Chapter 10
Acid-Base Titrations
A solution containing pure
protein, with no other ions
present except H+ and OHderived from the protein and
water, is said to be isoionic.
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-.
(Ve(mL))(0.100 0 M) = (50.00 mL)(0.020 00 M)  Ve = 10.00 mL
mmol of HBr
at equivalence point
mmol of OHbeing titrated
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.
Region 1: Before the equivalence Point
Region 2: At the Equivalence Point
H2O = H+ + OHx
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.
Region 3: After the Equivalence Point
Volume of
excess H+
Initial
concentration
of H+
Dilution
factor
Total volume
of solution
pH = -log[H+] = 3.08
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 strongacid-strong-base titration. If one or both of the reactants are weak, the
equivalence point pH is not 7.00.
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.
(Vb(mL))(0.100 0 M) = (50.00 mL)(0.020 00 M)  Vb = 10.00 mL
mmol of base
mmol of HA
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
Ka
HA =
H+ + A-
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
A- + H2O
Kb
=
HA + OH-
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-.
Region 1: Before Base Is Added
HA = H+ + AF-x
x
x
Ka = 10-6.27
Region 2: Before the Equivalence Point
Titration reaction:
Relative initial quantities(HA = 1)
Relative final quantities
Once we know the quotient [A-]/[HA] in any solution, we know its pH:
Titration reaction:
Relative initial quantities
Relative final quantities
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 Na+A- is merely a solution of a weak base.
A- + H2O = HA + OH-
F-x
x
x
Kb = Kw/Ka
Initial volume
of HA
Initial
concentration
of HA
Dilution
factor
Total volume
of solution
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.
Region 4: After the Equivalence Point
Volume of
excess OH-
Initial
concentration
of OH-
Dilution
factor
Total volume
of solution
The Titration Curve
If you look back at Figure 94b, you will note that the
maximum buffer capacity
occurs when pH = pKa.
It is not practical to titrate an acid or base when its strength is too weak or its
concentration too dilute.
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.
Kb
B + H2O = BH+ + OHF-x
x
x
2. Between the initial point and the equivalence point, there is a mixture of B and
BH+ㅡAha! A buffer! The pH is computed by using
pH = pKa (for BH+) + log([B]/[BH+])
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+
F’ – x
x
x
Ka = Kw/Kb
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+.
10-4 Ttitrations in Diprotic Systems
A typical Case
B + H+  BH+
BH+ + H+  BH22+
(Ve(mL))(0.100 0 M) = (10.00 mL)(0.100 0 M)  Ve = 10.00 mL
mmol of HCl
mmol of B
Point A
B + H2O
0.100 - x
Kb1
=
BH+ + OHx
x
Point B
The pH is calculated from the Henderson-Hasselbalch 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
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.
Initial volume
of B
Original
concentration
of B
Dilution
factor
Total volume
of solution
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.
Point D
pH = pKa1 + log([BH+]/[BH22+]) = 5.00 + log1 = 5.00
PointE
Original volume
of B
Total volume
of solution
BH22+ = BH+ + H+
F-x
x
x
Ka1 = Kw/Kb2
[H+] = (0.100 M)(5.00/35.00) = 1.43 X 10-2 M  pH = 1.85
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.
Nicotine (B)
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-] + 2[CO32-] + [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.
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)
Using Derivatives to Find the End Point
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+]γH+[A-]γA-)/[HA]γHA
It will be necessary to include activity coefficients in this discussion because a
pH electrode responds to hydrogen ion activity, not concentration.
moles of OH- delivered
total volume
original moles of HA – moles of OHtotal volume
Gran plot equation:
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.
Challenge Show that when
weak base, B, is titrated with a
strong acid, the Gran function is
(11-6)
where Va is the volume of
strong acid and Ka is the acid
dissociation constant of BH+.
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.
K
R =1 Y- + H+
pH = pK1 + log([Y-]/[R])
pH
0.7
1.7
2.7
[Y-]:[R]
1:10
1:1
10:1
(11-7)
Color
red
orange
yellow
The pH range (1.2 to 2.8) over which the color changes is called the transition
range.
Choosing an Indicator
The difference between the observed end point (color change) and the true
equivalence point is called the indicator error.
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?
p-Nitroaniline
B
p-Nitroanilinium ion
BH+
(for BH+)
(for CH+)
(for CH+)
(for BH+)
The acidity of a solvent that protonates
the weak base, B, is defined as the
Hammett acidity function:
Hammett acidity
function:
(for BH+)
When we refer to negative pH, we
usually mean H0 values.
Acid
H2SO4(100%)
H2SO4 · SO3
Name
sulfuric acid
fuming sulfuric acid
(oleum)
HSO3F
fluorosulfuric acid
HSO3F + 10% SbF5
“super acid”
HSO3F + 7% SbF5 · 3SO3
ㅡ
H0
-11.93
-14.14
-15.07
-18.94
-19.35
In general, we seek an indicator whose
transition range overlaps the steepest
part of the titration curve as closely as
possible.
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
BOX 10-3 Kjeldahl Nitrogen Analysis Behind the Headlines
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-
HClO4 + CH3CO2H = CH3CO2H2+ + ClO4- K = 1.3 X 10-5
Acetic acid solvent
HCl + CH3CO2H = CH3CO2H2+ + ClTitration with HClO4 in H2O:
K = 2.8 X 10-9
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.
Titration with HClO4 in CH3CO2H:
B + HClO4 = BH+ClO4An ion pair
(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.)
10-10 Calculating Titration Curves with Spreadsheets
Titrating a Weak Acid with a strong Base
Charge balance:
Fraction of titration for
weak acid by strong base:
[H+] + [Na+] = [A-] + [OH-]
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 αA- = Ka/([H+] + Ka)
Kw = 10-14
is the input
is the output
Titrating a Weak Acid with a Weak Base
Charge balance:
[H+] + [BH+] = [A-] + [OH-]
[HA] = αHAFHA
αHA = [H+]/([H+] + Ka)
[BH+] = αBH · FB
αBH = [H+]/([H+] + KBH )
+
Fraction of titration for
weak acid by weak base:
+
+