Introduction To Analytical Chemistry

Introduction to
Analytical Chemistry
Chapter 6
Titrations: Taking Advantage of
Stoichiometric Reactions
Copyright©2011 Cengage Learning

Titrations: Taking Advantage
of Stoichiometric Reactions
• Titrimetry includes a group of analytical
methods based on determining the quantity
of a reagent of known concentration that is
required to react completely with the analyte.
• Volumetric titrimetry is a type of titrimetry in
which the standard reagent is measured
volumetrically.
4-2
Volumetric titrimetry involves measuring
the volume of solution of known
concentration that is needed to react
essentially completely with the analyte.
• Gravimetric Titrimetry differs from volumetric
titrimetry in that the amount of solution added
to complete the reaction is measured by mass
rather than by volume.
4-3
Titrations: Taking Advantage
of Stoichiometric Reactions
• Coulometric titrimetry is a type of titrimetry in
which the quantity of charge in coulombs
required to complete a reaction with the analyte
is measured.
Coulometric titration is an absolute
determination technique in which the mass of a
given substance is determined by measuring the
quantity of electricity required to electrolyze that
substance.
4-4
6A-1 Defining Some Terms
• A standard solution is a reagent of known
concentration that is used in a titrimetric analysis.
• Titration is a process in which a standard reagent
is added to a solution of an analyte until the
reaction between the analyte and reagent is
judged to be complete.
(Lesson 1 Principles of Volumetric Analysis )
4-5
6A-1 Defining Some Terms
• Back-titration is a process in which the excess
of a standard solution used to consume an
analyte is determined by titration with a
second standard solution.
• Back-titrations are often required when the
rate of reaction between the analyte and
reagent is slow or when the standard solution
lacks stability.
4-6
6A-2 Equivalence Points and
End Points
• The equivalence point of a titration cannot be
determined experimentally.
• The equivalence point is the point in a titration
when the amount of added standard reagent is
equivalent to the amount of analyte.
• The difference in volume or mass between the
equivalence point and the end point is the
titration error.
4-7
6A-2 Equivalence Points and
End Points
• Indicators are often added to the analyte
solution to give an observable physical change
(the end point) at or near the equivalence
point.
• The end point is the point in a titration when a
physical change occurs that is associated with
the condition of chemical equivalence.
4-8
6A-3 Primary Standards
• A primary standard is a highly purified
compound that serves as a reference material
in all volumetric and mass titrimetric methods.
• Important requirements for a primary
standard are
− 1.High purity (established methods for confirming
purity should be available)
− 2. Atmospheric stability
4-9
− 3. Absence of hydrate water so that the
composition of the solid does not change
with variations in relative humidity
− 4. Ready availability at modest cost
− 5. Reasonable solubility in the titration medium
− 6. Reasonably large molar mass so that the
relative error associated with weighing the
standard is minimized
4-10
• A secondary standard is a compound whose
purity has been established by chemical
analysis and that serves as the reference
material for a titrimetric method of analysis.
4-11
6B-1 Desirable Properties of Standard
Solutions
• The ideal standard solution for a titrimetric
method will
− 1. Be sufficiently stable so that it is only necessary to
determine its concentration once
− 2. React rapidly with the analyte so that the time required
between additions of reagent is minimized
− 3. React completely with the analyte so that satisfactory
end points are realized
− 4. Undergo a selective reaction with the analyte that can
be described by a balanced equation
4-12
6B-2 Establishing the Concentration
of Standard Solutions
• Two basic methods are used to establish the
concentration of such solutions.
• The first is the direct method in which a
carefully weighed quantity of a primary
standard is dissolved in a suitable solvent and
diluted to a known volume in a volumetric
flask.
4-13
• The second is by standardization in which the
titrant to be standardized is used to titrate (1)
a weighed quantity of a primary standard, (2)
a weighed quantity of a secondary standard,
or (3) a measured volume of another standard
solution.
4-14
• A titrant that is standardized against a secondary
standard or against another standard solution is
sometimes referred to as a secondary standard
solution. The concentration of a secondary standard
solution is subject to a larger uncertainty than that
for a primary standard solution. Thus, if there is a
choice, solutions are best prepared by the direct
method. On the other hand, many reagents lack the
properties required for a primary standard and
therefore require standardization
4-15
6B-3 Expressing the Concentration
• The concentrations of standard solutions are
generally expressed in units of either molarity
c or normality cN .
4-16
6C-1 Some Useful Algebraic Relationships
(6-1)
(6-2)
4-17
6C VOLUMETRIC CALCULATIONS
(6-3)
(6-4)
4-18
6C-3 Treating Titration Data
• Calculating Molarities from Standardization
Data
4-19
6C-3 Treating Titration Data
• Calculating the Quantity of Analyte from
Titration Data
– Titration curves are plots of a concentration-
related variable as a function of reagent volume.
4-20
Example 6-6
• A 0.8040-g sample of an iron ore is dissolved in acid.
The iron is then reduced to Fe²⁺ and titrated with
47.22 mL of 0.02242 M KMnO₄ solution. Calculate
the results of this analysis in terms of (a) % Fe
(55.847 g/mol) and (b) % Fe₃O₄(231.54 g/mol). The
reaction of the analyte with the reagent is described
by the equation
4-21
Example 6-6
• The mass of Fe²⁺is then given by
4-22
Example 6-6
• The percent Fe²⁺ is
• (b) To determine the correct stoichiometric

ratio, we note that
4-23
Example 6-6
• Therefore,
• and
4-24
Example 6-6
• As in part (a),
4-25
Calculations Involved during Titration
1.Recall what you have learned in Stoichiometry and use the following guide:
4-26
Example 6-6
Titration data: 47.22 mL of 0.02242 M KMnO4
Wt. sample = 0.8040
g Fe = 47.22 mL KMnO4 x 0.02242 mmol/mL KMnO4
x 5mmol Fe___ x 55.847 g Fe x 1 mol____
1mmol KMnO4 1 mol 1000 mmol
g Fe = 0.29562 g
% Fe = 0.29562 g x 100 % = 36.77 %
0.8040 g
4-27
Calculations Involved during Titration
• If concentration of solutions are in Normality, recall what you have

learned on concentration units
4-28
6D Titration Curves
• The two most widely used end points involve
(1) changes in color due to the reagent, the
analyte, or an indicator and (2) a change in
potential of an electrode that responds to the
concentration of the reagent or the analyte.
4-29
Figure 6-1
Figure 6-1 Two types of titration
curves.
4-30
6D-1 Types of Titration Curves
• A sigmoidal curve,important observations are
confined to a small region (typically ± 0.1 to
± 0.5 mL) surrounding the equivalence point.
• Linear segment curve, measurements are
made on both sides of but well away from the
equivalence point. Measurements near
equivalence are avoided.
4-31
Figure 6-2
Figure 6-2
Titration curves
of pH and pOH
versus volume
of base for the
titration of
0.1000 M HCl
with 0.1000 M
NaOH.
4-32
Types of Volumetric Titrimetry
Volumetric analyses are classified according to the types of

reactions which the analytes and titrants undergo.
1.Neutralization Methods – Acidimetry/Alkalimetry
Acidimetry – method in which an acidic substance is titrated
with a standard solution of an alkali (ex. Determination of
the Acetic acid content of Vinegar)
Alkalimetry – method in which a basic substance is titrated
with a standard solution of an acid ( ex. Determination of
the Total Alkaline strength of Pearl ash)
4-33
Types of Volumetric Titrimetry
2. Oxidation-Reduction Methods
A reducing substance is titrated with a standard solution of an
oxidizing agent, or an oxidizing substance is titrated with a
standard solution of a reducing agent. (Permanganimetry;
Iodimetry/Iodometry; Dichromate Process; Ceric Process)
3. Precipitation Methods
A substance is titrated by precipitating it with a standard
solution of a precipitating agent.
4. Complex-ion Formation Methods
A substance is titrated with a standard reagent to the formation
of a complex ion.
4-34
Lesson 2 Neutralization Titration
• An acid-base titration is used to determine the unknown
concentration of an acid or base by neutralizing it with an acid or
base of known concentration (standard solutions).
• Standard Solutions for neutralization titrations are always

prepared from strong acids and strong base. Acid solutions are
commonly prepared from
 HCl
 HClO4
 H2SO4,
(Lesson 2 Acid-base Titration)
4-35
Neutralization Titration
Base solutions are commonly prepared from
 NaOH
 KOH.
 Ba(OH)2

•The concentrations of these solutions must be established by
standardization. Weak acids and weak bases are never used as
standard reagents because they react incompletely with analytes.
4-36
• Standardization is the process of determining the exact
concentration of a solution by reacting it with a known
quantity of a primary or a secondary standard substance. The
primary standards for the standardization of the prepared acid
solutions are
 sodium carbonate (Na2CO3).
 tris-(hydroxymethyl)aminomethane (HOCH2)3CNH2 also
known as TRIS or THAM
 sodium tetraborate decahydrate Na2B4O7.10H2O.
4-37
• For standardization of the base solutions, the primary
standards are
 potassium hydrogen phthalate KHC8H4O4
 benzoic acid
 potassium hydrogen iodate, KH(IO3)2
4-38
Types of Acid-Base titrations
4-39
• Acid-base indicators are substances which change colour or
develop turbidity at a certain pH. They locate equivalence
point and also measure pH. They are themselves acids or bases
and are soluble, stable and show strong colour changes. They
are organic in nature.
For additional information on titration curves and choice of indicators for specific type
of titration, please read
• https://byjus.com/chemistry/acid-base-titration/
•
https://courses.lumenlearning.com/boundless-chemistry/chapter/acid-base-titrati
ons/
4-40
Sample Problem
4-41
Sample Problem
4-42
4-43
4-44
Example 6-6
Titration data: 47.22 mL of 0.02242 M KMnO4
Wt. sample = 0.8040
Calculate % Fe
From the formula N = n x M, where n = no of electrons lost
N = 5 x 0.02242 M KMnO4 = 0.1121 N
% Fe = V KMnO4 x N KMnO4 x MEW Fe x 100 %
wt of sample
% Fe = 47.22 mL x 0.1121 meq/mL x 55.847 g/1000 meq x 100 %

0.8040 g
= 36.77 %
4-45
Lesson 3 Reduction-Oxidation Titration
• Redox Titration is a laboratory method of determining the

concentration of a given analyte by causing a redox reaction
between the titrant and the analyte (or titrand). These types of
titrations sometime require the use of a potentiometer or a
redox indicator. Recall what you have learned about redox
reactions.
4-46
Selecting and Standardizing a Titrant
• If a titrant is to be used quantitatively, it’s concentration must

remain stable during the analysis. Because a titrant in a reduced
state is susceptible to air oxidation, most redox titrations use an
oxidizing agent as the titrant. There are several common
oxidizing titrants, including MnO4─, Ce4+, Cr2O7-2 , and I3-.
• Which titrant is used often depends on how easily it oxidizes

the titrand. A titrand that is a weak reducing agent needs a
strong oxidizing titrant if the titration reaction is to have a
suitable end point.
4-47
Selecting and Standardizing a Titrant
• The two strongest oxidizing titrants are MnO4─ and Ce4+, for

which the reduction half-reactions are
MnO4−(aq) + 8H+(aq) + 5e− ⇌ Mn+2(aq) + 4H2O(l)
Ce+4(aq) + e− ⇌ Ce+3(aq)
• An oxidizing titrant such as MnO4−, Ce4+, Cr2O7 2−, and I3−, is

used when the titrand is in a reduced state. If the titrand is in
an oxidized state, it can be reduce first with an auxiliary
reducing agent and then complete the titration using an
oxidizing titrant.
4-48
Adjusting the Titrand's Oxidation State
• The titrand initially must be present in a single oxidation state.
Ex: Determination of Fe by a redox titration in which

Ce4+ oxidizes Fe2+ to Fe3+.
Fe initially may be present in both the +2 and +3 oxidation
states. Before titrating, any Fe3+ must be reduce to Fe2+ if the
total concentration of iron in the sample is to be determined.
This type of pretreatment is accomplished using an auxiliary
reducing agent.
4-49
Adjusting the Titrand's Oxidation State
A metal that is easy to oxidize—such as Zn, Al, and Ag—
can serve as an auxiliary reducing agent.
The metal, as a coiled wire or powder, is added to the

sample where it reduces the titrand. Because any
unreacted auxiliary reducing agent will react with the
titrant, it is remove before the titration is done by
removing the coiled wire or by filtering
4-50
A. Permanganimetry
• A solution of MnO4─ is prepared from KMnO4, which is not

available as a primary standard. An aqueous solution of
permanganate is thermodynamically unstable due to its ability
to oxidize water.
4MnO4─(aq) + 2H2O(l) ⇌ 4MnO2(s) + 3O2(g) + 4OH−(aq)
• This reaction is catalyzed by the presence of MnO2, Mn2+, heat,
light, and the presence of acids and bases. A moderately stable
solution of permanganate is prepared by boiling it for an hour
and filtering through a sintered glass filter to remove any solid
MnO2 that precipitates.
4-51
A. Permanganimetry
• Standardization is accomplished against a primary standard

reducing agent such as Na2C2O4 or Fe2+ (prepared from iron
wire), with the pink color of excess MnO4─ signaling the end
point.
• A solution of MnO4─ prepared in this fashion is stable for 1–2
weeks, although the standardization should be recheck
periodically.
• The standardization reactions are
MnO4− (aq) + 5Fe2+(aq) + 8H+(aq) → Mn2+(aq) + 5Fe3+(aq) + 4H2O(l)
2MnO4−(aq) + 5H2C2O4(aq) + 6H+(aq) → 2Mn2+(aq) + 10CO2(g) + 8H2O(l)

4-52
B. Ceric Process/Titration
• A solution of Ce4+ in 1 M H2SO4 usually is prepared from the

primary standard cerium ammonium nitrate,
Ce(NO3)4•2NH4NO3.
• When prepared using a reagent grade material, such as
Ce(OH)4, the solution is standardized against a primary
standard reducing agent such as Na2C2O4 or Fe2+ (prepared
from iron wire) using ferroin as an indicator.
• Endpoint is signaled by a color change with ferroin indicator
from pale blue to red
4-53
B. Ceric Process/Titration
• Despite its availability as a primary standard and its ease of

preparation, Ce4+ is not used as frequently as MnO4- because it
is more expensive.
• The standardization reactions are

Ce4+(aq) + Fe2+(aq) → Fe3+(aq) + Ce3+(aq)
2Ce4+(aq) + H2C2O4(aq) → 2Ce3+(aq) + 2CO2(g) + 2H+(aq)
4-54
C. Dichromate Process/Titration
• Potassium dichromate is a relatively strong oxidizing agent
whose principal advantages are its availability as a primary
standard and its long term stability when in solution. It is not,
however, as strong an oxidizing agent as MnO4− or Ce4+, which
makes it less useful when the titrand is a weak reducing agent.
• Its reduction half-reaction is

Cr2O7 2−(aq) + 14H+(aq) + 6e− ⇌ 2Cr3+(aq) + 7H2O(l)

4-55
C. Dichromate Process/Titration
• Although a solution of Cr2O72− is orange and a solution of

Cr3+ is green, neither color is intense enough to serve as a
useful indicator.
• Diphenylamine sulfonic acid, whose oxidized form is red-violet

and reduced form is colorless, gives a very distinct end point
signal with Cr2O72−.
4-56
D. Iodimetry/Iodometry
• Iodine is another important oxidizing titrant. Because it is a
weaker oxidizing agent than MnO4−, Ce4+, and Cr2O72−, it is
useful only when the titrand is a stronger reducing agent.
• This apparent limitation, however, makes I2 a more selective

titrant for the analysis of a strong reducing agent in the
presence of a weaker reducing agent.
• The reduction half-reaction for I2 is

I2(aq) + 2e− ⇌ 2I−(aq)
4-57
• Because iodine is not very soluble in water, solutions are

prepared by adding an excess of I–. The complexation reaction
I2(aq) + I−(aq) ⇌ I−3(aq)
increases the solubility of I2 by forming the more soluble
triiodide ion, I3−.
• Even though iodine is present as I3− instead of I2, the number

of electrons in the reduction half-reaction is unaffected.
I−3(aq) + 2e−(aq )⇌ 3I−(aq)
4-58
• Solutions of I3− normally are standardized against

Na2S2O3 using starch as a specific indicator for I3−.

• The standardization reaction is
I−3(aq) + 2S2O3−2(aq) → 3I−(aq) + 2S4O62−(aq)
• For additional information on titration curves for redox titration, choice of indicator
• and sample calculations, please read

• https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Book%3A_Analytic
al_Chemistry_2.1_(Harvey)/09%3A_Titrimetric_Methods/9.04%3A_Redox_Titratio
ns
4-59
Application of Redox Titrimetry
1. evaluating the chlorination of public water supplies.
2. determination of dissolved oxygen in natural waters,
such as lakes and rivers
3. determination of the chemical oxygen demand (COD) of
natural waters and wastewaters.
4. analysis of ascorbic acid (vitamin C)
5. the analysis of reducing sugars, such as glucose
4-60
Sample Problem
4-61
Sample Problem
4-62
Lesson 4 Precipitation Titrations
• To understand what precipitation titration is, the principle

involved and examples, please watch the following video

Precipitation Titrations
https://www.youtube.com/watch?v=rijEMcWsI9s
4-63
Lesson 5 Complexation Titration/Complexometry
• To understand what complexation titration is, the principle

involved and sample computation please watch the following
video
Complexometric Titrations Animation/Principle &

Mechanism/Complexometry/MgSO4 Estimation
https://www.youtube.com/watch?v=oVbSsjGh-UI

4-64
THE END
4-65

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Introduction to

Copyright©2011 Cengage Learning

• The mass of Fe²⁺is then given by

• (b) To determine the correct stoichiometric

• If concentration of solutions are in Normality, recall what you have

Volumetric analyses are classified according to the types of

• Standard Solutions for neutralization titrations are always

% Fe = 47.22 mL x 0.1121 meq/mL x 55.847 g/1000 meq x 100 %

• Redox Titration is a laboratory method of determining the

• If a titrant is to be used quantitatively, it’s concentration must

• Which titrant is used often depends on how easily it oxidizes

• The two strongest oxidizing titrants are MnO4─ and Ce4+, for

• An oxidizing titrant such as MnO4−, Ce4+, Cr2O7 2−, and I3−, is

Ex: Determination of Fe by a redox titration in which

The metal, as a coiled wire or powder, is added to the

• A solution of MnO4─ is prepared from KMnO4, which is not

• Standardization is accomplished against a primary standard

• A solution of Ce4+ in 1 M H2SO4 usually is prepared from the

• Despite its availability as a primary standard and its ease of

• The standardization reactions are

• Its reduction half-reaction is

• Although a solution of Cr2O72− is orange and a solution of

• Diphenylamine sulfonic acid, whose oxidized form is red-violet

• This apparent limitation, however, makes I2 a more selective

• The reduction half-reaction for I2 is

• Because iodine is not very soluble in water, solutions are

• Even though iodine is present as I3− instead of I2, the number

• Solutions of I3− normally are standardized against

• and sample calculations, please read

• To understand what precipitation titration is, the principle

• To understand what complexation titration is, the principle

Complexometric Titrations Animation/Principle &

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