8.2. Chemical reactions[[Student version, January 17, 2003]] 269
Disturbing the peace Another famous result is now easy to understand: Suppose we begin
with concentrationsnotobeying Equation 8.16. Perhaps we took an equilibrium and dumped in a
little more X 1 .Then the chemical reaction will run forward, or in other words in the direction that
partially undoesthe change we made, in order to reestablish Equation 8.16, and so increase the
world’s entropy. Chemists call this form of the Second LawSecond Law!as Le Chˆatelier’s Principle
Le Chˆatelier’s Principle.
Wehave arrived at the promised extension of the matching rule (Equation 8.2) for systems of
interconverting molecules. When several species are present in a system at equilibrium, once again
each one’s chemical potential must be constant throughout the system. But we found that the
possibility of interconversions imposes additional conditions for equilibrium:
When one or more chemical reactions can occur at rates fast enough to equi-
librate on the time scale of the experiment, equilibrium also implies relations
betweenthe variousμα,namely one Mass Action rule (Equation 8.16) for each
relevant reaction.(8.17)
Remarks The discussion of this subsection has glossed over an important difference between
thermal equilibrium and ordinary mechanical equilibrium. Suppose we gently place a piano onto a
heavy spring. The piano moves downward, compressing the spring, which stores elastic potential
energy. At some point the gravitational force on the piano equals the elastic force from the spring,
and theneverything stops. But in statistical equilibrium nothing ever stops. Water continues to
permeate the membrane of our osmotic machine at equilibrium; isomer #1 continues to convert
to #2 and vice versa. Statistical equilibrium just means there’s nonetflow of any macroscopic
quantity. We already saw this in the discussion of buffalo equilibrium, Section 6.6.2 on page 194.
Weare partway to understanding the Focus Question for this chapter. The caveat about reaction
rates in Idea 8.17 reminds us that, for example, a mixture of hydrogen and oxygen at room tem-
perature can stay out of equilibrium essentially forever; the activation barrier to the spontaneous
oxidation of hydrogen is so great that we instead get an apparent equilibrium, where Equation 8.11
doesnothold. The deviation from complete equilibrium representsstored free energy,waiting to
beharnessed to do our bidding. Thus hydrogen can be burned to fuel a car, and so on.
T 2 Section 8.2.2′on page 294 mentions some finer points about free-energy changes and the Mass
Action rule.
8.2.3 Kinetic interpretation of complex equilibria
More complicated reactions have more complex kinetics, but the interpretation of equilibrium is
the same. There can be some surprises along the way to this conclusion, however. Consider a
hypothetical reaction, in which two diatomic molecules X 2 and Y 2 join and recombine to make two
XY molecules: X 2 +Y 2 →2XY. It all seems straightforward at first. The rate at which any given
X 2 molecule finds and bumps into a Y 2 molecule should be proportional to Y 2 ’s number density,
cY 2 .The rate of all such collisions is then this quantity times the total number of X 2 molecules,
which in turn is a constant (the volume) timescX 2.
It seems reasonable that at low concentrations a certain fixed fraction of those collisions would
overcome an activation barrier. Thus we might conclude that the rater+of the forward reaction
(reactions per time) should also be proportional tocX 2 cY 2 ,and likewise for the reverse reaction:
r+=?k+cX 2 cY 2 and r-=?k-(cXY)^2. (8.18)