CHAPTER 8 PHASE TRANSITIONS AND EQUILIBRIA OF PURE SUBSTANCES
8.4 COEXISTENCECURVES 213
8.3.2 Calorimetric measurement of transition enthalpies
The most precise measurement of the molar enthalpy of an equilibrium phase transition uses
electrical work. A known quantity of electrical work is performed on a system containing
coexisting phases, in a constant-pressure adiabatic calorimeter, and the resulting amount of
substance transferred between the phases is measured. The first law shows that the electrical
workI^2 RelÅtequals the heat that would be needed to cause the same change of state. This
heat, at constantp, is the enthalpy change of the process.
The method is similar to that used to measure the heat capacity of a phase at constant
pressure (Sec.7.3.2), except that now the temperature remains constant and there is no need
to make a correction for the heat capacity of the calorimeter.
8.3.3 Standard molar transition quantities
Thestandardmolar enthalpy of vaporization,ÅvapH, is the enthalpy change when pure
liquid in its standard state at a specified temperature changes to gas in its standard state at
the same temperature, divided by the amount changed.
Note that the initial state of this process is a real one (the pure liquid at pressurep), but
the final state (the gas behaving ideally at pressurep) is hypothetical. The liquid and gas
are not necessarily in equilibrium with one another at pressurepand the temperature of
interest, and we cannot evaluateÅvapHfrom a calorimetric measurement with electrical
work without further corrections. The same difficulty applies to the evaluation ofÅsubH.
In contrast,ÅvapHandÅsubH (without thesymbol), as well asÅfusH, all refer to
reversible transitions between tworealphases coexisting in equilibrium.
LetXrepresent one of the thermodynamic potentials or the entropy of a phase. The
standard molar transition quantitiesÅvapXDXm(g) Xm(l) andÅsubX DXm(g)
Xm(s) are functions only ofT. To evaluateÅvapXorÅsubXat a given temperature, we
must calculate the change ofXmfor a path that connects the standard state of the liquid or
solid with that of the gas. The simplest choice of path is one of constant temperatureTwith
the following steps:
1.Isothermal change of the pressure of the liquid or solid, starting with the standard
state at pressurepand ending with the pressure equal to the vapor pressurepvapof
the condensed phase at temperatureT. The value ofÅXmin this step can be obtained
from an expression in the second column of Table7.4, or from an approximation in
the last column of the table.
2.Reversible vaporization or sublimation to form the real gas atTandpvap. The change
ofXmin this step is eitherÅvapXorÅsubX, which can be evaluated experimentally.
3.Isothermal change of the real gas at pressurepvapto the hypothetical ideal gas at
pressurep. Table7.5has the relevant formulas relating molar quantities of a real
gas to the corresponding standard molar quantities.
The sum ofÅXmfor these three steps is the desired quantityÅvapXorÅsubX.
8.4 Coexistence Curves
A coexistence curve on a pressure–temperature phase diagram shows the conditions under
which two phases can coexist in equilibrium, as explained in Sec.8.2.2.