Calculating K Using Non-equilibrium Values

All the examples to this point have been relatively easy because we knew the concentration of every substance in the K expression, at equilibrium.

In earlier questions, we developed the following principle:

Previous examples were relatively easy because step 2 didn't really need any work – we always were given each concentration at equilibrium.  In the examples on this page we will not have all the concentrations at equilibrium, but each problem will have enough information to get to that point, so that we can then calculate K_eq.

To do this, we need to make use of the balanced chemical equation, and what we know about the coefficients in the reaction.  Remember that the coefficients tell us the ratio in which the reactants react, and the products are formed, but not how much there is of any substance at equilibrium (nor at the start of the reaction).  In general we always have, or can figure out, three pieces of information about any chemical reaction:

• the concentrations of the reactants and/or products when the reaction started (initial values)
• how the concentrations change because of the chemical reaction (reaction change)
• the concentrations of each reactant and product when the reaction is finished (equilibrium values)

To keep track of these it is really useful to make up an "IRE" table and complete it with the information we have available about the intitial, reaction change, and equilibrium concentrations.   Here is an example of an empty table:

Provided that we know the inital (white row) value of each reactant or product, and at least one equilibrium value (pink row), we can complete this table to get all the pink values.  Here is an example of how we do this.

Example 2:  0.100 mol of HI, 0.200 mol of I2 and 0.300 mol of H2 gases are placed in a 1.00 L flask and heated to 425 ºC.  After equilibrium has been reached the concentration of H2 (g) is 0.141 mol/L.  What is K? Can you actually do this?  Start a reaction with products in the container?  Make sure you know the right answer before going on. Step 1: Write out the K expression for the balanced equation: From the way this problem is stated, the reaction could be either or 2HI (g) I2 (g) + H2 (g) (1) I2 (g) + H2 (g) 2HI (g) (2) It really doesn't matter which one you pick, but you must include the reaction with the K expression, since the two equations will have K values that are reciprocals of each other.  Let's use version (2) for which  Step 2: Identify each concentration at equilibrium.  To do this we set up and complete the IRE table.  This gives equilibrium concentrations of: [I2] = 0.0141 mol/L [H2] = 0.141 mol/L [HI] = 0.418  mol/L Click here for a step by step explanation of how to use an IRE table to solve this problem. Step 3: Substitute these values for equilibrium into K and do the math

Summary:

Try the following sample problems to check your understanding.