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160 Modern Analytical Chemistry

reactions, must be included in the charge balance equation. The charge balance
equation for an aqueous solution of Ca(NO 3 ) 2 is
–
2+
+
–
2 ´[Ca ]+[H 3 O ] = [OH ] + [NO 3 ]
Note that the concentration of Ca 2+ is multiplied by 2, and that the concentrations
+
–
of H 3 O and OH are also included. Charge balance equations must be written
carefully since every ion in solution must be included. This presents a problem
when the concentration of one ion in solution is held constant by a reagent of un-
specified composition. For example, in many situations pH is held constant using a
buffer. If the composition of the buffer is not specified, then a charge balance equa-
tion cannot be written.
EXAMPLE 6.10

Write a mass balance and charge balance equations for a 0.10 M solution of
NaHCO 3 .
SOLUTION

It is easier to keep track of what species are in solution if we write down the
reactions that control the solution’s composition. These reactions are the
dissolution of a soluble salt
+
–
NaHCO 3 (s) ® Na (aq) + HCO 3 (aq)
–
and the acid–base dissociation reactions of HCO 3 and H 2 O
2–
+
–
HCO 3 (aq)+H 2 O(l) t H 3 O (aq)+CO 3 (aq)
–
–
HCO 3 (aq)+H 2 O(l) t OH (aq)+H 2 CO 3 (aq)
+
–
2H 2 O(l) t H 3 O (aq)+OH (aq)
The mass balance equations are
2–
–
0.10 M = [H 2 CO 3 ] + [HCO 3 ] + [CO 3 ]
+
0.10 M = [Na ]
The charge balance equation is
2–
–
–
+
+
[Na ]+[H 3O ] = [OH ] + [HCO 3 ]+2 ´[CO 3 ]
6G. 4 pH of a Monoprotic Weak Acid
To illustrate the systematic approach, let us calculate the pH of 1.0 M HF. Two
equilbria affect the pH of this system. The first, and most obvious, is the acid disso-
ciation reaction for HF
+
–
HF(aq)+H 2 O(l) t H 3 O (aq)+F (aq)
for which the equilibrium constant expression is
+
–
[ HO ][ F ]
3
K a = = .68 ´10 –4 6.35
[ HF]