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The procedure for finding the equilibrium concentrations of the species in a
reaction is somewhat similar to that of finding the
value of K from experimental data.
- Write the balanced equation for the reaction
- Use the balanced reaction to write the equilibrium
constant expression.
- Express the equilibrium pressures or concentrations in terms of a single
variable (x). You can do this by looking at the balanced equation for the
reaction.
- Substitute all the above concentrations/pressures back into the
equilibrium constant expression. This will give you an expression in terms of
x.
- Solve for x
- Use x to find the concentrations/pressures of the various species.
An example makes this easier to see.
Example The following reaction has a K value of 0.64 at
900oC. If the initial partial pressures are
PCO2 = 1.00 atm, PH2 = 1.00 atm,
PCO = 0.00 atm and PH2O = 0.00 atm, what are
the equilibrium partial pressures of all of the species?
- CO2(g) + H2(g) < = > CO(g) +
H2O(g)
Solution First, write the equilibrium constant expression
- K = PCOPH2O/
PCO2PH2
We are given only
the initial pressures. However, we can express the equilibrium pressures in
terms of the initial pressures. For every mole of CO2 and
H2 used up, one mole of CO and one mole of H2O are formed.
Since the partial pressures of the gases are proportional to the number of moles
of that gas, we can use the pressures in place of the number of moles. If we
denote the pressure of CO and H2O formed as x, then the pressures of
H2 and CO2 decrease by x.
|
CO2 |
H2 |
CO |
H2O |
| Initial partial pressure (atm) |
1.00 |
1.00 |
0.0 |
0.0 |
| Change in partial pressure (atm) |
-x |
-x |
+x |
+x |
| Equilibrium partial pressure (atm) |
1.00-x |
1.00-x |
x |
x | Now, substitute the expressions above back
into the equilibrium constant expression
- 0.64 = (x)(x)/(1.00-x)(1.00-x)
The above expression is a perfect
square. To make life easy, take the sqaure root of both sides
- 0.80 = x/(1.00-x)
- x = 0.44
Now that we have x, we can expression the
equilibrium partial pressures just by substituting back in:
- PCO2 = 1.00-x = 0.56 atm
- PH2 = 1.00-x = 0.56 atm
- PCO = x = 0.44 atm
- PH2O = x = 0.44 atm
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