So, once all the NaOH is consumed in the 1:1 reaction of NaOH and HA, the mixture consists of:
- .
where is the concentration of hydronium ions at equilibrium. Solving this with the usual assumptions - that - will give:
The same result will be obtained using the Henderson-Hasselbalch equation:
And there is only one small problem with this calculation and answer... it is clearly wrong! If I take a weak acid solution and neutralise less than half of it, I can't possibly get a basic solution.
So, where is the problem?
The Henderson-Hasselbalch solution is incorrect as it is derived for a system at equilibrium, and so with the concentrations of the acidic and basic forms being equilibrium concentrations. More problematically, the ICE table has started with a solution of HA and A- and the hydronium concentration being zero. This is impossible in any aqueous system, but is usually not a problem as the contribution of the equilibrium system to the hydronium concentration is much greater than is the contribution from the auto-ionisation of the water / solvent. If you look at the calculated hydronium concentration above, you can see that it is smaller than than the amount in neutral water at room temperature. So, to find the actual pH, a quick-and-dirty solution is to add in the contribution from the solvent to the contribution from the equilibrium:
I don't think figuring this out is a reasonable expectation at HSC level.