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Equilibrium expressions have a useful rule:
If you can express a reaction
as the sum of two or more separate reactions, the equilibrium constant
expression for the reaction is the product of the equilibrium expressions of
each of the other reactions.
An example makes this clear: Consider the following two reactions
- 2BrCl(g) < - > Cl2(g) + Br2(g)
KP,1 =
PCl2PBr2/PBrCl2
-
- Br2(g) +I2(g) < - > 2IBr(g)
KP,2 =
PIBr2/PBr2PI2
If you sum these two reactions, the bromine cancels out, leaving the
reaction
- 2BrCl(g) + I2(g) < - > 2IBr(g) + Cl2(g)
KP, 3 =
PIBr2PCl2/PBrCl2PI2
By inspection, it should be obvious (Or it would be, if HTML allowed
better equation formatting.) that
- KP, 3 =
PIBr2PCl2/PBrCl2PI2
=
(PCl2PBr2/PBrCl2)
*
(PIBr2/PBr2PI2)
= KP, 1*KP, 2
Example: The following two reactions have the equilibrium constants
listed.
- SO2(g) + 1/2O2(g) < - > SO3(g)
K = 2.2
- NO2(g) < - > NO(g) + 1/2O2(g)
K = 4.0
What is the equilibrium constant for
the reaction
- SO2(g) + NO2(g) < - > SO3(g) +
NO(g)
Solution: The third reaction is just the sum of the first two: when we
sum the reactions, the oxygen cancels out leaving reaction 3. The equilibrium
constant for this reaction is thus the product of the two equilibrium constants
for the first two reactions.
- K3 = K1*K2 = 2.2 * 4.0 =
8.0
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