Page 19 - Partition & Adsorption of Organic Contaminants in Environmental Systems

10 IMPORTANT THERMODYNAMIC PROPERTIES

where f i ° is the reference fugacity of substance i at P i ° and T and f i is the fugac-
ity of substance i at P and T. To a good approximation, except at extremely
high vapor pressure, f i ° = P i ° and f i = P i. The most useful and convenient ref-
erence states for gases, liquids, and solids are chosen as follows:

For gases: f i ∞= 1 atm of the gas (1.38)

For liquids: f i ∞= ∞ of the pure liquid (1.39)
f i
For solids: f i ∞= ∞ of the pure supercooled liquid (1.40)
f i

By Eqs. (1.37) and (1.39), one sees that a i = 1 for a pure liquid at T. Contrar-
ily, one sees with Eq. (1.40) that a i < 1 for a pure solid at T below its melting
point, because the vapor pressure of the solid is less than that of its super-
cooled liquid, as shown later in Figure 1.2. From the relations above, one also
gets

dm= RTdln P i = RTdln f i = RTdln a i (1.41)
i
Therefore, an alternative way of stating the equilibrium of a chemical between
any two separate phases is that the activity or fugacity (or partial pressure) of
the chemical is the same in the two phases.

1.9 VAPOR–LIQUID AND VAPOR–SOLID EQUILIBRIA

It was indicated earlier that when a chemical species in two phases (A and B)
reaches equilibrium,

i = 0 or dm = dm
i - m ,B
DG i = m ,A i,A i,B
For a pure liquid in equilibrium with its vapor, one therefore gets

l (
v (
dm liquid) = dm vapor) (1.42)
or

V dP - S dT = V dP - S dT (1.43)
l
l
v
v
that is,
dP dT = ( S v - S l ) ( V v - V l ) (1.44)

With