hard · MCAT chem-phys
A 0.10 M solution of the diprotic acid H_2A has pK_a1=2.0 and pK_a2=10.0. A student wants the pH at the first equivalence point (after exactly 1 equivalent of strong base, giving NaHA). They reason that HA^- is amphoteric so pH≈tfrac12(pK_a1+pK_a2)=6.0.
Given the wide separation and the dilution at the equivalence point, which is the best estimate and the key caveat?
- pH is near 6.0, but the simple average is an approximation valid only when both Cgg K_a1 and Cgg K_w/K_a2; here the second condition is marginal, so the true pH is slightly below 6.0
- pH equals exactly 6.0 because the amphoteric formula tfrac12(pK_a1+pK_a2) is treated as fully independent of concentration for any diprotic acid at any dilution
- pH is near 4.0 because at the first equivalence point the solution is assumed to still behave as a simple buffer of H_2A/HA^- centered right on pK_a1 instead
- pH is near 8.0 because at the first equivalence point the solution is assumed to be a buffer of HA^-/A^2- centered on pK_a2, ignoring the amphoteric species actually present
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