A common end point for acid-base titrations is the color change associated with
an acid-base indicator. An acid-base indicator is usually an organic weak acid or base
that has a different color in solution than its conjugate form. These substances strongly
absorb light so that even a very small concentration in solution produces an obvious
color. If the weak acid form of the indicator is taken as HIn
so do the relative amounts of the different colored
conjugate species in solution. Thus, the indicator in solution will take on a specific color
depending upon the solution pH.
As an example, consider the acid-base indicator methyl orange indicator. The
weak acid form is red in solution while the conjugate base form is yellow (that is, HIn =
red and In- = yellow). In order to anticipate the pH range in which this indicator changes
from yellow to red, or vice versa, assume that a 10-fold excess of one colored form over
the other is needed to establish the color of one of the conjugate pairs. Thus, to see
predominately yellow in solution,
In a similar way it can be shown that the red color dominates when the solution pH is
about equal to pKa
- 1. Therefore, an indicator color change is expected in a pH range
equal to pKa
± 1. The pKa
for methyl orange is 3.46, so it should change from red to
yellow as the pH increases from about 2.5 to 4.5.
.
Consequently, knowledge of the pH at the equivalence point allows one to select
an indicator that will undergo a color change in a pH range that brackets the
equivalence point pH.
Polyprotic Acid and Base Titrations
The titration of a polyprotic acid or base is very similar to that for a monoprotic
weak acid or base except that more than one equivalence point is observed. The
maleic acid experiment in lab involves such a titration. The titration curve for the
titration of 50.0 mL of 0.100 M Na2
CO3
with 0.100 M HCl is shown in Figure 9.5. Since
the analyte and titrant concentrations are the same, the first equivalence point occurs at
50 mL and the second one occurs at 100 mL.
Figure 9.5 Curve for the titration of Na2
CO3
with a HCl(aq)Acid-Base Titrations 10/11/12
page 4
Check for Understanding 9.4 Solutions
1. Estimate the pH at the second equivalence point in the carbonate titration.
2. Which indicators are suitable for use at the first and second equivalence
points in the carbonate titration?
The titration reaction to the first equivalence point involves neutralization of the
weak base carbonate.
CO3
2- + H3
O
+
6 HCO3
-
+ H2
O
As this process occurs, a CO3
2-/HCO3
-
buffer is formed. The region before the first
equivalence point where the pH is changing slowly with added titrant corresponds to this
first buffer region. Throughout this portion of the titration pH ~ pKa
and at the halfway
point (25 mL), pH = pKa
= 10.33. Note that the Ka
is that for the weak acid in the buffer,
that is, HCO3
-
, which corresponds to Ka2 for H2
CO3
.
At the first equivalence point, all the CO3
2- has been converted to HCO3
-
and
additional titrant starts neutralizing the bicarbonate.
HCO3
-
+ H3
O
+
6 H2
CO3
+ H2
O
As this process occurs, a HCO3
-
/H2
CO3
buffer is formed. The region between the first
and second equivalence points where the pH is changing slowly with added titrant
corresponds to this second buffer region. Throughout this portion of the titration pH ~
pKa
and halfway between the first and second equivalence points (75 mL), pH = pKa
=
6.35. Here Ka
is that for the weak acid H2
CO3
and is thus Ka1 for carbonic acid.
An estimate of each equivalence point pH can be made as before by taking the
average of the pH plateau values before and after the equivalence point. For the first
equivalence point pH ~ (10.33 + 6.35)/2 = 8.3.
Because the pH jump at either equivalence point in the carbonate titration is not
very large, an indicator color change is not a very sharp end point. An indicator color
match can be used instead as the end point. For this to be a valid end point, the
indicator must have the same color in the comparison solution as it has in the titrationAcid-Base Titrations 10/11/12
page 5
Check for Understanding 9.5 Solution
1. What is the pH at the second equivalence point in the titration of Na2
CO3
with
0.100 M HCl? Use activities and assume a 0.200-g sample of Na2
CO3
is
dissolved in 60.0 mL of deionized water and titrated.
solution at the second equivalence point. This is true only if the pH of the comparison
solution is the same as the pH at the second equivalence point. Previously you have
calculated, using activities, the pH of a CO3
2-/HCO3
-
buffer solution that is suitable for
use as a comparison solution for the carbonate titration, and above you have estimated
the pH at the second equivalence point. To make a more careful comparison of pH,
make the following calculation of the second equivalence point pH.
Gran Plots
For the maleic acid experiment, you will use a graphical method known as a
Gran plot to determine the second equivalence point in your titration. In this approach,
the pH of your maleic acid solution is recorded as a function of the volume of added
base (Vb
) and a graph of Vb
@10-pH versus Vb
is made using data just before the
equivalence point. Assuming that the ionic strength of the solution is constant, the xintercept of this linear plot is the equivalence point volume (Ve
). An example of a Gran
plot is shown below. Derivation of relationship used for Gran plot
Figure 9.6 Gran plot for a weak acid-strong
base titration
© 2011 W. H. Freeman and CompanyAcid-Base Titrations 10/11/12
page 6
The ionic strength of the maleic acid solution is fixed by adding a large amount of
KCl to the titration solution. The key advantage of using a Gran plot is that the
equivalence point can be determined by using only data before the equivalence point
(typically the data between 0.9Ve
and Ve
). The slope of the Gran plot also allows one to
determine the Ka
of the weak acid (for a weak acid-strong base titration, slope = - Ka
γ
HA /γ
A-).
Exercises for Acid-Base Titrations
