1.
Finding the End Point with a Visual Indicator
Acid/Base Indicators
 Many naturally occurring and synthetic compounds exhibit colors that depend on the pH
of the solutions in which they are dissolved.
 An acid/base indicator is a weak organic acid or a weak organic base whose
undissociated form differs in color from its conjugate base or its conjugate acid form.
 For example, the behavior of an acid-type indicator, HIn, is described by the equilibrium

2.
Selecting and Evaluating the End Point
 The equivalence point occurs when stoichiometrically equal amounts of
analyte and titrant react.
 For example, if the analyte is a triprotic weak acid, a titration with NaOH
will have three equivalence points corresponding to the addition of one,
two, and three moles of OH– for each mole of the weak acid.
 An end point for a titration is determined experimentally and represents
the analyst’s best estimate of the corresponding equivalence point.

3.
Where Is the Equivalence Point?
 It has been shown that for most acid–base titrations the inflection point, which corresponds to
the greatest slope in the titration curve, very nearly coincides with the equivalence point.
 The principal limitation to using a titration curve to locate the equivalence point is that an
inflection point must be present. Sometimes, however, an inflection point may be missing or
difficult to detect.
 The inflection point is visible, for acid dissociation constants larger than 10-9, but is missing
when Ka is 10–11 (Smaller).

4.
 Another situation in which an inflection point may be missing or difficult to
detect occurs when the analyte is a multiprotic weak acid or base whose
successive dissociation constants are similar in magnitude.
 let’s consider the titration of a diprotic weak acid, H2A, with NaOH. During the
titration the following two reactions occur.

5.
• In general, separate inflection points are seen
when successive acid dissociation constants Differ
by a factor of at least 500.
Ka1 is approximately 20,000 times larger
than Ka2, shows two very distinct
inflection points.
dissociation constants that differ by
a factor of approximately 690.
Ka values differ by a factor of only 27,

6.
Locating Titration End Points from pH Measurements
 pH electrode and pH meter allow the direct measurement of pH as a function of
titrant volume.
The end point can be taken as the inflection point of the titration curve. With a
sigmoid-shape titration curve,
 The inflection point is the steepest part of the titration curve where the pH
change with respect to volume is a maximum.
 This point can be estimated visually from the plot. The first derivative, which is
approximately ▲pH/▲V, is the slope of the titration curve

7.
Figure 9.14d shows a typical
result. This method of data
analysis, which converts a
portion of a titration curve
into a straight-line, is a Gran
plot.

8.
Finding the End Point by Monitoring Temperature
• The reaction between an acid and a base is exothermic.
• Thermometric titration curve (Figure 6) consists of three distinct
linear regions.
• Before adding titrant, any change in temperature is due to the
cooling or warming of the solution containing the analyte.
• Titration branch - Adding titrant initiates the exothermic acid–base
reaction, resulting in an increase in temperature.
• After the equivalence point, any change in temperature is due to the
difference between the temperatures of the analytical solution and
the titrant.

9.
Figutre 7: Thermometric titration curves
showing curvature at the intersection of
the titration and excess titrant branches

10.
• Actual thermometric titration curves (Figure 7) frequently show
curvature at the intersection of the titration branch and the excess
titrant branch
• due to the incompleteness of the neutralization reaction, or
excessive dilution of the analyte during the titration
• The problem is minimized by using a titrant that is 10–100 times
more concentrated than the analyte,
• When the intersection between the two branches shows curvature,
the end point can be found by extrapolation (Figure 7).

11.
• For example, the titration of boric acid, H3BO3, for which Ka is 5.8 *
10–10
, yields a poorly defined equivalence point (Figure 8). The
enthalpy of neutralization for boric acid with NaOH, however, is only
23% less than that for a strong acid (–42.7 kJ/mol for H3BO3 versus –
55.6 kJ/mol for HCl), resulting in a favorable thermometric titration
curve (Figure 9).
Figure 9: Titration curves for 50.00 mL of 0.0100 M
H3BO3 with 0.100 M NaOH determined by
monitoring temperature.
Figure 8: Titration curves for 50.00 mL of 0.0100 M
H3BO3 with 0.100 M NaOH determined by
monitoring pH.

12.
Selecting and Standardizing a Titrant
• Most common acid–base titrants are not readily available as primary
standards and must be standardized
• Standardization is done by titrating a known amount of an appropriate
acidic or basic primary standard.
• The majority of titrations involving basic analytes, whether conducted
in aqueous or nonaqueous solvents, use HCl, HClO4, or H2SO4 as the
titrant.
• Since the concentrations of concentrated acids are known only
approximately, the titrant’s concentration is determined by
standardizing against one of the primary standard weak bases.