Ice Box Calculations
By: Clifford Beaton
Introduction
• An ice box is a table that is used for equilibrium calculations when we are
given starting concentrations for chemicals.
• The starting concentrations have to be changed to equilibrium
concentrations before they can be used in an equilibrium expression.
• The I stands for initial, the C for change and the E for equilibrium.
• An ice box looks like this:
Molarity
H+
Cl-
HCl
Initial
Change
1.0M
0.5M
0M
-0.3M
-0.3M
+0.3M
Equilibrium
0.7M
0.2M
0.3M
Example 1
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A 10.0L bulb is filled with 4.0 mol of NO(g), 2.0 mol of O2(g). The gases then reached
equilibrium according to the equation 2NO(g) + O2(g) ↔ 2NO2(g). At Equilibrium, the bulb only
contained 2.8 mol of NO(g). Calculate the Keq for this reaction.
Since we aren’t given all of the equilibrium concentrations, we need to use an ice box. First
we calculate the initial concentrations and fill them into the ice box. Since we weren’t given a
concentration for the product, we assume it starts at 0M. Then with the one given
equilibrium concentration, we find the change in concentrations. The concentrations change
according to the mol ratio in the balanced equation, so O2 will change half as much as NO.
Generally, reactants are used up and products are produced so the reactants will have
negative changes and the products will have positive ones.
NO
O2
NO2
0.4M
0.2M
0M
-0.12
-0.06
+0.12
0.28M
0.14M
0.12M
Then we calculate the Keq. Keq = (0.12)2/(0.28)2(0.14) = 1.3
Since the Keq is greater than one, the products are favoured. If it was less than one the
reactants would be favoured.
Example 2
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You can also use variables to represent the change in concentrations in an ice box.
You know you need to use variables if the starting concentrations are given but no
equilibrium concentrations are given.
For the following reaction, find all equilibrium concentrations if you started off
with 0.5M of H2 and 0.5M of I2 0.5M and Keq = 32. H2(g) + I2(g) ↔ 2HI(g)
H2
I2
HI
0.5M
0.5M
0M
-x
-x
+2x
0.5-x
0.5-x
2x
You start by setting up your equilibrium expression. 32 = (2x)2/(0.5-x)2
Solve for x and you get x = 0.37. Then you go back to the equilibrium
concentrations and plug in x to get 0.13M for H2 and I2 and 0.74M for HI.
Example 3
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Sometimes when using variables, it doesn’t work out so that you can take the
square root of every term in the equilibrium expression. For these questions you
would need to use the quadratic formula: x = -b ± √(b2-4ac)
2a
Find all equilibrium concentrations for the following reaction if you begin with
0.2M of PCl5 and the equilibrium constant is 1.3. PCl5(g) ↔ PCl3(g) + Cl2(g)
PCl5
PCl3
Cl2
0.2M
0M
0M
-x
+x
+x
0.2-x
x
x
Again you set up you equilibrium expression. 1.3 = (x)2/(0.2-x)
This equilibrium expression is a quadratic so you need the quadratic formula to
solve for x. Once you solve, you get x = -1.48 and x = 0.176. x = -1.48 gives you
negative concentrations so you need to discard it which leaves x = 0.176 as your
answer. Plug it back into the equilibrium concentrations and you get 0.024M for
PCl5 and 0.176M for PCl3 and Cl2.
Ice Boxes for Acids and Bases
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Ice boxes are often needed for finding the ionization constants for acids or bases.
You can use ice boxes to calculate the pH or ionization percentage of an acid.
Example: An unknown acid HX has a concentration of 10M and its Ka = 0.25. Find
its pH.
HX
H+
X-
10M
0M
0M
-x
+x
+x
10-x
x
x
For this example, you would need the quadratic formula to solve for x but in some
cases you can disregard the –x in the ice box.
The rule is: if the molarity of the acid divided by the Ka is greater than 1000, you
can drop the –x because it does not make a significant difference in the
calculation. If the number is less than 1000, you need to keep the –x and use the
quadratic equation to solve for x.
Remember
• Ice boxes are used often for equilibrium calculations and ionization
constants for acids and bases.
• You know you need an ice box when:
1) You are given starting concentrations instead of equilibrium calculations.
2) You are dealing with ionization constants for weak acids or bases (Ka or
Kb)
• The ICE in ice box stands for Initial, Change, Equilibrium.
• Only equilibrium concentrations are used in an equilibrium expression.
• Always make sure the chemical equation is balanced before you find the
changes in concentrations because they are related to the mol ratio.
THE END
• Information provided by Mr. Therrien’s
Chemistry 12 booklet.
HCl
+
=
H+
Cl-
I
1M 0M 0M
C
-.5
E
0.5 0.5 0.5
+.5 +.5