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

D AS dominates. A residence time of solids in the mixed layer can be calculated as
the volume of solids in the mixed layer divided by G S. For example, if the depth of
the mixed layer is 3 cm, and the solids concentration is 25%, then the volume of
solids is 75,000 m 3 and the residence time is 260,000 hours, or 30 years. The
residence time of water is probably longer, because the water content is likely to be
higher in the active sediment than in the buried sediment. In reality, the water would
exchange diffusively with the overlaying water during that time period.
As discussed in Chapter 5, there are occasions in which it is convenient to
calculate a “bulk” Z value for a medium containing a dispersed phase such as an
aerosol. This can be used to calculate a “bulk” Z value, thus expressing two loss
processes as one. D is then GZ where G is the total flow and Z is the bulk value.
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6.3 DEGRADING REACTIONS
The word reaction requires definition. We regard reactions as processes that alter
the chemical nature of the solute, i.e., change its chemical abstract system (CAS)
number. For example, hydrolysis of ethyl acetate to ethanol and acetic acid is
definitely a reaction, as is conversion of 1,2-dichlorobenzene to 1,3-dichlorobenzene,
or even conversion of cis butene 2 to trans butene 2. In contrast, processes that
merely convey the chemical from one phase to another, or store it in inaccessible
form, are not reactions. Uptake by biota, sorption to suspended material, or even
uptake by enzymes are not reactions. A reaction may subsequently occur in these
locations, but it is not until the chemical structure is actually changed that we
consider reaction to have occurred. In the literature, the word reaction is occasionally,
and wrongly, applied to these processes, especially to sorption.
We have two tasks. The first is to assemble the necessary mathematical framework
for treating reaction rates using rate constants, and the second is to devise
methods of obtaining information on values of these rate constants.
6.3.1 Reaction Rate Expressions
We prefer, when possible, to use a simple first-order kinetic expression for all
reactions. The basic rate equation is
rate N = VCk = Mk mol/h
where V is the volume of the phase (m 3 ), C is the concentration of the chemical
(mol/m 3 ), M is the amount of chemical, and k is the first-order rate constant with
units of reciprocal time. The group VCk thus has units of mol/h.
The classical application of this equation is to radioactive decay, which is usually
expressed in the forms
dM/dt = –kM or dC/dt = –Ck
The use of C instead of M implies that V does not change with time.