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An unknown compound, X, is though to have a carboxyl group with a pKa of 2.0 and another ionizable group with a pKa between 5 and 8. When 75 mL of 0.1M NaOH is added to 100 mL of a 0.1M solution of X at pH 2.0, the pH increases to 6.72. Calculate the pKa of the second ionizable group of X. Can someone please tell me how do I know that at the initial pH the carboxylic acid will be 50% dissociated?

The Henderson-Hasselbalch equation is
pH = pKa + log(B/A)
pH = 2
pKa = 2
2 = 2 + log(B/A)
so B/A = 1 or base = acid
So RCOOH ==> RCOO^- + H^+
RCOO^- is base.
RCOOH is acid.
If base = acid it must be 50% dissociated.

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