d.Because money is moving in and out of the account, even though the av-
erage monthly balance maintains the equilibrium amount of $1000, it is a
dynamic equilibrium.Why does any system come to equilibrium? Consider the rock on the side
of the mountain in Figure 5.1a. From physics, we know that gravity is at-
tracting the rock, and the slope of the mountain is not sufficient to counter
that attraction and keep the rock from moving. So the rock tumbles down
the side of the mountain until it gets to the bottom (Figure 5.1b). At this po-
sition, the ground counteracts the force of gravity, and the situation becomes
a stable, static equilibrium. One way of considering this system is from the
perspective of energy: a rock on the side of the hill has excess gravitational
potential energy that it can get rid of by moving down the side of the hill.
That is, the rock will spontaneously move to a position that decreases its
(gravitational potential) energy. From a physical standpoint, the minimum-
energy equilibrium is described in terms of Newton’s first law of motion.
There are balanced forces acting on the rock, so it remains at rest: at equi-
librium.
What about chemical reactions? Why do chemical systems eventually reach
equilibrium? The answer is analogous to that for the rock: there are balanced
“forces” acting on the chemical species in the system. These forces are actually
energies—chemical potentials of the different chemical species involved in the
system at equilibrium. The next section introduces chemical equilibrium in
those terms.
5.3 Chemical Equilibrium
For a chemical reaction occurring in a closed system, species that have some
initial chemical identity (“reactants”) change to some different chemical iden-
tity (“products”). In the previous chapter, we made the point that the Gibbs
free energy is dependent on the amount of any substance, and defined the
chemical potential as the change in the Gibbs free energy with respect to
amount:
i
nG
i
T,p,nj(ji)Since Gvaries with each ni, it should be no surprise that during the course of
a chemical process,the total Gibbs free energy of the entire system changes.
We now define the extent as a measure of the progress of a reaction. If the
number of moles of the ith chemical species in the system at time t0 is ni,0,
the extent is given by the expression
ni(^) i
ni,0
(5.1)
where niis the number of moles at some time tand (^) iis the stoichiometric
coefficient of the ith chemical species in the reaction. (Remember that (^) iis
positive for products and negative for reactants.) The possible numerical
values of may vary depending on the initial conditions and the reaction
stoichiometry, but at any point in a reaction will have the same value no
matter which species is used in equation 5.1.
5.3 Chemical Equilibrium 121