Chapter 12: Principles of Neutralization Titrations
Solutions and Indicators Used

Standard Solutions: strong acids or strong bases because they will react completely
o Acids: hydrochloric (HCl), perchloric (HClO4), and sulfuric (H2SO4)
o Bases: sodium hydroxide (NaOH), potassium hydroxide (KOH)

Acid/Base Indicators: a weak organic acid or weak organic base whose undissociated
form differs in color from its conjugate form (In would be indicator):
HIn + H2O
 In- + H3O
(acid color)
(base color)
In + H2O
 HIn+ + OH-
(base color)
(acid color)
or
Ka = [H3O+][In-]
[HIn]

[H3O+] = Ka[HIn]
[In-]
o HIn pure acid color: [HIn]/[In-] ≥ 10, HIn pure base color: [HIn]/[In-] ≤ 0.1.
~The ratios change from indicator to indicator~
o Substitute the ratios into the rearranged Ka:
[H3O+] = 10Ka
[H3O+] = 0.1Ka
(acid color)
(base color)
o pH range for indicator = pKa ± 1
acid color pH = -log(10Ka) = pKa + 1
base color pH = -log(0.1Ka) = pKa – 1

Variables: temperature, ionic strength of medium and presence of organic solvents or
colloidal particles

Common Acid/Base Indicators
Indicator
Thymol Blue
pH Range
1.2-2.8
Acid
red
Base
yellow
Thymol blue
8.0-9.6
yellow
blue
Methyl yellow
2.9-4.0
red
yellow
Methyl orange
3.1-4.4
red
orange
Bromcresol green
4.0-5.6
yellow
blue
Methyl red
4.4-6.2
red
yellow
Bromcresol purple 5.2-6.8
yellow
purple
Bromothymol Blue 6.2-7.8
yellow
blue
Phenol red
6.4-8.0
yellow
red
Cresol purple
7.6-9.2
yellow
purple
Phenolphthalein
8.0-10.0
colorless red
Thymolphthalein
9.4-10.6
colorless blue
Alizarin yellow GG 10.0-12.0 colorless yellow
Calculating pH in Titrations of Strong Acids and Strong Bases
In a solution of a strong acid that is more concentrated than about 1x10-6, we can assume
that [H3O+] = [acid]  same is true for [base] = [OH-]

Titrating a Strong Acid with a Strong Base (hypothetical titration curves of pH versus
volume of titrant)
1. Preequivalence: calculate the concentration of the acid from is starting
concentration and the amount of base that has been added, the concentration
of the acid is equal to the concentration of the hydroxide ion and you can
calculate pH from the concentration
2. Equivalence: the hydronium and hydroxide ions are present in equal
concentrations
3. Postequivalence: the concentration of the excess base is calculated and the
hydroxide ion concentration is assumed to be equal to or a multiple of the
analytical concentration, the pH can be calculated from the pOH
Ex.: Do the calculations needed to generate the hypothetical titration curve for the
titration of 50.00 mL of 0.0500 M HCl with 0.1000 M NaOH
1. Initial Point: the solution is 0.0500 M in H3O+, so pH = -log(.0500) = 1.30
2. Preequivalence Point (after addition of 10 mL reagent)
CHCl = mmol remaining (original mmol HCl – mmol NaOH added)
total volume (mL)
= (50.0 mL x 0.0500 M) – (10.00 mL x 0.1000 M)
50.0 mL + 10.00 mL
= 2.500 x 10 -2 M
pH = -log(2.500 x 10-2) = 1.602
3. Equivalence Point
[OH-] = [H3O+], pH = 7
4. Postequivalence Point (after addition of 25.10 mL reagent)
CHCl = mmol NaOH added – original mmol HCl
total volume solution
= (21.10 mL x 0.1000 M) – (50.00 mL x 0.0500 M)
50.0 mL + 25.10 mL
= 1.33 x 10-4 M
pOH = -log(1.33 x 10-4) = 3.88
pH = 14 – pOH = 10.12
o Concentrations: with a higher concentration titrant (0.1 M NaOH versus 0.001 M
NaOH), the change in pH equivalence-point region is large
o Choosing an indicator: you need to choose an indicator that has a color change in
the same range as your equivalence point

Titrating a Strong Base with a Strong Acid (hypothetical titration curves): similar to
those for strong acids, but opposite

Preequivalence: calculate the concentration of the base from is starting
concentration and the amount of acid that has been added, the concentration of
the base is equal to the concentration of the hydronium ion and you can
calculate pOH from the concentration, and then the pH

Equivalence: the hydronium and hydroxide ions are present in equal
concentrations, so the pH is 7

Postequivalence: the concentration of the excess acid is calculated and the
hydronium ion concentration is the same as the concentration of the acid, and
the pH can be calculated
Buffer Solutions
Buffer: a mixture of a weak acid and its conjugate base or a weak base and its conjugate
acid that resists changes in pH of a solution

Calculating pH of Buffer Solutions
HA + H2O  H3O+ + A-
Ka = [H3O+][A-]
[HA]
A- + H2O  OH- + HA
Kb = [OH-][HA]
[A-]
Mass-Balance Equation for [HA]: [HA]=cHA – [H3O+] + [OH-]
Mass-Balance Equation for [A-]: [A-] = cNaA + [H3O+] – [OH-]

[HA] ≈ cHA
[A-] ≈ cNaA
*we can eliminate the rest of the mass-balance equations
because of the inverse relationship between the hydronium
and the hydroxide ion, as well as because the difference in
concentration is so small relative to the concentrations of
the acid and conjugate base*
If we substitute the concentration equations for [HA] & [A-] into the dissociation constant
expression, we get
[H3O+] = Ka cHA
cNaA
*the hydronium ion concentration is dependent only on the
ratio of the molar concentrations of the weak acid and its
conjugate base, and is independent of dilution because the
molar concentrations change proportionately*
o Buffers Formed from a Weak Acid and Its Conjugate Base
Ex.: What is the pH of a solution that is 0.400 M in formic acid and 1.00 M in sodium
formate?
HCOOH + H2O  H3O+ + HCOOHCOO- + H2O  HCOOH + OH-
Ka = 1.80 x 10-4
Kb = Kw/Ka = 5.56 x 10-11

[HCOO-] ≈ cHCOO- = 1.00 M
[HCOOH] ≈ cHCOOH = 0.400 M
[H3O+] = (1.80 x 10-4) (0.400) = 7.20 x 10-5
(1.00)
pH = -log(7.20 x 10-5) = 4.14
o Buffers Formed from a Weak Base and its Conjugate Acid
Ex.: Calculate the pH of a solution that is 0.200 M in NH3 and 0.300 M in NH4Cl.
NH4+ + H2O  NH3 + H3O+
NH3 + H2O  NH4+ + OH-
Ka = 5.70 x 10-10
Kb = Kw/Ka = 1.75 x 10-5

[NH4+] ≈ cNH4Cl = 0.300 M
[NH3] ≈ cNH3 = 0.200 M
[H3O+] = (5.70 x 10-10) (0.300) = 8.55 x 10-10
(0.200)
pH = -log(8.55 x 10-10) = 9.07

What are the unique properties of buffer solutions?
o Dilution: the pH of a buffer solution is essentially independent of dilution until
the concentrations of the species are decreased to the point so that we cannot
assume that the differences between the hydronium and hydroxide ion
concentrations is negligible when calculating the concentration of the species
o Added Acids and Bases: buffers are resistant to pH change after addition of small
amounts of strong acids or bases
o Buffer Capacity: The number of moles of strong acid or strong base that causes
one liter of the buffer to change pH by one unit

The higher the buffer concentration, the smaller the change in pH when an
acid or base is added

Ex.: Calculate the pH change that takes place when a 100 mL portion of
0.0500 M NaOH is added to a 400 mL buffer consisting of 0.2 M NH3 and 0.3
M NH4Cl (see example for “Buffers Formed from a Weak Base and its
Conjugate Acid”).
An addition of a base converts NH4+ to NH3: NH4+ + OH-  NH3 + H2O
The concentration of the NH3 and NH4Cl change:
cNH3 = original mol base + mol base added
total volume
cNH3 = (400 x 0.200) + (100 x 0.300) = 0.170 M
500
cNH4Cl = original mol acid – mol base added
total volume
cNH3 = (400 x 0.300) + (100 x 0.300) = 0.230 M
500
[H3O+] = (5.70 x 10-10) (0.230) =7.71 x 10-10
(0.170)
pH = -log(7.71 x 10-10) = 9.11
∆pH = 9.11 – 9.07 = 0.04
o Preparing Buffers (in principle the calculations work, but there are uncertainties in
numerical values of dissociation constants & simplifications used in calculations)

Making up a solution of approximately the desired pH and then adjust by
adding acid or conjugate base until the required pH is indicated by a pH meter

Empirically derived recipes are available in chemical handbooks and
reference works

Biological supply houses
Calculating pH in Weak Acid (or Base) Titrations
o Steps
a. At the beginning: pH is calculated from the concentration of that solute
and its dissociation constant
b. After various increments of titrant has been added: pH is calculated by the
analytical concentrations of the conjugate base or acid and the residual
concentrations of the weak acid or base
c. At the equivalence point: the pH is calculated from the concentration of
the conjugate of the weak acid or base ~ a salt
d. Beyond the equivalence point: pH is determined by the concentration of
the excess titrant
o The Effect of Concentration: the change in pH in the equivalence-point region
becomes smaller with lower analyte and reagent concentrations
o The Effect of Reaction Completeness: pH change in the equivalence-point region
becomes smaller as the acid become weaker (the reaction between the acid and
the base becomes less complete)
o Choosing an Indicator: the color change must occur in the equivalence-point
region
Ex.: Determine the pH for the titration of 50.00 mL of 0.1000 M acetic acid after adding
0.00, 5.00, 50.00, and 50.01 mL of 0.100 M sodium hydroxide
HOAc + H2O  H3O+ + OAcOAc- + H2O  HOAc + OHKa = 1.75 x 10 -5
1) Starting Point:
[H3O+] = 1.32 x 10-3
pH = -log(1.32 x 10-3) = 2.88
2) After Titrant Has Been Added (5.00 mL NaOH):
*the buffer solution now has NaOAc & HOAc*
cHOAc = mol original acid – mol base added
total volume
cHOAc = (50.00 x 0.100) – (5.00 x 0.100) = 0.075
60.0
cNaOAc = mol base added
total volume
cNaOAc = (5.00 x 0.100) = 0.008333
60.0
*we can then substitute these concentrations into the
dissociation-constant expression for acetic acid*
Ka = [H3O+][OAc-]
[HOAc]
Ka = 1.75 x 10-5 = [H3O+][0.008333]
[0.075]
[H3O+] = 1.58 x 10-4
pH = -log(1.58 x 10-4) = 3.80
3) Equivalence Point (50.00 mL NaOH):
*all the acetic acid has been converted to sodium acetate*
[NaOAc]= 0.0500 M
*we can substitute this in to the base-dissociation constant
for OAc-*
Kb = [OH-][HOAc] = Kw
[OAc-]
Ka
[HOAc] = [OH-]

[OH-]2 = 1.00 x 10-14
0.0500
1.75 x 10-5
[OH-] = 5.34 x 10-6
pH = 14.00 – (-log(5.34 x 10-6))
pH = 8.73
4) Beyond the Equivalence Point (50.01 mL NaOH):
*the excess base and acetate ion are sources of the
hydroxide ion, but the acetate ion concentration is so small
it is negligible*
[OH-] = cNaOH = mol base added – original mol acid
total volume
[OH-] = (50.01 x 0.100) – (50.00 x 0.100)
100.01
[OH-] = 1.00 x 10-5
pH = 14.00 – (-log(1.00 x 10-5))
pH = 9.00
How Do Buffer Solutions Change as a Function of pH?
o Alpha values: the relative equilibrium concentration of the weak acid/base and its
conjugate base/acid (titrating with HOAc with NaOH):
*at any point in a titration, cT = cHOAc + cNaOAc*
α0 = [HOAc]
cT
α1 = [OAc-]
cT
*alpha values are unitless and are equal to one*
α0 + α1 = 1

Derivations
*alpha values depend only on [H3O+] and Ka, not cT*
*mass-balance requires that cT = [HOAc] + [OAc-]*
o For α0, we rearrange the dissociation-constant expression to:
[OAc-] = Ka[HOAc]
[H3O+]
*substitute mass-balance into the dissociation-constant expression*
α0 = [HOAc] = [H3O+]
cT
[H3O+] + Ka
o For α1, we rearrange the dissociation-constant expression to:
[HOAc] = [H3O+] [OAc-]
Ka
*substitute mass-balance into the dissociation-constant expression*
α1 = [OAc-] = _____Ka________
cT
[H3O+] + Ka