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Chapter 11 TABLE 11.1
Reaction Equilibrium
in Nonideal Systems
Summary of Standard States and Chemical Potentials a

Substance Standard state M M° RT ln a
i i i
Gas (pure or in Pure ideal gas at m m°(T ) RT ln ( f /P°)
i i i
gas mixture) 1 bar and T P

Pure liquid or Pure substance at m i m° i 1T2 V m,i dP¿
pure solid 1 bar and T P°
Solution component, Pure i at T and m m*(T, P) RT ln (g x )
i i I,i i
Convention I P of solution
Solvent A Pure A at T and m m*(T, P) RT ln (g x )
A A A A
P of solution
Nonelectrolyte solute:
Convention II Fictitious state with m m° (T, P) RT ln (g x )
i II,i II,i i
x 1 g
i II,i
molality scale Fictitious state with m m° (T, P) RT ln (g m /m°)
i m,i m,i i
m /m° 1 g
i m,i
concentration scale Fictitious state with
c /c° 1 g m m° (T, P) RT ln (g c /c°)
i c,i i c,i c,i i
Electrolyte solute:
molality scale Fictitious state with m m°(T, P) RT ln (n g m /m°) n
i i i
g 1 n m /m°
i
a Limiting behaviors: f → 1 as P → 0, where f f x P; g → 1 as x → 1; g 1; g q 1; g q
q
i
I,i
i i
i
i
i
A
m,i
II,i
q
1; g 1; g 1.
q
c,i

the actual change in the reaction mixture but to a hypothetical change from stan-
dard states of the separated reactants to standard states of the separated products.
2. ( G/ j) . Equation (4.99) reads dG/dj n m at constant T and P, where j is
i
T,P
i
i
the extent of reaction, the m ’s are the actual chemical potentials in the reaction mix-
i
ture at some particular value of j, and dG is the infinitesimal change in Gibbs energy
of the reaction mixture due to a change in the extent of reaction from j to j dj:
0G
a b a n m i (11.34)
i
0j T,P i
The sum on the right side of (11.34) is frequently denoted by G or G, but this
r
notation is misleading in that n m is not the change in G of the system as the
i
i
i
reaction occurs but is the instantaneous rate of change in G with respect to j. If
the reaction mixture were of infinite mass, so that a finite change in j would not
change the m ’s in the mixture, then n m 1 mol would be G for a change
i
i
i
i
j 1 mol. Note that ( G/ j) T,P is the slope of the G-versus-j curve (Fig. 4.7).
3. G. From Eq. (9.23), the Gibbs energy G of a homogeneous reaction mixture at
a given instant is equal to n m , where n (not to be confused with the stoichio-
i
i
i
i
metric coefficient n ) is the number of moles of i in the mixture and m is its
i
i
chemical potential in the mixture. If at times t and t these quantities are n , m i,1
i,1
1
2
and n , m , respectively, then the actual change G in the Gibbs energy of the
i,2
i,2
reacting system from time t to time t is G n m n m .
i,1 i,1
i
1
i
2
i,2 i,2
The quantities G° and ( G/ j) are related. Substitution of m m° RT ln a
T,P i i i
[Eq. (11.2)] into (11.34) gives
0G
a b a n m° RT a n ln a i
i
i
i
0j T,P i i