Page 327 - Modern Analytical Chemistry

1400-CH09 9/9/99 2:13 PM Page 310

310 Modern Analytical Chemistry

The possible formula weights for the unknown weak acid are
for n = 1: FW = EW = 58.78 g/mol
for n =2: FW=2 ´EW = 117.6 g/mol
for n =3: FW=3 ´EW = 176.3 g/mol
If the weak acid is monoprotic, then the FW must be 58.78 g/mol, eliminating
ascorbic acid as a possibility. If the weak acid is diprotic, then the FW may be
either 58.78 g/mol or 117.6 g/mol, depending on whether the titration was to
the first or second equivalence point. Succinic acid, with a formula weight of
118.1 g/mol is a possibility, but malonic acid is not. If the analyte is a triprotic
weak acid, then its FW must be 58.78 g/mol, 117.6 g/mol, or 176.3 g/mol. None
of these values is close to the formula weight for citric acid, eliminating it as a
possibility. Only succinic acid provides a possible match.

Equilibrium Constants Another application of acid–base titrimetry is the determi-
nation of equilibrium constants. Consider, for example, the titration of a weak acid,
HA, with a strong base. The dissociation constant for the weak acid is
-
+
[ A ][ H 3 O ]
K a = 9.9
[ HA]
–
When the concentrations of HA and A are equal, equation 9.9 reduces to
+
K a =[H 3 O ], or pH = pK a . Thus, the pK a for a weak acid can be determined by
measuring the pH for a solution in which half of the weak acid has been neutralized.
On a titration curve, the point of half-neutralization is approximated by the volume
of titrant that is half of that needed to reach the equivalence point. As shown in Fig-
ure 9.20, an estimate of the weak acid’s pK a can be obtained directly from the titra-
tion curve.
This method provides a reasonable estimate of the pK a , provided that the weak
acid is neither too strong nor too weak. These limitations are easily appreciated by
considering two limiting cases. For the first case let’s assume that the acid is strong
enough that it is more than 50% dissociated before the titration begins. As a result
the concentration of HA before the equivalence point is always less than the con-
–
–
centration of A , and there is no point along the titration curve where [HA] = [A ].
At the other extreme, if the acid is too weak, the equilibrium constant for the titra-
tion reaction
–
–
HA(aq)+OH (aq) t H 2 O(l)+A (aq)
may be so small that less than 50% of HA will have reacted at the equivalence point.
In this case the concentration of HA before the equivalence point is always greater

14.0 V eq pt
12.0
10.0
V
pH 8.0 pK a 2 ´ eq pt
6.0
4.0
2.0
Figure 9.20 0.0
Estimating the pK a for a weak acid from its 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00
titration curve with a strong base. Volume of titrant