Page 165 - Modern physical chemistry

7.13 Equilibria in Ideal Gaseous Phases 157

Z 13 Equilibria in Ideal Gaseous Phases

When a reacting gaseous solution is at a low enough pressure at the given tempera-
ture so that it is approximately ideal, the partial pressures represent the activities and
the equilibrium
aA + bB ~ lL + mM [7.60]
is governed by the constant
P~P:; =Kp. [7.61 ]
PtP~
This is related to the standard Gibbs energy change by

6.Go
InKp =---. [7.62]
RT
In the ideal gaseous solution, the pressure exerted by the ith constituent is

n·
Pi = _t RT = ciRT, [7.63]
V
where cj is the concentration of constituent i. Substituting (7.63) into (7.61) gives

Kp = cLcl:{ (RT)I+m-a-b = Kc(RT)~n. [7.64]
c~c~
Here dn is the change in moles in the reaction while the concentration equilibrium
constant is
1m
CLCM -K [7.65]
-
c
c~c~
In a common problem, one starts with a given amount of each reactant and product
in a given volume at a given temperature and lets the reaction proceed to equilibrium.
From the final conditions, one can calculate the equilibrium constant. Or alternatively,
from the equilibrium constant one can calculate the final conditions. The expressions
needed depend on the form of the reaction.
As a first example, consider the water gas equilibrium

[7.66]
In a container of volume V, a moles H2 0, b moles CO, C moles CO2 , and d moles H2 are
mixed. On going to equilibrium, x moles H2 0 react with x moles CO. One may organize
the pertinent expressions as in table 7.A.

TABLE 7A

Moles Equilibrium Equilibrium
Constituent at Start Moles Concentration
H2 O a a-x (a-x)/V
CO b b-x (b -x)N
c c+x (c+x)N
CO2
H2 d d+x (d +x)/V