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General acid (A) Base (B) titration curve is represented as follows :

Sketch of pH against titrant added: the curve starts at point L on the pH axis, rises gently to M, climbs steeply through N and levels off at O

What should be the equation for estimation of pH at point (L) :

  • A.\(\mathrm{pH = pK_{w} + \log\,[B]}\)
  • B.\(\mathrm{pH = \frac{1}{2}pK_{a} + \frac{1}{2}pK_{w}}\)
  • C.\(\mathrm{pH = \frac{1}{2}pK_{a} - \frac{1}{2}\log\,[A]_{initial}}\)
  • D.\(\mathrm{pH = pK_{a}}\)

Answer: C

At point L the pH is given by pH = ½ pKa - ½ log [A]initial.

Point L is the start of the curve, before any titrant is added, so the solution contains only the weak acid at its initial concentration c. For a weak acid, [H+] = √(Kac), and taking negative logarithms:

\[ \mathrm{pH} = \tfrac{1}{2}pK_{a} - \tfrac{1}{2}\log c \]

pH = pKa holds at M, the half-equivalence point in the buffer region. pH = ½pKa + ½pKw (plus a concentration term) is used at the equivalence point N, where the salt hydrolyses. The expression with pKw and log [B] belongs to the region past equivalence, where excess base controls the pH.

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