PROBLEM
The brown gas NO
2
and the colorless gas N
2
O
4
exist in equilibrium, 2 NO
2
N
2
O
4
. In an
experiment, 0.625 mol of N
2
O
4
was introduced into a 5.0 L vessel and was allowed to
decompose until equilibrium was reached. The concentration of N
2
O
4
at equilibrium was
0.0750 M. Calculate K
c
for the reaction.
SOLUTION:
1. Start solving this problem using the ‘ICE’ Table:
2 NO
2
1 N
2
O
4
No. of moles (initially): 0.000 mol 0.625 mol
Changes in moles:
No. of moles (at equilibrium):
Equilibrium Conc. [mol/L]: 0.0750 mol/L
2. The concentration of N
2
O
4
at equilibrium is 0.0750 mol/L. Hence, the number of moles of this
compound is 0.0750 mol/L · 5.0 L = 0.375 mol, and the change in moles of this compound
from initial to equilibrium condition is: 0.375 mol – 0.625 mol = -0.250 mol:
2 NO
2
1 N
2
O
4
No. of moles (initially): 0.000 mol 0.625 mol
Changes in moles: -0.250 mol
No. of moles (at equilibrium): 0.375 mol
Equilibrium Conc. [mol/L]: 0.0750 mol/L
3. As there is twice the number of NO
2
molecules compared with N
2
O
4
, the number of NO
2
molecules must be increasing by: 0.250 mol · 2 = 0.500 mol. Accordingly, the number of NO
2
molecules at equilibrium must be 0.500 mol:
2 NO
2
1 N
2
O
4
No. of moles (initially): 0.000 mol 0.625 mol
Changes in moles: 0.500 mol -0.250 mol
No. of moles (at equilibrium): 0.500 mol 0.375 mol
Equilibrium Conc. [mol/L]: 0.1000 mol/L 0.0750 mol/L
4. Calculate equilibrium constant by using equilibrium concentrations as follows:
7.5
0.01
0.075
0.1
0.075
][NO
]O[N
22
2
42
====
c
K
