Multicomponent Equilibrium Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 51

E XAMPLE 3.4 M EAN I ONIC A CTIVITY C OEFFICIENT C ALCULATION

Problemstatement : Determine γ ± for a 0.002 molal solution of NaCl in water at 298 K.
Solution : For a 1:1 electrolyte such as NaCl, m + = m − = m and hence I =
0.002 mol/kg. Since I < 0.002, we can use the Debye-Huckel limiting law, log γ ± =
− ( 0.509 )( 0.002 ) 1 / 2 =− 0.023, γ ± = 0.949.

3.2.5 F UGACITY AND E NVIRONMENTAL M ODELS
Fugacity is useful to estimate the tendency of molecules to partition into the various
environmental compartments (Mackay, 1979). Since fugacity is identical to partial
pressure in ideal gases, it is also related to the vapor pressures of liquids and solids.
Fugacity is directly measurable (e.g., at low pressures fugacity and partial pressure of
an ideal gas are the same) and since it is linearly related to partial pressure or concen-
tration, it is a better criterion for equilibrium than the elusive chemical potential. In
fact, the criterion of equal chemical potential for equilibrium can be replaced without
loss of generality with the criterion of equal fugacity between phases. If an aqueous
solution of a compound i is brought into contact with a given volume of air, the species
i will transfer from water into air until the following criterion is established:

RT ln f i
f w0
i

RT ln f i
f a0
i

.

w0
i

a0
i

μ + = μ + (3.16)

If we choose the same standard states for both phases, we have the following criterion
for equilibrium:

f i = f i . (3.17)

The above equality will hold even when the standard states are so chosen that they are
at the same temperature, but at different pressures and compositions. We then have
an exact relation between the standard states, that is,

RT ln f w0

.

w0
i

a0
i

i
f a0
i

μ − μ =

(3.18)

The equality of fugacity can be generalized for many different phases in equilibrium
with one another and containing multi-components. We now have three equivalent
criteria for equilibrium between phases as described in Table 3.5.
Mackay (1991) proposed a term fugacity capacity , Z , that related fugacity (of any
phase expressed in Pa) to concentration (expressed in mol/m 3 ) . Thus

C( mol / m 3 )
f ( Pa )

Z( mol / m 3 / Pa )

= . (3.19)