PH at the equivalence point?

How do I find Ka from pH at equivalence point?

• In my chem lab, I titrated an unknown acid with NaOH; the pH at equivalence point is around 7.8 and this occurs at 24.4 mL of NaOH added. The concentration of NaOH is 0.10002 M. the total amount of acid titrated is 25 mL. How would i find the pKa of the acid from this info, WITHOUT using the half-way equivalence point method? The equation im supposed to use is Ka = [H+][A-]/[HA]. Please help! Thanks!

• Answer:

  Based on your titration data, the concentration of acid is about 0.10 M (you may be able to add another decimal to that if you measured out your acid carefully). Since your pH was 7.8, that means that [H+] = 10^-7.8. Therefore, [OH-] = 10^-6.2, since Ka.Kb = Kw = 10^-14. You should have been taught about the basic nature of salts of weak acids and how to do calculations of pH for their solutions. Essentially, what you've done at the equivalence point of a weak acid-strong base titration is to create the same solution that you would obtain by dissolving the sodium salt of the acid in water to make a 0.1M solution. The conjugate base of the acid reacts as a weak base, which is why the pH is basic: A- + H2O <==> HA + OH-. Applying the ICE box method, [HA] = [OH-] = x, and [A-] = 0.1-x ~ 0.1M. Kb = [OH-][HA]/[A-] = x^2/0.1 = ?? Since you measured [OH-] (indirectly, by measuring pH), Kb = (10^-6.2)^2/0.1 = 10^-11.4, and pKb = 11.4. pKa + pKb = 14, so the pKa of your acid must be 14-11.4 = 2.6. I've never seen the pKa measured this way, and I suspect that's for good reason: the method is likely to be highly inaccurate. The biggest problem is that close to the endpoint, the pH changes dramatically with even a drop or two of titrant, and it's very hard to catch the endpoint accurately if you're using an indicator to do it (which I assume you must be). That inaccuracy i finding the endpoint translates to a very large inaccuracy in the pH. That's why the half-equivalence method is usually used. Oh well... not your choice to do the experiment that way, but if you're asked to quote sources of error, that's one that you can mention!