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

containing nonequilibrium quantities of benzene to flow into and out of the tank at
constant rates as shown in Figure 2.1B. But equilibrium and a steady-state condition
are maintained, since the concentrations in the tank and in the outflows are at a
ratio of 1:4. It is possible for near equilibrium to apply in the vessel, even when
the inflow concentrations are not in equilibrium, if benzene transfer between air
and water is very rapid. Figure 2.1B thus illustrates a flow, equilibrium, and steadystate
conditions, whereas Figure 2.1A is a nonflow, equilibrium, and steady-state
situation.
In Figure 2.1C, there is a deficiency of benzene in the inflow water (or excess
in the air) and, although in the time available some benzene transfers from air to
water, there is insufficient time for equilibrium to be reached. Steady state applies,
because all concentrations are constant with time. This is a flow, nonequilibrium,
steady-state condition in which the continuous flow causes a constant displacement
from equilibrium.
In Figure 2.1D, the inflow water and/or air concentration or rates change with
time, but there is sufficient time for the air and water to reach equilibrium in the
vessel, thus equilibrium applies (the concentration ratio is always 4), but unsteadystate
conditions prevail. Similar behavior could occur if the tank temperature changes
with time. This represents a flow, equilibrium, and unsteady-state condition.
Finally, in Figure 2.1E, the concentrations change with time, and they are not
in equilibrium; thus, a flow, nonequilibrium, unsteady-state condition applies, which
is obviously quite complex.
The important point is that equilibrium and steady state are not synonymous;
neither, either, or both can apply. Equilibrium implies that phases have concentrations
(or temperatures or pressures) such that they experience no tendency for net transfer
of mass. Steady state merely implies constancy with time. In the real environment,
we observe a complex assembly of phases in which some are (approximately) in
steady state, others in equilibrium, and still others in both steady state and equilibrium.
By carefully determining which applies, we can greatly simplify the mathematics
used to describe chemical fate in the environment.
A couple of complications are worthy of note. Chemical reactions also tend to
proceed to equilibrium but may be prevented from doing so by kinetic or activation
considerations. An unlit candle seems to be in equilibrium with air, but in reality it
is in a metastable equilibrium state. If lit, it proceeds toward a “burned” state. Thus,
some reaction equilibria are not achieved easily, or not at all.
Second, “steady state” depends on the time frame of interest. Blood circulation
in a sleeping child is nearly in steady state; the flow rates are fairly constant, and
no change is discernible over several hours. But, over a period of years, the child
grows, and the circulation rate changes; thus, it is not a true steady state when
viewed in the long term. The child is in a “pseudo” or “short-term” steady state.
In many cases, it is useful to assume steady state to apply for short periods,
knowing that it is not valid over long periods. Mathematically, a differential
equation that truly describes the system is approximated by an algebraic equation
by setting the differential or the d(contents)/dt term to zero. This can be justified
by examining the relative magnitude of the input, output, and inventory change
terms.
©2001 CRC Press LLC