As a continuation of the posts
Anthony has sent the text below, which he has permitted me to post. It reads
I promised to get back to you about the best way of estimating latent heats from equilibrium vapor pressure data as a function of temperature.
It is fortuitous that I was assigned to teach our advanced chemistry laboratory this semester because it required that I pursue several physical chemistry laboratory texts including the classic text, “Experiments in Physical Chemistry” by Shoemaker, Garland, Steinfield, and Nibler, fourth edition. One of the experiments in this text is the measurement of equilibrium vapor pressure of a liquid as a function of temperature employing an isoteniscope which ensures fairly accurate values for pressure. The authors suggest plotting ln P vs. 1/T which they note is nearly linear and then manually determining the slopes by drawing tangent lines. The edition was written prior to the advent of fast personal computers. Today we would fit the data to a polynomial regression to the highest order consistent with the statistical reliability of the various coefficients as determined by Excel’s ANOVA software. A simple derivative of the polynomial should yield fairly reliable values for latent heat as a function of temperature as I suggested in an earlier communication. There are two additional points:
- Chemists generally refer to the equilibrium heat or enthalpy of vaporization which, I believe is identical to latent heat.
- Precise work introduces another term, the compressibility factor (z), which corrects for the vapor’s deviation from ideality. Thus one gets
d(ln P)/d(1/T) = -L/Rz
where R is the universal gas constant and
z = PV/RT.
The compressibility factor is very nearly equal to one but is slightly less than one in the P–V–T regime experienced here. It requires knowing V, the molar volume of the vapor at a given P and T. There are tables for these values.
I recognize that this approach is an appeal to authority rather than a convincing demonstration. If I get time in the future (not a promise), I’ll compare the actual values of the latent heat as determined by calorimetry to those estimated using the procedure outlined above.