 'Bancroft point'?

On Dec 18, 6:50 pm, Bruce Bathurst <bruce.bathu...@xxxxxxxxx> wrote:
Classical thermodynamics is more the subject of engineers these days
than physical chemists. (Well, both Carnot and Gibbs were engineers.)

Has anyone else read of the 'Bancroft point?' Primary references,
anyone?

Though classical thermodynamics says little of equations of state, but
to impose a relation or two upon them, someone once proposed a
'Bancroft point'. This was, I vague remember, an azeotrope caused by
the melting or boiling points of two substances becoming 'too close'.

In elementary texts one sees many two-component, isobaric diagrams of
liquid and vapor compositions as a function of temperature. The pair
of curves touch at the composition of pure water or alcohol, then
often graze one another at an azeotrope between.

Prigogine and Defay, if I can find mine, hava discussion of 'deltas'
that empirically relate the azeotropic temperature to (I believe) the
boiling points of the pure substances. (It's been a while.) However,
somewhere, there is the claim that as any solution's pure substances
boiling point approach one another, an azeotrope must form. Now, this
is not the normal thing that classical thermodynamics predicts.
<SNIP>

Actually, this IS what classical thermodynamics predicts. Classical
thermodynamics tells us that an azeotrope corresponds to a maximum or
minimum in the curve of boiling temperature versus composition (at a
fixed pressure), or of pressure versus composition at a fixed
temperature.

A Bancroft point (sorry, I don't know about the coining of the name)
between two substances is defined as a crossing of vapor-pressure (p
versus T) curves. For example, the vapor pressures of ordinary water
and heavy water cross at about 221 degrees C. So if you plot pressure
versus composition at that temperature, the two pure-component
endpoints will have the same pressure. Mathematically, the p-x curve
between those points must go through a maximum and/or a minimum
(discounting the case where it is completely flat, which is also
azeotropic). Any pair of fluids whose vapor pressure curves cross
(Bancroft point) must have an azeotrope at the corresponding pressure
(looking at a T-x diagram) and the corresponding temperature (looking
at a p-x diagram). Because of nonideality, typically one also gets
azeotropy in some range of temperatures and pressures around that
point, since if the vapor pressures are close it only takes a little
nonideality to bend the curve enough to get a maximum or minimum.

Dr. Allan H. Harvey, Boulder, CO
"Usual disclaimers here."
.