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G-5
lines at C and D. Averaging the values of pH at the two intersection points gives the value of the pH at the
equivalence point. The volume of titrant added to reach this point is called the equivalence point volume.
At the equivalence point, the pH of the solution is determined by the reaction of the conjugate base A
-
with
water.
A
-
(aq)
+ H2O
(l)
HA
(aq)
+ OH
-
(aq)
(7)
The concentration of the conjugate base can be determined using the following relationship:
[A
-
]
at equiv. pt.
=
moles A
-
total volume at the equivalence point
(8)
The pH at the equivalence point is then the same as the pH of a solution of A
-
at this concentration. (Note that
in the titration of polyprotic acids, which can donate more than one proton, there will be more than one
equivalence point.)
The value of K
a
for a weak acid can also be determined from the titration curve (see Figure 2). On the
titration curve, the point at which the initial acid has been half neutralized gives the pH of the solution where
the number of moles of A
-
formed through the neutralization reaction is exactly equal to the number of moles of
HA remaining in the solution. In the equilibrium expression
K
a
=
[H3O
+
][A
-
]
[HA]
[HA] will equal [A
-
] at this point, therefore these will cancel out of the relation leaving
K
a
= [H3O
+
]. On the titration curve, the pH of the solution when the acid is half neutralized will therefore
equal the pK
a
value (pK
a
= -log K
a
). This point occurs when one half the volume of NaOH required to reach
the equivalence point has been added. The inverse log of the negative of the pH value at this point will equal
the K
a
value (i.e. K
a
= 1 x 10
-pH
)
Note that this procedure cannot be used for a strong acid. The procedure for weak acids depends on the
existence of a point along the titration curve where [A
-
]
= [HA]. When a strong acid is added to water, it is
essentially all dissociated. There is no point along the titration curve of a strong acid where [A
-
]
= [HA]. The
concentration of undissociated HA is extremely small and cannot be accurately determined, so we will assume
that for strong acids, like HCl
(aq)
, [HA] is zero. For this reason, K
a
values are not defined for strong acids (the
denominator of the relation is essentially zero), therefore, the K
a
value, by definition, would approach infinity.
