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
K_{c} or K_{p} 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

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.
Example: Calculate the value of the equilibrium constant, K_{c}
, for the system shown, if
0.1908 moles of CO_{2}, 0.0908 moles of H_{2}, 0.0092 moles
of CO, and 0.0092 moles of H_{2}O vapor were present in a 2.00 L reaction vessel were
present at equilibrium.

Since K_{c} 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.
[CO_{2}] = 0.1908 mol CO_{2}/2.00
L = 0.0954 M
[H_{2}] = 0.0454 M
[CO] = 0.0046 M
[H_{2}O] = 0.0046 M

Substitute each concentration into the equilibrium
expression and calculate the value of the equilibrium constant.
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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
Example: Initially, a mixture
of 0.100 M NO, 0.050 M H_{2}, 0.100 M H_{2}
O was allowed to reach equilibrium (initially
there was no N_{2} ). At equilibrium the concentration of
NO was found to be 0.062 M. Determine the value of the equilibrium
constant, K_{c} , for the reaction:

Check to see if the amounts are expressed in moles
per liter (molarity) since K_{c}
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.

NO

H_{2}

N_{2}

H_{2}O

Initial Concentration (M) 
0.100

0.0500

0

0.100

Change in Concentration (M) 
 2 x 
 2 x 
+ x 
+ 2 x 
Equilibrium Concentration (M) 
0.062




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.

NO

H_{2}

N_{2}

H_{2}O

Initial Concentration (M) 
0.100

0.0500

0

0.100

Change in Concentration (M) 
 0.038

 0.038

+ 0.019

+ 0.038

Equilibrium Concentration (M) 
0.062

0.012

0.019

0.138


Substitute the equilibrium concentrations into the equilibrium expression
and solve for K_{c}.
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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.
Example: A flask is charged with 3.00 atm of dinitrogen tetroxide
gas and 2.00 atm of nitrogen dioxide gas at 25^{o}C and allowed
to reach equilibrium. It was found that the pressure of the nitrogen
dioxide decreased by 0.952 atm. Estimate the value of K_{p}
for this system:

Check to see that the given amounts are measured in
appropriate pressure units since K_{p} 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.

N_{2}O_{4}

NO_{2}

Initial Pressure (atm) 
3.00

2.00

Change in Pressure (atm) 
+ 0.476

 0.952

Equilibrium Pressure (atm) 
3.476

1.048


Substitute the equilibrium pressures into the expression for K_{p}
and solve for K_{p}.
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