Page 299 - Modern Analytical Chemistry

1400-CH09 9/9/99 2:12 PM Page 282

282 Modern Analytical Chemistry

Before adding any NaOH the pH is that for a solution of 0.100 M acetic acid.
Since acetic acid is a weak acid, we calculate the pH using the method outlined in
Chapter 6.
–
+
CH 3 COOH(aq)+H 2 O(l) t H 3 O (aq)+CH 3 COO (aq)
xx()
[H O + ][CH COO - ] ()
3
3
K a = = = .175 ´10 - 5
3
[CH COOH] . 0 100 - x
+
x =[H 3 O ] = 1.32 ´10 –3
At the beginning of the titration the pH is 2.88.
Adding NaOH converts a portion of the acetic acid to its conjugate base.
–
–
CH 3 COOH(aq)+OH (aq) t H 2 O(l)+CH 3 COO (aq) 9.2
Any solution containing comparable amounts of a weak acid, HA, and its conjugate
–
weak base, A , is a buffer. As we learned in Chapter 6, we can calculate the pH of a
buffer using the Henderson–Hasselbalch equation.
-
[ A ]
K
pH = p a +log
[ HA]
9
The equilibrium constant for reaction 9.2 is large (K = K a /K w = 1.75 ´10 ), so we
can treat the reaction as one that goes to completion. Before the equivalence point,
the concentration of unreacted acetic acid is
moles unreacted CH COOH MV b b
a a -M V
3
[CH COOH] = =
3
total volume V a +V b
and the concentration of acetate is
moles NaOH added MV
bb
-
[CH COO ] = =
3
total volume V a +V b
For example, after adding 10.0 mL of NaOH the concentrations of CH 3 COOH and
–
CH 3 COO are
)
0
0
50
0
0
(.100 M )( . mL - (.100 M )( . mL )
10
[CH COOH] = = . 0 0667 M
3
0
0
50 . mL +10 . mL
(.100 M )( . mL )
10
0
0
[CH COO - ] = = . 0 0167 M
3
0
0
50 . mL +10 . mL
giving a pH of
0 0167
.
.
.
pH = 476 +log =416
.
0 0667
A similar calculation shows that the pH after adding 20.0 mL of NaOH is 4.58.
At the equivalence point, the moles of acetic acid initially present and the moles
of NaOH added are identical. Since their reaction effectively proceeds to comple-
–
tion, the predominate ion in solution is CH 3 COO , which is a weak base. To calcu-
–
late the pH we first determine the concentration of CH 3 COO .
0
moles CH COOH (.100 M )( . mL )
0
50
3
[CH COO - ] = = = . 0 0500 M
3
0
0
total volume 50 . mL +50 . mL
The pH is then calculated as shown in Chapter 6 for a weak base.