c07 JWBS043-Rogers September 13, 2010 11:25 Printer Name: Yet to Come
VARIATION OF THE EQUILIBRIUM CONSTANT WITH TEMPERATURE 97Notice that this implies a hyperspace inU,V,T,andξi. Energy has been selected
here to illustrate the principle that analogous equations exist for the other state
variables—for example,G,H, andS.7.4 FUGACITY AND ACTIVITY
For nonideal systems the concentration variable is replaced by a new variable that
expresses theeffectiveconcentration of the species in a mixture. For example, a solute
may be more chemically active in methanol solution than it is in water. Or it may be
more active in water solution than in methanol. A pure gas may behave in a nonideal
way, and its degree of nonideality may be influenced by other gases in a mixture.
These deviations from ideal behavior are expressed by acoefficientγwhich yields
theactivityof a solute orfugacityof a gas when multiplied into the concentration
variable, for example,aA=γA[A] or fA=γApAThe activity and fugacity coefficients are simply numbers telling us whether the
behavior of the species is greater or less than it would be in the standard state. They
are concentration- or pressure-dependent and are usually determined for real systems
by rather painstaking empirical methods.7.5 VARIATION OF THE EQUILIBRIUM CONSTANT
WITH TEMPERATURE
Combining the Gibbs–Helmholtz equation for the temperature variation of free energy
with the equation connecting the free energy in the standard state to the equilibrium
constant gives⎡
⎢
⎢
⎣∂
(
G◦
T
)
∂
(
1
T
)
⎤
⎥
⎥
⎦
p=
⎡
⎢
⎢
⎣
∂
(
−RTlnKeq
T)
∂
(
1
T
)
⎤
⎥
⎥
⎦
p=−
⎡
⎢
⎢
⎣
∂
(
RlnKeq)
∂
(
1
T
)
⎤
⎥
⎥
⎦
pbut⎡
⎢
⎢
⎣∂
(
G◦
T
)
∂
(
1
T
)
⎤
⎥
⎥
⎦
p