Quantitative Chemical Analysis 7e

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Chapter 10 Acid-Base Titrations
A solution containing pure protein, with no other
ions present except H and OH- derived from the
protein and water, is said to be isoionic.
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In medicinal chemistry, the pKa and lipophilicity
of a candidate drug predict how easily it will
cross cell membranes.
10-1 Titration of Strong Base with Strong Acid
Our goal is to construct a graph showing how the
pH canges as titrant is added.
The titration of 50.00 mL of 0.0200 M KOH with
0.1000 M HBr
H OH- ? H2O K 1/KW 1014
Any amount of H added will consume a
stoichiometric amount of OH-.
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1. Before the equivalence point, the pH is
   determined by excess OH- in the solution.
2. At the equivalence point, H is just sufficient
   to react with all OH- to make H2O.
3. After the equvalence point, pH is determined by
   excess H in the solution.

As a reminder, the equivalence point occurs when
the added titrant is exactly enough for
stoichometric reaction with the analyte. What we
actually measure is the end point, which is
marked by a sudden physical change, such as
indicator color or an electrode potential.
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Region 1 Before the equivalence Point
Region 2 At the Equivalence Point
H2O H OH-
x x KW x 2 ? x
1.00 X 10-7 M ? pH 7.00
As we will soon discover, the pH is not 7.00 at
the equivalence point in the tirtration of weak
acids or bases.
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Region 3 After the Equivalence Point
The Titration Curve
The equivalence point is where the slope
(dpH/dVa) is greatest ( and the second derivative
is 0, which makes it an inflection point). To
repeat an important statement, the pH at the
equivalence point is 7.00 only in a
strong-acid-strong-base titration. If one or both
of the reactants are weak, the equivalence point
pH is not 7.00.
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10-2 Titration of Weak Acid with Strong Base
The titration reaction is
As we saw in Box 9-3, strong plus weak react
completely.
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1. Before any base is added, the solution
contains just HA in water. This is a weak acid
whose pH is determined by the equilibrium
2. From the first addition of NaOH until
immediately before the equivalence point, there
is a mixture of unreacted HA plus the A- produced
by Reaction 11-2. Aha! A buffer! We can use the
Henderson-Hasselbalch equation to find the
pH. 3. At the equivalence point, all HA has
been converted into A-. The same solution could
have been made by dissolving A- in water. We have
a weak base whose pH is determined by the reaction
4. Beyond the equivalence point, excess NaOH is
being added to a solution of A-. To a good
approximation, pH is determined by the strong
base. We calculate the pH as if we had simply
added excess NaOH to water. We neglect the tiny
effect of A-.
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Region 1 Before Base Is Added
Region 2 Before the Equivalence Point
Once we know the quotient A-/HA in any
solution, we know its pH
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Advice As soon as you recognize a mixture of HA
and A- in any solution, you have a buffer! You
can calculate the pH from the quotient A-/HA.
Region 3 At the Equivalence Point
A solution of NaA- is merely a solution of a
weak base.
A- H2O HA OH- Kb
Kw/Ka F-x x x
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The pH at the equivalence point in this titration
is 9.25. It is not 7.00. The equivalence point pH
will always be above 7 for the titration of a
weak acid, because the acid is converted into its
conjugate base at the equivalence point.
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Region 4 After the Equivalence Point
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The Titration Curve
If you look back at Figure 9-4b, you will note
that the maximum buffer capacity occurs when pH
pKa.
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It is not practical to titrate an acid or base
when its strength is too weak or its
concentration too dilute.
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10-3 Titration of Weak Base with Strong Acid
The titration of a weak base with a strong acid
is just the reverse of the titration of a weak
acid with a strong base. The titration reaction is
B H BH
1. Before acid is added, the solution contains
just the weak base, B, in water. The pH is
determined by the Kb reaction.
2. Between the initial point and the equivalence
point, there is a mixture of B and BH?Aha! A
buffer! The pH is computed by using
pH pKa (for BH) log(B/BH)
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3. At the equivalence point, B has been converted
into BH, a weak acid. The pH is calculated by
considering the acid dissociation reaction of BH.
BH B H Ka Kw/Kb
F x x x
The pH at the equivalence point must be below
7. 4. After the equivalence point, the excess
strong acid determines the pH. We neglect the
contribution of weak acid, BH.
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10-4 Ttitrations in Diprotic Systems
A typical Case
B H ? BH BH H ? BH22
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Point A
Point B
The pH is calculated from the Henderson-Hasselbalc
h equation for the weak acid, BH, whose acid
dissociation constant is Ka2 (for BH22) Kw/Kb1
10-10.00
pH pKa2 log(B/BH) 10.00 log1 10.00
B/BH 8.5/1.5
pH 10.00 log(8.5/1.5) 10.75
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Point C
At the first equivalence point, B has been
converted into BH, the intermediate form of the
diprotic acid, BH22. BH is both an acid and a
base.
This is the least-buffered point on the whole
curve, because the pH changes most rapidly if
small amounts of acid or base are added. There is
a misconception that the intermediate form of a
diprotic acid behaves as a buffer when, in fact,
it is the worst choice for a buffer.
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Point D
pH pKa1 log(BH/BH22) 5.00 log1
5.00
PointE
BH22 BH H Ka1
Kw/Kb2 F-x x x
H (0.100 M)(5.00/35.00) 1.43 X 10-2 M ? pH
1.85
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Blurred End Points
Titrations of many diprotic acids or bases show
two clear end points, as in curve a in Figure
11-4. Some titrations do not show both end
points, as illustrated by curve b, which is
calculated for the titration of 10.0 mL of 0.100
M nicotine (pKb1 6.15, pKb2 10.85) with 0.100
M HCl.
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10-5 Finding the End Point with a pH Electrode
Box 10-1 Alkalinity and Acidity
Alkalinity is defined as the capacity of natural
water to react with H to reach pH 4.5, which is
the second equivalence point in the titration of
carbonate (CO32-) with H.
Alkalinity OH- 2CO32- HCO3-
Alkalinity and hardness (dissolved Ca2 and Mg,
Box 12-3) are important characteristics of
irrigation water. Acidity of natural waters
refers to the total acid content that can be
titrated to pH 8.3 with NaOH.
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Figure 2-12 shows an autotitrator, which performs
the entire operation automatically.4 Figure
11-6a shows two clear breaks, near 90 and 120 µL,
which correspond to titration of the third and
fourth protons of H6A.
H4A2- OH- ? H3A3- H2O (90µL equivalence
point) H3A3- OH- ? H2A4- H2O (120µL
equivalence point)
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Using Derivatives to Find the End Point
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Using a Gran Plot to Find the End Point7,8
Gran plot uses data from before the end point
(typically from 0.8 Ve or 0.9 Ve up to Ve) to
locate the end point.
HA H A- Ka (H?HA-?A-)/HA?HA
It will be necessary to include activity
coefficients in this discussion because a pH
electrode responds to hydrogen ion activity, not
concentration.
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A graph of Vb10-pH versus Vb is called a Gran
plot. The beauty of a Gran plot is that it
enables us to use data taken before the end point
to find the end point.
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Challenge Show that when weak base, B, is
titrated with a strong acid, the Gran function is
where Va is the volume of strong acid and Ka is
the acid dissociation constant of BH.
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10-6 Finding the End Point with Indicators
An acid-base indicator is itself an acid or base
whose various protonated species have different
colors.
The pH range (1.2 to 2.8) over which the color
changes is called the transition range.
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Choosing an Indicator
The difference between the observed end point
(color change) and the true equivalence point is
called the indicator error.
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Demonstration 10-1 Indicators and the Acidity of
CO2
Add 20 mL of 6 M HCl to the bottom of each
cylinder, using a length of Tygon tubing attached
to a funnel.
Box 10-2 What Does a Negative pH Mean?
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The acidity of a solvent that protonates the weak
base, B, is defined as the Hammett acidity
function
When we refer to negative pH, we usually mean H0
values.
In general, we seek an indicator whose transition
range overlaps the steepest part of the titration
curve as closely as possible.
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10-7 Practical Notes
Acids and bases in Table 11-5 can be obtained
pure enough to be primary standards.17
OH- CO2 ? HCO3-
10-8 Kjeldahl Nitrogen Analysis
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BOX 10-3 Kjeldahl Nitrogen Analysis Behind the
Headlines
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10-9 The Leveling Effect
The strongest acid that can exist in water is
H3O and the strongest base is OH-. Because of
this leveling effect, HClO4 and HCl behave as if
they had the same acid strength both are leveled
to H3O
HClO4 H2O ? H3O ClO4- HCl H2O ? H3O
Cl-
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HClO4 CH3CO2H CH3CO2H2 ClO4- K 1.3 X
10-5 Acetic acid solvent HCl
CH3CO2H CH3CO2H2 Cl- K 2.8 X
10-9
Titration with HClO4 in H2O B H3O BH
H2O
The end point cannot be recognized, because the
equilibrium constant for the titration reaction
is not large enough. If an acid stronger than
H3O were available, the titration reaction might
have an equilibrium constant large enough to give
a distinct end point.
(The product in this reaction is written as an
ion pair because the dielectric constant of
acetic acid is too low to allow ions to separate
extensively.)
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10-10 Calculating Titration Curves with
Spreadsheets
Titrating a Weak Acid with a strong Base
Charge balance H Na A- OH-
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We put in a concentration of H and get out the
volume of titrant that produces that
concentration.
Cb 0.1 H 10-pH Ca 0.02 OH-
Kw/H Va 50 Ka 5.37 X 10-7 aA-
Ka/(H Ka) Kw 10-14
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Titrating a Weak Acid with a Weak Base
Charge balance H BH A- OH-
HA aHAFHA aHA H/(H Ka)
BH aBH FB aBH H/(H KBH)