Calculations with the Equilibrium Constant

ICE tables are composed of the concentrations of molecules in solution in different stages of a reaction, and are usually used to calculate the K, or equilibrium constant expression, of a reaction (in some instances, K may be given, and one or more of the concentrations in the table will be the unknown to be solved for). ICE tables automatically set up and organize the variables and constants needed when calculating the unknown.

ICE is a simple acronym for the titles of the first column of the table.

• I stands for initial concentration. This is the concentration that the reaction starts out in.
• C stands for the change in concentration. This is the concentration change needed to get the reaction from start to equilibrium. It is the difference between the equilibrium and initial rows. The concentrations in this row are, unlike the other rows, expressed with either an appropriate positive (+) or negative (-) sign because this row represents change up or down (or no change).
• E is for the concentration when the reaction is at equilibrium. This is the summation of the initial and change rows. If you are looking for K_c, as you often will be at this stage of chemistry, this is the goal. Once you have the values in this row, you can easily obtain K_c by plugging them into the equation for K_c.

We will learn by doing a few examples. Setting up an actual ICE table will familiarize you with them better than abstract definitions, so let us consider an example of a reaction of general form:

Example 2

Using an ICE table to determine the K_c for the balance general reaction:

`2X(g) ? (g) + 4Z(g)`

where the captial letters represent the products and reactants.

• This equation will be placed horizontally above the table, with each product and reactant having a separate column.

A sample consisting of 0.500 mol of X is placed into a system with volume 0.750 Liter

• This statement implies that there are no initial amounts of Y and Z. For the I row of the Y and Z columns, 0.000 mol will be entered.
• Notice that we are using amounts. The amounts can either be converted to concentrations after putting them into the ICE table or after the equilibrium constants have been calculated. IN this example, we will use the number of moles when filling in the ICE table (concentration can be calculated later).

At equilibrium, the amount of sample X is known to be 0.350 mol.

• For the quilibrium row of X, 0.350 mol will be entered. As you will see, this and the initial amount will help us find the other unkown amounts in the ICE table.

Desired Unkown

`K_c = ?`

Solution:

We know that the quilibrium constant expression can be expressed as products over reactants, with each to the power of the respective amounts:

`K_c = ([Y]^3 [Z]^4)/([X]^2)`

Example 3:

The water–gas shift reaction is important in several chemical processes, such as the production of H₂ for fuel cells. This reaction can be written as follows:

`H_2 (g)+CO_2 (g) -> H_2O(g)+CO(g)K = 0.106" at "700 K`.

If a mixture of gases that initially contains 0.0150 M H₂ and 0.0150 M CO₂ is allowed to equilibrate at 700 K, what are the final concentrations of all substances present?

Worked Problem Here

Checklist for ICE tables

• Make sure the reversible equation is balanced at the start of the problem; otherwise, you could end up with wrong amounts in the table (in our example, we were given a balanced equation…but do not assume the equation always is!).
• The given data should be in amounts, concentrations, partial pressures, or somehow able to be converted to such. If it is not, then an ICE table will not help solve the problem.
• If the ICE table has the equilibrium in amounts, make sure to convert equilibrium values to concentrationsbefore plugging in to solve for K_c.
• If the given data is in amounts or concentrations, use the ICE table to find K_c. If the given data is in partial pressures, use the ICE table to find K_p. If you desire to convert from one to the other, remember that Kp=Kc(RT)?ngas; it is simpler to use the ICE table with the appropriate givens and convert at the end of the problem.
• Enter in known data first, and that should enable you to calculate the unknown data in the table.
• If ever you have a negative value in the Initial or Equilibrium rows, double check your work! A negative concentration, amount, or partial pressure is physically impossible. Obviously, the Change row can contain a value that is a negative number.
• Pay attention to the state of each reactant and product. If a compound is a solid or a liquid, its concentrations are not relevant to the calculations. Only concentrations of gaseous and aqueous compounds are used.
• In the 'change' row the values will usually be a variable, denoted by x. It must first be understood which direction the equation is going to reach equilibrium (from left to right or from right to left). The value for 'change' in the 'from' direction of the reaction will be the opposite of x and the 'to' direction will be the positive of x (adding concentration to one side and take away an equal amount from the other side).
• Know the direction of the reaction. This knowledge will affect the Change row of the ICE table (for our example, we knew the reaction would proceed forward, as there was no initial products). Direction of reaction can be calculated using Q, the reaction quotient. Q is then compared to a known (read:given) K value.
• It is easiest to use the same units every time you use an ICE table (usually molarity is preferred). This will minimize confusion when calculating the equilibrium constants. ICE tables are usually used for weak acid or weak base reactions because all of the nature of these solutions. The amount of acid or base that will dissociate is unknown (for strong acids and strong bases it can be assumed that all of the acid or base will dissociate, meaning that the concentration of the strong acid or base is the same as its dissociated particles).

*"Partial pressure" may also be substituted for "concentrations" in the ICE table, if desired (i.e., if the concentrations are not known, K_p instead of K_c is desired, etc.). "Amount" is also acceptable (the ICE table may be done in amounts until the equilibrium amounts are found, after which they will be converted to concentrations). For simplicity, assume that the word "concentration" can be replaced with "partial pressure" or "amounts" throughout the non-example portions of this module.

Subpages (2): Example 2 Example 3