There's a REALLY LONG way, and there's a much shorter way.
Here's the short way, because **** the long way.
Lol I say short, but my post is long. That's only because I just really really want you to understand it sorry. The working out when you come to write it is short.
You agree that you have some moles of HA.
The question is saying that the student adds some NaOH. This amount is equal to a third of the amount needed to neutralise it.
In other words, a third of the HA has reacted with the NaOH. If it said, half the amount was added, then half of the HA would have been neutralised, and so on.
When we react the HA and NaOH, this forms our A
-.
So as a result, the amount of A
- we formed is equal to one third of the HA we started with.
In other words...
A−=31×HA.If you want to represent this as concentration, by all means divide it by the volume. But the volume will cancel out, which allows me to just use the moles.
In fact I don't need to do that because...
H+=A−Kc×HA becomes
H+=31×HAKc×HAAnd now the HAs cancel out, which just leaves...
H+=Kc×3This is now solvable for pH
It's just like that first question of where the HA is half the number of A