Page 153 - Essentials of physical chemistry

Gibbs’ Free Energy and Equilibria 115

Then we note that the chemical potential of each component is equal within each phase P by virtue
of the implicit equilibrium of the C components, so there is also one less degree of freedom relating
the chemical potentials within each phase for a reduction of C(P 1) degrees of freedom.

b
a
g
d
m ¼ m ¼ m ¼ m ¼ ¼ m P
1 1 1 1 1
b
g
d
a
m ¼ m ¼ m ¼ m ¼ ¼ m P 2
2
2
2
2
______________________
g
b
d
a
m ¼ m ¼ m ¼ m ¼ ¼ m P C
C
C
C
C
Thus, we can calculate the total number of degrees of freedom in the system as
F ¼ (PC) þ 2 P C(P 1) ¼ C P þ 2:
One laboratory experiment that illustrates the Gibbs phase rule is the equilibrium between SO 2 and
aniline.
SO 2(gas) þ C 6 H 5 NH 2(liquid) ƒ C 6 H 5 NH 2 : SO 2(solid)
ƒ!
The SO 2 is a noxious gas injurious to mucous membranes, aniline is a slightly tan organic liquid and
the complex is a bright orange solid. Thus, P ¼ 3 and C ¼ 2so F ¼ 2 3 þ 2 ¼ 1. The author has done
this experiment many times. The reaction flask must be tightly sealed because of the noxious SO 2 gas.
In preparing the equilibrium, one bubbles the SO 2 gas into about 100 mL of aniline from a small
lecture bottle and the orange solid will begin to appear. This must be done in a closed hood. When all
three phases are apparent in the reaction flask it is sealed with a fitting for a hose connected to a
barometer and the flask is placed into a heating mantle. The equilibrium reaction flask needs to also
have a thermometer fitting so that the temperature can be measured. Then there is only one degree of
freedom and if the heating mantle determines the temperature of the equilibrium it is only necessary to
record the pressure of the system as the remaining degree of freedom to characterize the equilibrium.
This experiment also illustrates another convention relating to the ‘‘activity’’ of pure substances. In the
case of a solid or a pure liquid, we use the concept of ‘‘unit activity’’ for a pure substance since one can
ponder over the question as to what is the ‘‘concentration’’ of a pure liquid or solid? It is not in
solution, so no matter how much of a pure solid or liquid is there its concentration is ‘‘one.’’ On the
other hand the pressure of the gas phase can be measured in moles=liter to relate it to a concentration.
Once the orange complex is formed, it is more convenient to write the equilibrium as the
dissociation of the complex.
P SO 2 ½ 1 C 6 H 5 NH 2 Š
:
ƒ!
¼ P SO 2
C 6 H 5 NH 2 : SO 2 ƒ C 6 H 5 NH 2 þ SO 2 , so K P ¼
1 C 6 H 5 NH 2 :SO 2
½ Š

1
0
Since DG versus should
rxn ¼ RT ln K P ¼ RT ln P SO 2 , a plot of the natural log of P SO 2
T(K)
DG 0 rxn
be linear with a slope of . This is a real, but tricky, experiment due to the noxious SO 2 and
R
poses the added problem of disposal of the contents of the reaction flask.
IODINE TRIPLE POINT
One of the oldest forensic techniques is fingerprint analysis. This technique is based on the fact that
relatively clean fingertips exude small amounts of fatty acids and other slight secretions from the skin
of the fingers. In the case of fresh, sweaty fingerprints on a clean surface, it is sufficient to apply carbon
black with a soft brush and then pick up the image of the fingerprint using transparent tape on the