Every reversible reaction system has a unique equilibrium constant that describes the ratio of the amounts of reactants and products when the system has reached equilibrium. The equilibrium constant value can be calculated from knowledge of the initial concentrations and the concentration of at least one product. An ICE Table is a convenient tool that facilitates such calculations. 
 

This Concept Builder has two goals:

1. To learn how to create an ICE Table for a reversible system.
2. To use the ICE Table to calculate the value of the equilibrium constant.

There are six steps to the process of accomplsihing the above two goals. This page provides guidance for each of the individual steps.


Step 1: Write an Equilibrium Constant Expression (a K Expression)

Every reaction has its own unique equilibrium constant – a number that describes the quantitative relationship between the amounts of reactants and products and equilibrium. At equilibrium, the equilibrium constant (the number) is equal to the equilibrium constant expression.

Here's how to write the equilirium constant expression.

1. Use concentrations. Use brackets “[ A ]” for concentration of A.
2. List product concentrations in numerator; reactant concentrations are included in the denominator.
3. Raise concentrations to a power equal to the coefficient of that reactant or product as seen in the balanced chemical equation.
4. For more than one product, multiply concentration values.
5. Only use gaseous and acqueous state subsances. Do not include solids and liquids in the expression. 

As an example, consider the reversible reaction:  A_(g)  +   B_(g)   ⇄     C_(g)

The K expression would be [C] / ([A] • [B]). And so the K equation would become ...

K = [C] / ([A] • [B])

Step 2: The I of ICE - Initial Concentrations
An ICE Table lists concentrations of reactants and products.  The concentrations are organized into three rows. The first row lists the initial concentrations of reactants and products. In this Concept Builder, those values are explicitly stated in the problem statement. Read it carefully and fill in the cells with the stated concentration values. One thing to note: if a reactant or product concentration is not stated, then it is absent from the initial mix of chemicals. Its concentration is 0 M.

 

Step3: The C of ICE - Change in Concentrations
A reversible system will always proceed towards equilibrium. That is, the system will undergo change until the rate of forward and reverse reactions are equal. The C row shows the amount of change in concentrations of reactants and products. These are expressed in terms of the variable x. Possible options of answers include +x, +2x, -x, -4x, etc. Let's talk about it.

The + expressions indicate that the particular reactant or product is increasing in amount. The - expressions indicate that the particular reactant or product is decreasing in amount. The key to understanding whether to use the + or the - is to read the last part of the problem statement where it says something like ...

"The reaction proceeds to equilibrium. The equilibrium concentration of PCl₅ is 0.40 M."

Inspect the equilibrium amount of PCl₅ and see if it shows an increase or a decrease relative to the initial amount (mentioned earlier in the sentence). Use a + for PCl₅ if it increased and a - if it decreased. And of course, use the opposite sign for the Cl2 and the PCl3 since they are on the opposite side of the chemical equation. 

So that takes care of the + and the -. What about the integer in front of the x? The key to the integer is to inspect the coefficients in the balanced chemical equation. If the coefficient is 1, then use the integer 1. It the coefficient is 2, then use the integer 2. And so forth. It is simply stoichiometry. After all, those coefficients tell you the relative amounts of reactants and products that are reacting. In this question, the coefficients are all 1. It won't be so easy in the Master and the Wizard Levels.



Step 4: Find the Value of X
... but first, note how the bottom row is completed. The bottom row is the E row. E stands for equilibrium concentration of reactants and products. These are the important values because they will be used to calculate the equilibrium constnat value (step 6). As noted in the on-screen prompts, the bottom row of the table is the sum of the two rows above it. After all, the amount present at equilibrium is the initial amount plus the change amount. And so the bottom row lists an expression for the equilibrium concnentration of three reactants and products. 

The problem statement also lists the actual concentration value of the PCl₅. This value can be equated with the expression in the PCl₅ column of that row. Do the algebra to determine the value of x.  Do your algebra in steps. Here's an example of solving for x starting with 3.0 = 4.5 - x.

3.0 = 4.5 - x
Add x to each side of the equation to get ...
3.0 + x = 4.5
Add 3.0 to each side of the equation to get ...
x = 4.5 - 3.0
Simplify the right side.
x = 1.5

Step 5: Determine all Equilibrium Concentrations
After Step 4, you know the value of x and you have an expression for each reactant and product that expresses their concentration in terms of x. It's now time to substitute x into those expressions and solve for the equilibrium concentration values. Substitute and solve.




Step 6: Determine the K Value
After Step 5, you know the value of reactant and product concentrations and you have an equation (from Step 1) that relates the K value to the equilibrium concentrations of reactants and products. So now substitute the concentration values into the equation from Step 1. Use your calculator to solve for K.
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