# How to determine the pH range at which maximum hydrate is present?

Question:

Find the $\mathrm{pH}$ range at which maximum hydrate is present in a solution of oxaloacetic acid (given $\mathrm{pK_a}$ of $\ce{-COOH}$ in the left is $=2.2$ and on the right is $=3.98$):

I understand that the hydrate will be formed at the carbonyl group position, resulting in a product like this:

I know that the gem-diols are usually stablized by H-bonding, as is the case here as well (between the lower hydroxy and left acid group). I can also see that loss of the $\ce{H+}$ ion from the carboxylic acid group on the left will create an $\ce{O-}$ ion which will have an even stronger H-bonding. However, I am not sure how I can use this fact to relate the given $\mathrm{pK_a}$ values and the expected $\mathrm{pH}$ range.

I need help completing my train of thought. Thank you!

• chemistry.stackexchange.com/a/42796/9961 – Mithoron Feb 14 '18 at 17:28
• @Mithoron That question doesn't have $\pu{pH, pK_a}$ nor does it have a hydrate alongside carboxylic acids. It's only slightly related, due to both question discussing formation of a stable hydrate. – Gaurang Tandon Feb 15 '18 at 1:27
• Your thought about H-bonding stabilization is leading you astray. Ron's answer ^ says what's important for diol - ketone equilibrium. – Mithoron Feb 15 '18 at 1:40