The concentrations of all species in Equation 2.68 are typically expressed
in mol/L for three-dimensional condensed-phase systems. Equilibrium
constants for gas-phase systems can be expressed in terms of partial
pressures; the corresponding equilibrium constant, K p , for the reaction
occurring in Equation 2.68 is
K p =
P
c
C P
d
D
P
a
A P
b
B
(2.69)
Treating each gaseous species as an ideal gas, the molar concentration
can be related to the partial pressure (Equation 2.70):
P =
n
V
RT = CRT
(2.70)
Substituting Equation 2.70 into Equation 2.69 and simplifying yields
K p =
C
c
C
ð Þ C
d
D
À Á
C
a
A
ð Þ C
b
B
À Á RT
ð Þ
c+d
ð
Þ− a+b
ð
Þ
(2.71)
which provides the relationship between K and K p (Equation 2.72):
K p = K RT
ð Þ
Δn
(2.72)
When expressing concentrations and partial pressures in equilibrium
constants, we often divide the values by some reference value. For
instance, the partial pressure of component i is referenced to a pressure of
1 atm. Likewise, the concentration of component i is always divided by
1 mol/L. These quantities are known as activities (a i ), and being unitless,
ensure that K and K p are unitless (Equation 2.73):
K =
a
c
C a
d
D
a
a
A a
b
B
(2.73)
2.6.2 Heterogeneous equilibria
A heterogeneous system, where more than one phase is involved in the
reaction, is of particular importance to nanosystems. For example, solid
phase nanoparticles are often synthesized in a liquid phase solvent
system. A simple case of a heterogeneous equilibrium system is the
vaporization of liquid water to gaseous water at its boiling point.
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