Environmental Engineering Reference
In-Depth Information
As mentioned in Chapter 1, processes in natural systems are generally driven by
nonequilibrium conditions. True
chemical equilibrium
in natural environmental sys-
tems is rare considering the complex and transient nature of energy and mass transport
in natural systems. Although only local phenomena can be affected in some cases,
they are coupled with global phenomena; hence any minor disturbance is easily prop-
agated and alters the rate of approach to equilibrium (Pankow and Morgan, 1981). If
the rate of input of a compound equals its rate of dissipation in a system, it is said
to be at
steady state
. For most natural systems this occurs for long periods of time
interrupted by periodic offsets in system inflows and outflows. Such a behavior is
characterized as
quasi-steady-state
. If the concentration of a compound changes con-
tinuously (either decreases or increases) with time due to reactions and/or continuous
changes in inflows and outflows, the system is said to show
unsteady-state
behavior.
The time rate of change of concentrations of metals and organic compounds in natural
systems can be ascertained by applying the appropriate equations for one or the other
of the above-mentioned states in environmental models.
5.1 PROGRESS TOWARD EQUILIBRIUM IN A CHEMICAL
REACTION
A chemical reaction is said to reach equilibrium if there is no perceptible change with
time for reactant and product concentrations. The process can then be characterized
by a unique parameter called the
equilibrium constant (K
eq
)
for the reaction. For a
general reaction represented by the following stoichiometric equation,
+
+
a
A
b
B
x
X
y
Y,
(5.1)
the equilibrium constant is defined by
a
x
X
a
y
Y
a
A
a
B
K
eq
=
,
(5.2)
where
a
denotes activity. In general, a double arrow indicates a reversible reaction at
equilibrium, whereas a single arrow indicates an irreversible reaction proceeding in
the indicated direction. The general stoichiometric relation that describes a chemical
reaction such as given in Equation 5.1 above is
i
ν
i
M
i
=
0,
(5.3)
where
ν
i
is the stoichiometric coefficient of the
i
th species and
M
i
is the molecular
weight of
i
. Note the convention that
ν
i
is positive for products and negative for
reactants. At constant
T
and
P
, the free energy change due to a reaction involving
changes d
n
i
in each species is
i
μ
i
d
n
i
.
d
G
=
(5.4)
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