Calculating Equilibrium Constants
We need to know two things in order to calculate the numeric value of the equilibrium constant:
- the balanced equation for the reaction system, including the physical states of each species. From this the equilibrium expression for calculating Kc or Kp is derived.
- the equilibrium concentrations or pressures of each species that occurs in the equilibrium expression, or enough information to determine them. These values are substitued into the equilibrium expression and the value of the equilibrium constant is then calculated.
- Calculating K from Known Equilibrium Amounts
- Calculating K from Initial amounts and One Known Equilibrium Amount
- Calculating K from Known Initial Amounts and the Known Change in Amount of One of the Species
- Write the equilibrium expression for the reaction.
- Determine the molar concentrations or partial pressures of each species involved.
- Subsititute into the equilibrium expression and solve for K.
- Write the equlibrium expression for the reaction system.
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Since Kc is being determined, check to see if the given equilibrium
amounts are expressed in moles per liter (molarity).
In this example they are not; conversion of each is requried.
[CO2] = 0.1908 mol CO2/2.00 L = 0.0954 M
[H2] = 0.0454 M
[CO] = 0.0046 M
[H2O] = 0.0046 M - Substitute each concentration into the equilibrium expression and calculate the value of the equilibrium constant.
Calculating K from Initial Amounts and One Known Equilibrium Amount
- Write the equilibrium expression for the reaction.
- Determine the molar concentrations or partial pressures of each species involved.
- Determine all equilibrium concentrations or partial pressures using an ICE chart.
- Substitute into the equilibrium expression and solve for K
- Write the equilibrium expression for the reaction.
- Check to see if the amounts are expressed in moles per liter (molarity) since Kc is being . In this example they are.
- Create an ICE chart that expresses the initial concentration, the change in concentration, and the equilibrium concentration for each species in the reaction. From the chart you can determine the changes in the concentrations of each species and the equilibrium concentrations. From the example, we start with the folowing information.
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| Initial Concentration (M) |
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| Change in Concentration (M) |
- 2 x |
- 2 x |
+ x |
+ 2 x |
| Equilibrium Concentration (M) |
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The change in concentration of the NO was (0.062 M -
0.100M) = - 0.038 M. Thus -2
x = - 0.038 and x =
0.019. Note: the negative sign indicates a decreasing concentration,
not a negative concentration. The changes in the other species must
agree with the stoichiometry dictated by the balance equation. The
hydrogen will also change by - 0.038 M, while the nitrogen will increase
by + 0.019 M and the water will increase by + 0.038 M. From these
changes we can complete the chart to find the equilibrium concentrations
for each species.
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| Initial Concentration (M) |
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| Change in Concentration (M) |
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| Equilibrium Concentration (M) |
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- Substitute the equilibrium concentrations into the equilibrium expression and solve for Kc.
Calculating K from Known Initial Amounts and the Known Change in Amount of One of the Species
- Write the equilibrium expression for the reaction.
- Determine the molar concentrations or partial pressures of each species involved.
- Determine all equilibrium concentrations or partial pressures using an ICE chart.
- Substitute into the equilibrium expression and solve for K.
- Write the equilibrium expression to find Kp.
- Check to see that the given amounts are measured in appropriate pressure units since Kp is to be . In this example they are (atmospheres).
- Create an ICE chart and calculate the changes in pressure and equilibrium pressures for each species.
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| Initial Pressure (atm) |
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| Change in Pressure (atm) |
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| Equilibrium Pressure (atm) |
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- Substitute the equilibrium pressures into the expression for Kp and solve for Kp.
