McKay, Donald. "Front matter" Multimedia Environmental Models ...

Z F = K FWZ W = 0.04
©2001 CRC Press LLC
f = 10/(1000 ¥ 4 ¥ 10 –4 + 20 ¥ 0.002 + 10 ¥ 0.03 + 0.05 ¥ 0.04)
= 10/0.742 = 13.48
C A = Z Af = 0.0054, C W = 0.027, C S = 0.405, C F = 0.54
And the amounts and percentages are as before.
The procedure is simply to tabulate the volumes, the Z values, calculate and sum
the VZ products, and divide this into the total amount to obtain the prevailing
fugacity. This is readily done using a computer spreadsheet or program, and there
is no increase in mathematical complexity with increasing numbers of phases.
5.6.3 A Digression: The Heat Capacity Analogy to Z
The fugacity capacity Z is at first a difficult concept to grasp, since it has
unfamiliar units of mol/(volume ¥ pressure). Heat capacity calculations provide a
precedent for introducing Z and may help to illustrate the fundamental nature of
this quantity.
The traditional heat capacity equation is written in the form
heat content (J) = mass of phase (kg) ¥ heat capacity (J/kg K) ¥ temperature (K)
For example, water has a heat capacity of 4180 J/kg K, which is more familiar as
1 cal/g°C. We can rearrange this equation in terms of volumes instead of masses to
give
heat concentration (J/m 3 ) = heat capacity (J/m 3 K) ¥ temperature (K)
This new volumetric heat capacity for water is 4,180,000 J/m 3 K. The use of mass
rather than volume in heat capacities is an “accident” resulting from the greater ease
and accuracy of mass measurements compared to volume measurements, and the
complication that volumes change on heating, while mass remains constant.
The equilibrium criterion used above is temperature (K), whereas we are concerned
with fugacity (Pa). The quantity that partitions above is heat (J), whereas we
are concerned with amount of matter (moles). Replacing K by Pa and J by mol leads
to the analogous fugacity equation,
C (mol/m 3 ) = Z (mol/m 3 Pa) ¥ f (Pa)
Z is thus analogous to a heat capacity. Experience with heat calculations leads to a
mental concept of heat capacity as a property describing the “capacity of a phase
to absorb heat for a certain temperature rise.” For example, if 1 g of water (heat
capacity 4.2 J/g°C) absorbs 4.2 J, its temperature will rise 1°C. Copper with a lower