Calculating pKa when pH is known

[BogMonkey]

I started this thread a while ago but never figured it out in the end can someone tell me if my idea of this is correct or not.

Lets say I add 2 moles of a weak acid acetic acid to a liter of water (at STP). If I'm not mistaken the acetic acid will dissociate slightly depending on its dissociation constant. If I measure the pH now I still won't know how many ions are present because I do not know the dissociation constant of the acid. Now I add 0.5 moles of a strong base NaOH. I know that these compounds react with each other in a 1:1 ratio and that the NaOH neutralize the acetic acid regardless of whether it has dissociated or not. With that in mind I now know the amount of dissociated ions that came from the acetic acid because they will be equal to the amount of dissociated ions from the NaOH.

Now if I take the pH of the solution I can use the henderson-hasselbach equation to find out the pKa of the acetic acid involved and from the pKa I can find its pK. The principle behind this if I'm not mistaken is that when the strong base neutralizes the weak acid then the resulting pH will be influenced by the dissociation constant of the acid which is how the pKa is then derived. I'm going to read up on pKa now since I don't fully understand it but if there's any errors in what I said there can you point them out for me.

 

[Cesium]

I think you idea is correct. You can definitely determine the pKa of an acid by titrating it with a base and using the Henderson-Hasselbach equation. Half way to the equivalence point of the titration, the pKa will be equal to the pH. This would be the best point to determine the pKa (smallest margin of error) because your conjugate base and acid concentrations will be equal. (Since the Henderson-Hasselbach equation is logarithimic, small changes in concentration outside of the half equivalence point result in large changes in pH.) You can also plug in the Henderson-Hasselbach equation at points outside of the half equivalence point and take an average of your calculated pKa's.

 

[Borek]

Lets say I add 2 moles of a weak acid acetic acid to a liter of water (at STP). If I'm not mistaken the acetic acid will dissociate slightly depending on its dissociation constant. If I measure the pH now I still won't know how many ions are present because I do not know the dissociation constant of the acid.

Write dissociation reaction - you know stoichiometry of the dissociation. Assuming H⁺ comes ONLY from acid dissociation - can you calculate concentrations of all other ions present in the solution?

Now I add 0.5 moles of a strong base NaOH. I know that these compounds react with each other in a 1:1 ratio and that the NaOH neutralize the acetic acid regardless of whether it has dissociated or not. With that in mind I now know the amount of dissociated ions that came from the acetic acid because they will be equal to the amount of dissociated ions from the NaOH.

It will better to add 1 mole of NaOH, so that pH=pKa (take a look at the HH equation to understand why). But the general idea is correct.