Page 141 - Essentials of physical chemistry

6 Gibbs’ Free Energy

and Equilibria

INTRODUCTION
In previous chapters, we have stressed that in nature energy tends to decrease while entropy tends to
increase. A naive first consideration of any machine or process is that energy is needed to continue
operation and we often overlook energy expended on various repair activities that are a form of
entropy management. It becomes more obvious that entropy is a factor when one studies chemical
processes that ‘‘should’’ occur based on energy considerations but nevertheless require some sort of
a catalyst or other special conditions, which imply geometric constraints that overcome the natural
tendency of randomness to increase. The value of DS is a change in a state variable but the path can
be modified by special conditions such as the introduction of a catalytic surface, which allows
reactants to meet side-by-side compared to random collisions in the gas phase. Josiah Willard Gibbs
(1839–1903) was a foremost U.S. scientist (Figure 6.1) who made important advances in thermo-
dynamics applying the new idea of ‘‘chemical potential’’ (DG=n) as a free energy per mole of a
substance in phase diagrams and applied to equilibria. At the time of his work, few people
understood it but it was later developed into the idea of free energy and greatly affected thinking,
teaching, and problem solving in chemical engineering. Gibbs’ research used what was advanced
mathematics in his time but remained at what we call ‘‘classical physics’’ today since he predated
quantum mechanics. Gibbs is especially noteworthy in that he carried out research in the United
States at a time when the turmoil of the U.S. Civil War and settling in the West were not as
conducive to research as was the case in Europe in the late 1800s. However, Gibbs had spent a year
each in Paris, Berlin, and Heidelberg and had written contact with foremost scientists in Europe.
Gibbs also held the very first PhD in chemical engineering in the United States, awarded in 1863
from Yale University. Other scientists including Albert Einstein regarded Gibbs as a foremost
founder of thermodynamics and a true genius. It is indeed humbling to realize that such pure thought
by Gibbs, Boltzmann, and others was carried out for the first time without the same sort of support
we have now in ‘‘the information age,’’ although scientists did study each other’s work. Truly we
stand on the shoulders of intellectual giants!
For our list of essential topics, we will focus on the main result from Gibbs:

DG ¼ DH TDS

Large lists of G 0 are available [1] as assembled from H 0 and S 0 values, so that one can calculate
298 298 298
values for chemical reactions as DG 0 (298) using balanced reactions and thermodynamic tables.
rxn
The main usefulness of this process is that one can obtain an equilibrium constant for gas reactions
and the concepts for gases can be extended to other phase concentrations. Following Gibbs, we
define a concept called the ‘‘chemical potential.’’ From the HUGA equations, we have

dG
¼ SdT þ Vdp
n
dG ¼ SdT þ VdP and we specify a new symbol (mu, m)as dm ¼
where we specify the equation is for 1 mol and the bar over the entropy and volume indicate values
per mole. We look ahead to consideration of an equilibrium at a specific temperature, so when T is

dG RT
dP ¼ RTd ln P and we can calculate
constant we have dm ¼ ¼ SdT þ Vdp ¼ 0 þ
n P
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