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that holds in the limit of infinite dilution (namely, m m° RT ln x ) holds for all Section 10.2
i i i
values of x , and we take the limit as x → 1 (Fig. 9.20). This gives a fictitious standard Excess Functions
i i
state with g 1, x 1, and m m°. This fictitious state corresponds to pure solute
II,i i i i
i in which each i molecule experiences the same intermolecular forces it experiences
in an ideally dilute solution in the solvent A.
The Convention II solute standard state is the same as that used for solutes in an
ideally dilute solution (Sec. 9.8 and Fig. 9.20), so the Convention II standard-state
thermodynamic properties are the same as for solutes in an ideally dilute solution. (See
Prob. 10.4.)
The Convention II solute and solvent standard states are the same as those used
for ideally dilute solutions. Therefore (by the same reasoning used earlier for
Convention I and ideal solutions), in an ideally dilute solution, g 1 and g 1.
II,A II,i
The deviations of g and g from 1 measure the deviations of the solution’s behav-
II,A II,i
ior from ideally dilute behavior.
The concepts of activity and activity coefficient were introduced by the American chemist
G. N. Lewis. (Recall Lewis dot structures, the Lewis octet rule, Lewis acids and bases.)
Lewis spent the early part of his career at Harvard and M.I.T. In 1912, he became head of
the chemistry department at the University of California at Berkeley. In 1916 he proposed
that a chemical bond consists of a shared pair of electrons, a novel idea at the time. He
measured G° for many compounds and cataloged the available free-energy data, draw-
f
ing the attention of chemists to the usefulness of such data. The concept of partial molar
quantities is due to Lewis. His 1923 book Thermodynamics (written with Merle Randall)
made thermodynamics accessible to chemists. Lewis was resentful that his early specula-
tive ideas on chemical bonding and the nature of light were not appreciated by Harvard
chemists, and in 1929 he refused an honorary degree from Harvard. His later years were
spent working on relativity and photochemistry.

Summary
The chemical potential of solution component i is expressed in terms of the activity a
i
and the activity coefficient g , where a and g are defined so that m m° RT ln a ,
i i i i i i
where a g x . Convention I chooses the standard state of each solution component
i i i
as the pure substance at the T and P of the solution; Convention I activity coefficients
measure deviations from ideal-solution behavior. Convention II uses the same stan-
dard states as for an ideally dilute solution, and deviations of Convention II activity
coefficients from 1 measure deviations from ideally dilute behavior. Whereas each g
I,i
goes to 1 as x goes to 1, Convention II activity coefficients all go to 1 as the solvent
i
mole fraction x → 1.
A
10.2 EXCESS FUNCTIONS

The thermodynamic properties of a solution of two liquids are often expressed in terms
E
of excess functions. The excess Gibbs energy G of a mixture of liquids is defined as
the difference between the actual Gibbs energy G of the solution and the Gibbs energy
id
G of a hypothetical ideal solution with the same T, P, and composition as the actual
E
id
solution: G G G . Similar definitions hold for other excess properties:
id
id
E
E
E
E
id
G G G , H H H , S S S , V V V id (10.11)
id
E
E
id
id
E
Subtraction of G H TS from G H TS gives G H TS .
We have G n m n (m* RT ln g x ) [Eqs. (9.23), (10.6), and (10.7)]
i i i i i i I,i i
id
and (since g 1 in an ideal solution) G n (m* RT ln x ). Subtraction gives
I,i i i i i
E
id
G G G RT a n ln g I,i (10.12)
i
i