A much harder class of Kc problem is where you are given Kc and the initial amounts. From this, you must determine the equilibrium amounts of all the substances. Here, we will need to use and ICE table and “x” for our unknown.
The example below is unlikely to appear on an A Level paper, but might might a good question for University Chemistry interviews.
| Question: The equilibrium reaction shown below has a Kc = 8.1. The initial concentration of PCl5 is 1 mol dm-3. Determine the equilibrium concentrations of each substance.
Answer: The first step is to write out an ICE table using what we know and to define the change in [PCl3] and [Cl2] as being x. This means that the change in [PCl5] is -x.
We now write out the Kc expression and substitute in everything that we know:
There is no getting around the fact that this will result in a quadratic expression. We re-arrange it to get it into the usual form of a quadratic polynomial:
You may remember / know from GCSE Maths that this can be solved using the quadratic formula:
Substituting in our values of a = 1, b = 8.1 and c = -8.1, we get:
Putting this back into the ICE table gives:
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There are actually two roots x = 0.9 and x = -9. The negative root can be ignored as you cannot have a negative concentration of something. The positive root, x = 0.9, is the change in [PCl3] and [Cl2].