CHAPTER 8 PHASE TRANSITIONS AND EQUILIBRIA OF PURE SUBSTANCES
8.3 PHASETRANSITIONS 211
The figure shows that the slopes of the isobars are large and positive in the liquid region,
smaller and negative in the gas and supercritical fluid regions, and approach zero at the
critical point. Thus the gas and the supercritical fluid have much larger cubic expansion
coefficients than the liquid. The value of approaches infinity at the critical point, meaning
that in the critical region the density distribution is greatly affected by temperature gradients.
This may account for the low position of the middle ball in Fig.8.7(b).
8.3 Phase Transitions
Recall (Sec.2.2.2) that an equilibrium phase transition of a pure substance is a process in
which some or all of the substance is transferred from one coexisting phase to another at
constant temperature and pressure.
8.3.1 Molar transition quantities
The quantityÅvapHis the molar enthalpy change for the reversible process in which liquid
changes to gasat a temperature and pressure at which the two phases coexist at equilibrium.
This quantity is called themolar enthalpy of vaporization.^8 Since the pressure is constant
during the process,ÅvapH is equal to the heat per amount of vaporization (Eq.5.3.8).
Hence,ÅvapHis also called themolar heat of vaporization.
The first edition of this book used the notationÅvapHm, with subscript m, in order to
make it clear that it refers to amolarenthalpy of vaporization. The most recent edition
of the IUPAC Green Book^9 recommends thatÅpbe interpreted as an operator symbol:
Åp defD @=@p, where “p” is the abbreviation for a process at constantTandp(in
this case “vap”) andpis its advancement. ThusÅvapHis the same as.@H=@vap/T;p
wherevapis the amount of liquid changed to gas.Here is a list of symbols for the molar enthalpy changes of various equilibrium phase
transitions:
ÅvapH molar enthalpy of vaporization (liquid!gas)
ÅsubH molar enthalpy of sublimation (solid!gas)
ÅfusH molar enthalpy of fusion (solid!liquid)
ÅtrsH molar enthalpy of a transition between any two phases in general
Molar enthalpies of vaporization, sublimation, and fusion arepositive. The reverse pro-
cesses of condensation (gas!liquid), condensation or deposition (gas!solid), and freezing
(liquid!solid) havenegativeenthalpy changes.
The subscripts in the list above are also used for other molar transition quantities. Thus,
there is the molar entropy of vaporizationÅvapS, the molar internal energy of sublimation
ÅsubU, and so on.
A molar transition quantity of a pure substance is the change of an extensive property
divided by the amount transferred between the phases. For example, when an amountn
in a liquid phase is allowed to vaporize to gas at constantTandp, the enthalpy change is
(^8) BecauseÅvapHis an enthalpychangeper amount of vaporization, it would be more accurate to call it the
“molar enthalpy change of vaporization.”
(^9) Ref. [ 36 ], p. 58.