Show [OH-] = [base] at Vbase = ∞ in acid – base titration.
Situation:
• add strong base to strong acid (or weak acid)
• acid & base are monoprotic
At Vbase > Vbase at end point,
[OH − ] =
At Vb
nOH −
=
Vtotal
nbase − nacid
Vtotal
=
[ B] Vb − [ A] Va
.
Va + Vb
= ∞,
lim [OH − ] =
Vb →∞
lim
Vb →∞
[ B] Vb − [ A] Va
Va + Vb
[ B] − [ A]
=
lim
Vb →∞
Va
+1
Vb
Va
Vb
[eqn.1]
= [ B]
alternatively, apply L’Hopital’s rule to [eqn. 1]. That is, at Vb = ∞, [OH-] = [base]; thus
at Vb = ∞, pH = pHbase
As such, when sketching an acid-base titration curve, the pH at Vb = ∞ is the pH of the
base. A similar argument would apply to the addition of a strong acid to strong / weak
base: [H+] = [acid] at Va = ∞.