# Titration curve of a diprotic acid with a strong base titrant

I have wonders regarding the titration curve of the titration of sulphuric acid, or any diprotic acid, with a strong base. I am aware of the fact that a diprotic acid is protolysed in two steps but, how does this affect the titration curve?

The pKa values for sulfuric acid from Wikipedia are −3, and 1.99. So for all practical purposes the first ionization happens completely and would be unobservable with a pH electrode in aqueous solutions. So if you had a 0.1 molar solution of sulfuric acid it would almost look like you were titrating a 0.2N of $\ce{H^+X^-}$ where that acid had a pKa of 1.69 (pH at half NaOH used). This would be a strong acid too and the inflection point would be that for water at pH 7.

Note that the pKa 1.69 is assuming $\ce{H^+X^-}$ and is taken at 1/2 of the $\ce{Na^+OH^-}$ used. Knowing that $\ce{H2SO4}$ has two protons, the second pKa should be taken at 150% on the plot which would give the correct pKa value of 1.99.

If you had an acid with two lower pKa values then you'd see two pH transitions in the titrations. Look at the figure below. With two widely separated pKa values maleic acid shows two nice transitions. With two pkA values closer together the two transitions for malonic acid aren't as sharp. For succinic acid the knee at a volume of about 5 ml is a hint that there are two dissociations but you don't see two nice complete transitions like you do for maleic acid.

To go back to the sulfuric acid tritration, we'd really expect to see a knee at a low pH something like the titration curve we got for succinic acid. Such a knee isn't seen because a pH electrode just doesn't work at such high acid levels (pH range from -3 to 0).

PS - Thanks to the commenters for help to vastly improve the answer.

• It's not true! Strong first dissotiation makes it even more visible that it's diprotic! Please don't add obviously wrong answers. – Mithoron Nov 5 '15 at 19:01
• I didn't do the math, but if I have 0.1 N $\ce{H2SO4}$ I'd expect about 0.1 moles $\ce{H^+}$ and $\ce{HSO^{-}_4}$ and very little $\ce{H2SO4}$ or $\ce{SO^{2-}_4}$. Right? – MaxW Nov 5 '15 at 19:09
• Geez, if you titrate even stronger HCL curve is completely normal! Base is reacting especially with dissociated protons. @samueltober you shouldn't accept wrong answers. – Mithoron Nov 5 '15 at 19:12
• For HCl the transition from acidic to basic solution would happen at pH 7 which is indicative that the HCl was completely dissociated. If you titrate acetic acid you just get one break, not one for acetic acid and another for water. – MaxW Nov 5 '15 at 19:19
• Ok, I did some major edits on the answer. Thanks for the help improving the clarity. – MaxW Nov 5 '15 at 20:43