[pantone159]

I am trying to understand the variation in boiling point with pressure of substances.

Specifically, there is this graph ("nomograph") that is used to estimate the change in boiling point with pressure.  This graph must be the representation of some equation, but which one?  (I know this is an approximation, btw.)

At first, I thought it might be the "Clausius-Clapeyron" equation, P = P0 * exp( (-DH/R) * (1/T - 1/T0)).

I found something called "Trouton's Rule" that says the entropy change upon vaporization is about 21 cal/mol-K for many substances.  Since DH = DS * T during vaporization, the above equation can be re-arranged to give:

T = T0 * (1 / (1 - 0.095 * ln(P/P0)))

where:
T = boiling point at reduced pressure, in K
T0 = boiling point at 1 atm, in K
P = reduced pressure
P0 = 1 atm

This doesn't seem to match the nomograph, however.  As an example, CU Boulder has some example questions about reduced pressure:
http://orgchem.colorado.edu/hndbksupport/dist/distsq.html
http://orgchem.colorado.edu/hndbksupport/dist/distsqans.html
Question 8 in this is as follows:
Eugenol has a boiling point at 760 torr of 255 C.  What is the boiling point at 25 torr (water aspirator) and at 0.1 torr (vacuum pump)?
Applying my equation, I get 125.6 C for the bp at 25 torr, and 12.6 C at 0.1 torr.  The example, however, shows that the mysterious nomograph gives 145 C at 25 torr, and 55 C at 0.1 torr, quite different.

So, the nomograph represents a different equation than mine.  Which one?

Thanks.

[mbeychok]

Mark:

I am not sure I understand what you are trying to do.  Every liquid has a unique set of vapor pressures versus temperatures (in other words, the boiling point temperatures versus vapor pressures) speciifc to that liquid. That vapor pressure-temperature relationship is a unique physical attribute of any specific liquid.  If one wants to know how pressure affects the boiling point temperature of a specific liquid, one should look up the vapor pressure versus temperature data for that specific liquid ... or use a pertinent Antoine equation to calculate the desired data.

Yes, there are certain generalized correlations that can be used for similar types of liquids ... but they are not as reliable as looking up (or calculating via an Antoine equation) the actual specific vapor pressure data for a specific liquid. For example, there is a nomograph (almost identical to the one you found at http://orgchem.colorado.edu/hndbksupport/dist/distsqans.html) available at http://www.sigmaaldrich.com/Area_of_Interest/Research_Essentials/Solvents/Key_Resources/nomograph.html by simply clicking on th launch button ... and which includes the following quote:

Calculate a boiling point or pressure using the Antoine Equation: The Pressure-Temperature Nomograph is a graphical application of the Clausius-Clapeyron Equation, which assumes the heat of vaporization is a constant over a pressure range. Antoine´s Equation gets around this by using empirical data for each unique liquid under consideration.

I interpret that to mean that the Clausius-Clapeyron equation (which assumes contant heat of vaporization] is not as accurate as using the specific Antoine equation applicable to a specific liquid.

 

[pantone159]

I know it can't be *that* accurate to use one chart for all substances.  I am under the impression, though, that there is one chart (i.e. that "nomograph") that (in practice) is used for approximating the corrections for all substances, and it is somewhat accurate.  (Close enough to be useful.)

I'm trying to understand where that nomograph comes from.

I tried starting with the Clausius-Clapeyron equation, which has this DH term in it.  I tried substituting for that, T * DS, and then assumed that DS was a constant 21 cal/mol-K, but that doesn't match what the nomograph does.  Perhaps one problem, is that the Clausius-Clapeyron equation is derived assuming a constant enthalpy of vaporization, but I then assumed constant entropy of vaporization, which is a contradiction to the first assumption.

I'll look into the Antoine equation stuff, also, thanks for that suggestion.