Physical Chemistry , 1st ed.

normal boiling point is that temperature at which a liquid can exist in equilib-

rium with its gas phase at 1 atm. Since the behavior of one of the phases—the

gas phase—is strongly dependent on the pressure, boiling points can vary

greatly with even small pressure changes. Therefore, we need to be certain that

we know the pressure when we discuss a boiling, sublimation, or condensation

process.

If the presence of two different phases in a single-component, closed sys-

tem represents a process at equilibrium, then we can use some of the ideas

and equations from the previous chapter. For example, consider the chemical

potentials of each phase for, say, a solid-liquid equilibrium as illustrated in

Figure 6.1. We are assuming constant pressure and temperature. The natural

variable equation for G, equation 4.48, must be satisfied, so we have

dGS dTV dp

0

phases

phasednphase

At equilibrium,dGis equal to zero at constant Tand p.The dTand dpterms in

the above equation are also zero. Therefore, for this phase equilibrium, we have



0

phases

phasednphase 0 (6.1)

For our solid-liquid equilibrium, this expands into two terms:

soliddnsolidliquiddnliquid 0

For a single-component system, it should be obvious that if the equilibrium

changes infinitesimally, then the amount of change in one phase equals the

amount of change in the other phase. However, as one goes down, the other

goes up, so there is also a negative numerical relationship between the two

infinitesimal changes. We write this mathematically as

dnliquiddnsolid (6.2)

We can substitute for either of the infinitesimal changes. In terms of the solid

phase, we get

soliddnsolidliquid(dnsolid) 0

soliddnsolidliquiddnsolid 0

(solidliquid) dnsolid 0

Although the infinitesimal dnsolidis indeed infinitesimally small, it is not zero.

In order for this equation to equal zero, the expression inside the parentheses

must therefore be zero:

solidliquid 0

We typically write that at the equilibrium between the solid and liquid phase,

solidliquid (6.3)

That is, the chemical potentials of the two phases are equal. We expand on this

theme and state that at equilibrium, the chemical potentials of multiple phases of

the same component are equal.

Since we are considering a closed system with a single component, there are

two other implicit conditions for a system at equilibrium:

Tphase1Tphase2

pphase1pphase2

144 CHAPTER 6 Equilibria in Single-Component Systems

Figure 6.1 Two different phases of the same

component can exist together in equilibrium with

each other. However, the conditions at which this

can occur are highly specific.

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