There are several possible variants of a Kc question.
The most straightforward is where you are given equilibrium concentrations and you just need to plug them into the correct Kc expression to get the answer and unit.
Alternatively, you might be given Kc and all but one of the equilibrium concentrations. With a bit of algebra and re-arranging, you can determine the missing equilibrium concentration.
A little bit more challenging is where you are given initial concentrations (or amounts) and one of the equilibrium amounts. From this you can use and ICE table to find the equilibrium concentrations and therefore Kc.
A much harder class of problem is where you are given Kc and the initial amounts. From this, you must determine the equilibrium amounts of all the substances. In these cases, we need to use “x” in our ICE table:
Here is a classic example that has come up on the A Level papers.
It looks hard but it is relatively quick to solve (if you know how!).
| Question: The equilibrium reaction shown below has a Kc = 100. The initial concentration of A is 4 mol dm-3. Determine the equilibrium concentrations of A, B and C.
Answer: The first step is to write out an ICE table using what we know and to define the change in [B] and [C] as being x. This means that the change in [A] is -2x.
We now write out the Kc expression and substitute in everything that we know:
You could now start expanding brackets but then you’d end up with a quadratic expression to solve. It is just about doable but perhaps not something you’d get at A Level. A trick – however – is to square root both sides:
This is much easier to re-arrange and solve for x:
Re-arranging gives x = 40 / 21 = 1.90. We can now substitute this back into our ICE table to determine the equilibrium concentrations of A, B and C:
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