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

1. Heat (moles) in water = 10 ¥ 4.2 ¥ 10 = 420 J (moles) 72%
2. Heat (moles) in copper (air) = 5 ¥ 0.38 ¥ 10 = 19 J (moles) 33%
3. Heat (moles) in hydrogen (sediment) = 1 ¥ 14.3 ¥ 10 = 143 J (moles) 25%
The concentrations are
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Total = 582 J and 100%
The distribution of heat (moles) is influenced by the relative phase masses
(volumes) and the heat capacities (Z values). Despite the fact that the third phase is
small, its much larger heat capacity (Z) results in accumulation of a substantial
fraction of the total (25%), and its concentration is a factor of 3.4 and 38 greater
than the other two phases—which is, of course, the ratio of the heat capacities (the
ratio of Z values, this ratio being the partition coefficient).
This example could have been solved using heat capacity partition coefficients
but, of course, no such quantities are tabulated in handbooks. Indeed, any suggestion
that heat partition coefficients are useful would be treated with derision. In environmental
calculations, on the other hand, the use of Z is less conventional, and the
use of partition coefficients is routine. In essence, the use of fugacity capacities is
an attempt to bring to environmental calculations some of the procedural benefits
that are routinely enjoyed by the use of heat capacities.
Worked Example 5.8
Water 4.2 ¥ 10 = 42 J/g (mol/m 3 )
Copper (air) 0.38 ¥ 10 = 3.8 J/g (mol/m 3 )
Hydrogen (sediment) 14.3 ¥ 10 = 143 J/g (mol/m 3 )
A three-phase system has Z values Z 1 = 5 ¥ 10 –4 , Z 2 = 1.0, and Z 3 = 20 (all
mol/m 3 Pa), and volumes V 1 = 1000, V 2 = 10, and V 3 = 0.1 (all m 3 ). Calculate the
distributions, concentrations, and fugacity when 1 mol of solute is distributed at
equilibrium between these phases. It is suggested that the calculations be done in
tabular form.
Phase Z V VZ C = Zf VC %
1 5 ¥ 10 –4 1000 0.5 4 ¥ 10 –5 0.04 4
2 1.0 10 10 0.08 0.80 80
3 20 0.1 2 1.6 0.16 16
Total 12.5 1.0 100
M = V 1Z 1f + V 2Z 2f + V 3Z 3f = f SV iZ i