Determining Equilibrium Quantities
from Initial Quantities and
K
To find the equilibrium quantities of each species from the initial
quantities we must know:

the balanced equation for the reaction

the equilibrium expression for the reaction

the value for the equilibrium constant

the initial quantities of each species, either as molarities, or partial
pressures

the direction the reaction will proceed in order to establish equilibrium
Once these have been determined, we can solve for the equilibrium concentrations
using the following steps:

Write the equilibrium expression
for the reaction.

Check to see that the quantities are expressed in the same units as used
in the equilibrium constant.

Determine the direction the reaction will shift. Calculate
Q if direction of shift is uncertain.

Make an ICE chart and determine the equilibrium
quantities in terms of a single unknown change.

Substitute into the equilibrium expression and
solve for the change.

Calculate the equilibrium quantity for each species from the initial quantity
and the change.

Check your work.
Determining
Equilibrium Concentrations
Example: 0.050 mol of H_{2} and 0.050 mol
of Br_{2} are placed in an evacuated 5.0 L flask and heated to
700 K. What is the concentration of each species in the flask when
equilibrium has been established? The equation for the reaction is
as follows:
H_{2}(g) + Br_{2}(g)
2 HBr(g) K_{c}
= 64 @ 700 K

Since K_{c} is used in this problem, check to see if the given
quantities are in moles per liter (molarity).
In this example they are not. A conversion is required.
[H_{2}]
= 0.050 mole H_{2}/5.0 L = 0.010 M
[Br_{2}] = 0.010 M
[HBr] = 0 M

The only direction that this reaction can proceed is forward due to the
fact that initially there are only H_{2} and Br_{2} in
the flask. The reverse reaction cannot begin to occur until some
HBr is formed.

Make an ICE chart with "x" representing the
change in the concentration of the H_{2} (or Br_{2}) as
the system moves towards equilibrium. All of the other changes are
expressed in terms of x.

H_{2}

Br_{2}

HBr

Initial Concentration (M) 
0.010

0.010

0

Change in Concentration (M) 
 x

 x

+ 2 x

Equilibrium Concentration (M) 
0.010  x

0.010  x

0 + 2 x


Substitute the expressions for the equilibrium concentrations into the equilibrium expression
and solve for "x".
x = 0.008 M
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Determining
Equilibrium Pressures
Example: 1.000 atm of SO_{3}, 0.150 atm of SO_{2},
0.200 atm of NO_{2}, and 2.000 atm of NO at 460^{o}C was allowed to reach
equilibrium. What is the equilibrium pressure of each gas
present in the flask?
SO_{2}(g) + NO_{2}(g)
NO(g) + SO_{3}(g) K_{p} = 85.0
@ 460^{o}C

Since we are using K_{p}, check to see if the given quantities
are in appropriate pressure units (atmospheres). In this example
they are, so no conversion is required.

Calculate the value of the reaction quotient,
Q, to determine the direction the reaction will proceed to reach equilibrium.
K_{p} < Q so the reaction will proceed in the reverse
direction.

Make an ICE chart. Let "x" represnt the change
in the pressure of the NO. Since the reaction proceeds in the reverse
direction, the NO and SO_{3} will decrease and the SO_{2}
and NO_{2} will increase as equilibrium is established.

SO_{2}

NO_{2}

NO

SO_{3}

Initial Pressure (atm) 
0.150

0.200

1.500

2.000

Change in Pressure (atm) 
+ x

+ x

 x

 x

Equilibrium Pressure (atm) 
0.150 + x

0.200 + x

1.500  x

2.000  x


Substitute the expressions for the equilibrium pressure into the equilibrium expression and
solve for "x".
x = 0.013 atm

Calculate the equilibrium pressure for each gas using the calculated value
of x.
P_{SO2} = 0.150 + x = 0.150 + 0.013 = 0.163 atm
P_{NO2} = 0.200 + x = 0.200 + 0.013 = 0.213 atm
P_{NO} = 1.500  x = 1.500  0.013 = 1.487 atm
P_{SO3} = 2.000  x = 2.000  0.013 = 1.987 atm

Check your final answers by substituting back into the equilibrium expression
to see if the equilibrium constant is obtained.
which equals 85.0 within the uncertainty of the calculation.
For more information on the mathematics employed in solving equilibrium
problems, click here.
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