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Computing K can be quite easy, or it might take a bit more work. Follow the basic procedure below to compute K:

  1. Write the balanced equation for the reaction
  2. Use the balanced reaction to write the equilibrium constant expression.
  3. Are you given the equilibrium concentrations or pressures for all species in the equilibrium constant expression? If so, simply plug in the numbers: if not, go on.
  4. Use the balanced chemical equation and the initial and equilibrium concentrations of one of the reactants to compute the equilibrium concentrations of all the species in the reaction.
  5. Compute K by plugging in the numbers.

Two examples should demonstrate this more easily:

Example 1: The following reaction has the equilibrium pressures listed. What is K?

CS2(g) + 4H2(g) < - > CH4(g) + 2H2S(g)
PCH4 = 0.131 atm, PH2S = 0.084, PCS2 = 0.428 atm, PH2 = 0.921 atm

Solution 1: First, write the equilibrium constant expression

K = PCH4(PH2S)2/ PCS2(PH2)4
We're given all the equilibrium pressures, so
K = (0.131 atm)(0.084 atm)2/(0.428 atm)(0.921 atm)4 = 0.00300 1/atm2

Example 2: The deadly gas phosgene is formed from CO and CL2 according to the reaction

CO(g) + Cl2(g) < - > COCl2(g)
The initial pressures of of the gases are PCO = 0.60 atm, PCl2 = 1.10 atm and PCOCl2 = 0 atm. If the final pressure of COCl2 is 0.10 atm at 600oC, what is K?

Solution 2: First, we write the equilibrium constant expression

K = PCOCl2/PCOPCl2
However, unlike the above example we do not have all of the equilibrium concentrations. We can figure these out from stoichiometry, since each molecule of COCl2 requires one molecule of CO and one of Cl2. The partial pressure of a gas is proportional to the number of moles of that gas, so we can treat the change in pressure as the same as a change in the number of moles. The table below summarizes the data

CO Cl2 COCl2
Initial partial pressure (atm) 0.60 1.10 0.0
Change in partial pressure (atm) -0.10 -0.10 +0.10
Equilibrium partial pressure (atm) 0.50 1.00 0.10

Now we have all the partial pressures, and we can compute K
K = PCOCl2/PCOPCl2 = (0.10 atm)/(0.50 atm)(1.00 atm) = 0.20 1/atm


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