[timzor]

I just have a query regarding finding the pKa of an unknown base or acid. I know that the pH = pKa at the half equivalence point and understand the derivation of it but don't understand how you would know when [HA] = [A-]? 

Say for example you have 1 mole of Acetic acid (HAc) and titrate it with 0.5 mol of NaOH and now you will have 0.5 mol of acetate ions and 0.5 mol of HAc. This is the half equivalence point. But does that mean at this point [HA] = [A-] ?  Because won't some of the HAc disassociate and form more acetate ions meaning that you will have more then 0.5 mol of acetate ions and so [HA] < [A-] at equilibrium or is the disassociation so small that it dosen't matter and so we can say pKa = pH at this point? Or else the +log([A-]/[HA] will not equal to 0 and the pKa = pH will not hold.

Thanks,
tim.

[Borek]

But does that mean at this point [HA] = [A-] ?

This is only an approximation, but quite a good one. For the reasons you have listed it won't hold for acids too strong (like pKa=1) or too weak (like pKa=13), but it is OK for everything between pKa 2 and 11.