Lecture6
Titrimetric analysis.
Acid–Base titration.
Associate prof . L.V. Vronska
Associate prof . M.M. Mykhalkiv
Outline
1.
2.
3.
4.
5.
6.
7.
Titrimetric method of the analysis: the basic concepts
and classification.
Technics of titrimetric analysis.
Types of titrimetric determinations.
Calculations in titrimetric analysis.
Protolytometry or acid–base titration (a neutralization
method): the basic concepts, titrants, defined
substances.
Indicator choice, calculation of errors of titration in a
method protolytometry.
Nonaqueous acid–base titration.
1. Titrimetric method of the
analysis: the basic concepts
and classification.
 Titrimetry - any method in which volume is the
signal.
 Titrimetry, in which we measure the volume of a
reagent reacting stoichiometrically with the
analyte.
Titration setup: the titrant drops from the burette into the analyte
solution in the flask. An indicator present then changes color
permanently at the endpoint.
Titration of an acid solution of unknown concentration
with a base solution of known concentration
 Titration is a procedure for determining the
concentration of a solution by allowing a carefully
measured volume to react with a standard solution
of another substance, whose concentration is
known.
 Standardization is the process of establishing a
technical standard
 In chemistry, an aliquot is usually a portion of a
total amount of a solution.
 Titrant - the reagent added to a solution containing
the analyte and whose volume is the signal.
 A reagent, called the titrant, of known
concentration (a standard solution) and volume is
used to react with a solution of the analyte, whose
concentration is not known.
 equivalence point - the point in a titration where
stoichiometrically equivalent amounts of analyte
and titrant react.
 End point - the point in a titration where we stop adding
titrant.
 Indicator - a colored compound whose change in color
signals the end point of a titration.
 Titration error - the determinate error in a titration due to
the difference between the end point and the equivalence
point.
 A primary standard is a standard that is accurate enough
that it is not calibrated by or subordinate to other
standards. A primary standard in chemistry is a reliable,
readily quantified substance.
 Secondary reagent - a reagent whose purity must
be established relative to a primary reagent
 A burette (also buret) is a vertical cylindrical
piece of laboratory glassware with a volumetric
graduation on its full length and a precision tap,
or stopcock, on the bottom (or calibrated glass
tube).
 Even the thickness of the lines printed on the
burette matters; the bottom of the meniscus of the
liquid should be touching the top of the line you
wish to measure from.
stopcock buret
Buret with bottle of standard solution
Gay-Lussac burette
Buret with rubber shutter
Mohr burette
Microburet:
а) Shilov air-powered Buret; б) stopcock buret
 A pipette (also called a pipet, pipettor or
chemical dropper) is a laboratory
instrument used to transport a measured
volume of liquid
Erlenmeyer flask or conical flask.
There are different ways of
preparation of standard solutions:
on accurately weighed sample
(primary standard)
by means of standard substance or a
standard
solution
(secondary
standard)
 “standard titrimetric substance”
(primary standard)
 Accurately weighed sample (primary
standard)
Because a volumetric flask contains a solution, it is useful
in preparing solutions with exact concentrations. The
reagent (the accurately weighed sample) is transferred to
the volumetric flask, and enough solvent is added to
dissolve the reagent. After the reagent is dissolved,
additional solvent is added in several portions, mixing
the solution after each addition. The final adjustment of
volume to the flask’s calibration mark is made using a
dropping pipet. To complete the mixing process, the
volumetric flask should be inverted at least ten times.
Volumetric flask
Volumetric flask — for preparing
liquids with volumes of high precision.
It is a flask with an approximately
pear-shaped body and a long neck with
a circumferential fill line.
Proper means of reading the meniscus on a
volumetric flask or pipet.
When filling a pipet or volumetric flask, set the liquid’s level exactly at
the calibration mark. The liquid’s top surface is curved into a meniscus,
the bottom of which should be exactly even with the glassware’s
calibration mark. The meniscus should be adjusted with the calibration
mark at eye level to avoid parallax errors.
Calculate concentration of primary
standard
m
C 
MV
M
m
C 
N E V
m
T  m/V
 by means of standard substance or a
standard solution (secondary standard)
 secondary reagent - a reagent whose purity must
be established relative to a primary reagent
 To prepare the solution we place calculated
amount of substance, weighed to the nearest
tenth of a gram, in a bottle or beaker and add
approximately volume of water
Establishment of secondary standard
concentration
А) a measured volume of another
primary standard solution
CN 2
CN1  V1

V2
where:
CN2 and V2 are concentration and volume
of secondary standard solution
CN1 and V1 are concentration and volume
of primary standard solution
B) a weighed quantity of a primary standard
m 1000
CN 
Em  V
where:
CN and V are concentration
and volume of secondary standard
solution
m and Em are mass and
equivalent weight of primary
standard
Typical
instrumentation for
performing
an
automatic titration.
Courtesy of Fisher
Scientific.
Features of a primary standard include:
1. It should have crystal structure and correspond the
chemical formula
2. High purity (it is the absence of impurity in a substance)
3. Stability (low reactivity)
4. Low hygroscopicity (it is the ability of a substance to
attract water molecules from the surrounding environment
through either absorption or adsorption) and efflorescence
(in chemistry, is the loss of water (or a solvent) of
crystallization from a hydrated or solvated salt to the
atmosphere on exposure to air).
5. High solubility (if used in titration)
6. High equivalent weight.
7. Not to contain extraneous impurity more than
admissible borders for substances of mark “chemically
pure”.
8. Methods of purification of standard substance from
impurity (crystallisation, extraction, sublimation etc.)
should be available in analytical laboratory.
Some examples of primary standards according to the
European Pharmacopoeia 5, ch. 4.2:
 Arsenic trioxide for making sodium arsenite solution for
standardisation of sodium periodate solution (also for
iodine and cerium (IV) sulfate solutions, since 2002
standardised by sodium thiosulfate)
 Benzoic acid for standardisation of waterless basic
solutions: ethanolic sodium and potassium hydroxide,
TBAH, and alkali methanolates in methanol, isopropanol,
or DMF
 Potassium bromate (KBrO3) for standardisation of sodium
thiosulfate solutions
 Potassium hydrogen phthalate (usually called KHP) for
standardisation of aqueous base and perchloric acid in
acetic acid solutions
 Sodium carbonate for standardisation of aqueous acids:
hydrochloric, sulfuric acid and nitric acid solutions (but
not acetic acid)
 Sodium chloride for standardisation of silver nitrate
solutions
 Sulfanilic acid for standardisation of sodium nitrite
solutions
 Zinc powder, after being dissolved in sulfuric or
hydrochloric acid, for standardisation of EDTA solutions
 “standard titrimetric
substance” (primary standard)
 More often in an
ampoule contains 0,1
mol (0,1 equivalents)
of substances, it is
necessary
for
preparation of 0,1
mol/L solution.
Preparation rules primary solutions
and definition of their titre.
1. The initial substance which is used for
preparation of a standard solution, should be
chemically pure.
2. The initial substance should easily and quickly
react with standartized solution.
3. The solution of initial substance don’t change
itself concentration long time.
4. It is necessary to use reactions between initial
and defined substance, which are possible in
direct titration.
5. Titration process should end quickly and
accurately. The end point of titration should will be
defined easily and precisely.
6. To establish of titre it is desirable either a method
of accurately weighed sample or dissolution of
precisely weighed initial substance in certain
volume.
7. For the prevention of errors by titration it is
necessary to choose volume of the primary
standard aliquot or weighed of standard substance,
that the volume of the secondary standard which
will react in titration was not less than 20 mL (buret
on 25 mL) or 40 mL (buret on 50 mL).
8. Titration should be carry out until then it will not be
received yet three reproduced results.
9. Prepared of standartized solution should be stored in
conditions which exclude absorption of air moisture
by them, and also evaporation. A titre should not
change at standing in time.
10.Wares and measuring devices which are used in
titrimetry, should be washed up, calibrated, prepared
for titration and should be stored in a pure place.
11.Accuracy measurement of volumes and the
calculations, should correspond to accuracy of
weighing.
Titrimetric methods are classified
into four groups based on the type of
reaction involved.
 acid–base titrations, in which an acidic or basic
titrant reacts with an analyte that is a base or an
acid;
 complexometric titrations involving a metal–
ligand complexation reaction;
 redox titrations, where the titrant is an oxidizing or
reducing agent;
 precipitation titrations, in which the analyte and
titrant react to form a precipitate.
Requirements to reactions in titrimetric analysis
 all reactions involving the titrant and analyte
must be of known stoichiometry, quantitatively
 the titration reaction must occur rapidly
 a suitable method must be available for
determining the end point with an acceptable
level of accuracy
 Reactions should proceed by room temperature
 Titration should not be accompanied by
collateral reactions which deform the results of
the analysis
 Reactions should be specific
2. Techniques of titrimetric
analysis.




Washing up and drying ware
Preparation of standard solutions
Sample preparation
Titration:
- Measurement of volumes
- An indicator choice
 Calculations
Common examples of glassware used to measure
volume:
The Buret (or burette)
beaker
volumetric flask
Graduated cylinders
transfer pipet;
measuring pipet
Calibration: volumetric flask - an injection method
pipettes, burettes - a pouring out method
Methods to determine the end
point
 visual indicators:
 Colour change: In some reactions, the solution changes colour without
any added indicator. This is often seen in redox titrations, for instance,
when the different oxidation states of the product and reactant produce
different colours.
 Precipitation: If the reaction forms a solid, then a precipitate will form
during the titration. A classic example is the reaction between Ag+ and
Cl- to form the very insoluble salt AgCl. This usually makes it difficult
to determine the endpoint precisely. As a result, precipitation titrations
often have to be done as "back" titrations (see below).
 Physical and chemical methods with the subsequent analysis of
curves of the titration showing changes which occur in the course of
titration (change of physical and chemical parametres standard
solutions)
3. Types of titrimetric
determinations.




Titration can be:
direct titration
back-titration (on residue)
substitute-titration (displacement titration)
revertive titration
direct titration – titrant add to an analyte solution and
react with determined substrance







Requirements to reactions in direct titration
reaction involving the titrant and analyte must be of
known stoichiometry, quantitatively
the titration reaction must occur rapidly
a suitable method must be available for determining the
end point with an acceptable level of accuracy
Reactions should proceed by room temperature
Titration should not be accompanied by collateral
reactions which deform the results of the analysis
Reactions should be specific
a suitable indicator is available
А + Т = product
Back titration. A titration in which a reagent is added
to a solution containing the analyte, and the excess
reagent remaining after its reaction with the analyte is
determined by a titration.
This titration is used, when:
 the titration reaction is too slow,
 a suitable indicator is not available,
 there is no useful direct titration reaction
 the standard solution lacks of stability (fugitive)
А + Тexcess = product1 + Тresidue
Тresidue + Тpadding = product2
displacement titration. A titration in which the
analyte displaces a species, usually from a
complex, and the amount of the displaced species
is determined by a titration.
This titration is used, when:
 the analytes are unstable substance
 It is impossible to indicate the equivalent (end) point in
direct reaction
 Analyte doesn’t react with titrant
 reaction involving the titrant and analyte mustn’t be of
known stoichiometry, quantitatively
А + Т1(padding compounds) = А1(substituent)
А1(substituent) + Т = product
CrCl2 + FeCl3 = CrCl3 + FeCl2
analyte
substitute
5FeCl2 + KMnO4 + HCl = 5FeCl3 + KCl + MnCl2 + 4H2O
Revertive titration.
 A standard solution is titrated by solution
of investigated substance in reversive
titration
А(in burette) + Т(in flask) = product
4. Calculations in titrimetric
analysis.
 Weight of investigated
substance by results of
direct, displacement or
reversive titration:
C K V E V
m
1000  V
П
H
T
m
k
a
T K V V
m
V
TA
П
T
a
k
 Weight of investigated substance by results
of back titration:
(C K V  C K V )E V
m
1000V
H1
П
T1
П
H2
a
T2
m
k
 Titre of titrant by investigated substance:
С ( T)  E ( A )
Т 
1000
Н
ТА
m
5. PROTOLYTOMETRY OR ACID–BASE
TITRATION (A NEUTRALIZATION METHOD): THE
BASIC CONCEPTS, TITRANTS, DEFINED
SUBSTANCES.
Acid–base titration - titration in which the
reaction between the analyte and titrant is an acid–
base reaction.
Protolytometry is titrimetric method of analysis which uses
solutions of acids or bases as titrants. In this method of the
analysis defined substances are the substances, capable to
react with acids and the bases.
The basic reaction of a method:
Н+ + ОН- = Н2О or
HA + B = BH+ + A-
Methods of acid-base titration or acid–base
titrimetry:
 acidimetry (titrants - HCl, H2SO4)
 alkalimetry (titrants - NaOH, KOH)
All titrants are secondary standard
solutions,
therefore
demand
of
standardization (definition of precise
concentration).
Standardization of acidic titrants - solutions of
acid HCl, H2SO4
 Standard (reference) substances – sodium
tetraboratic
Na2B4O75H2O
or
Na2B4O710H2O,
sodium
carbonate
Na2CO3:
Na2B4O7 + 2HCl + 5H2O = 2NaCl + 4H3BO3
Na2CO3 + 2HCl = 2NaCl + CO2 + H2O
Standardization of НСl solution on sodium
tetraborate.
 Weigh exact shot of Na2B4O75H2O or
Na2B4O710H2O and place it in a measured
flask, dissolve in hot water, after a solution is
cooled and diluted of solution by water to
necessary volume and it is mixed.
 In a flask for titration place an aliquot of
prepared
primary
standard
solution
Na2B4O75H2O or Na2B4O710H2O, add some
drops of the methyl orange. The received
solution is titrated by solution of НСl to change
of colour with yellow to orange with a rose
shade.
Standardization of НСl solution on sodium
tetraborate.
By 3-4 results of titration calculate average volume of used
titrant and calculate concentration of hydrochloric acid.
CN HCl 
CN Na B O  V
2 4
7
VHCl
Na2 B4O7
Standardization of HCl solution on sodium
carbonate
 In a flask for titration place exact shot of sodium
carbonate, dissolve in necessary volume of water, add
some drops methyl orange and titrate this solution by
chloric acid.
 Such titration repeat for 3-4 times. Each time calculate
concentration of HCl:
CN _ HCl 
mNa CO  1000
2
3
EmNa CO  VHCl
2
 By 3-4 results of titration
concenration of chloric acid.
3
calculate
average
Standardization of basic titrants - solutions of
bases of NaOH, KOH
Standard (reference) substances – oxalate
acid
H2C2O42H2O,
succinate
acid
H2C4H4O4:
H2C2O4 + 2NaOH = Na2C2O4 + 2H2O
H2C4H4O4 + 2NaOH = Na2C4H4O4 + 2H2O
Standardization of NaOH solution on oxalic
acid.
 Weigh exact shot of H2C2O42H2O and place it
in a measured flask, dissolve in hot water, after
a solution is cooled and diluted of solution by
water to necessary volume and it is mixed.
 In a flask for titration place an aliquot of
prepared
primary
standard
solution
H2C2O42H2O , add some drops of the
phenolphthalein. The received solution is
titrated by solution of NaOH to change of
colourless to rose (or red).
Standardization of NaOH solution on oxalic
acid.
By 3-4 results of titration calculate average volume of
used titrant and calculate concentration of NaOH.
CN _ NaOH 
CN H C O  V
2
2
4
VNaOH
H 2C2O4
According to force of acid and the base such
types of the acid-base interaction are possible:
 Between strong acid and the strong basis
NaOH + HCl = H2O + NaCl
 Between weak acid and the strong basis
 NaOH + CH3COOH ↔ CH3COONa + H2O
 Between strong acid and the weak basis
NH4OH + HCl = NH4Cl + H2O
 Between weak acid and the weak basis
CH3COOH + NH4OH = CH3COONH4 + H2O
6. INDICATOR CHOICE, CALCULATION
OF ERRORS OF TITRATION IN A
METHOD PROTOLYTOMETRY.
Indicators of acid-base titration
 The substances which colouring changes depending on size
change рН of solution.
Requirements to indicators:
 Indicator colouring at near values рН should differ well
 Change of colouring of the indicator should occur sharply in a
small interval of рН
 Indicator colouring should be as it is possible more intensively
 The quantity of base or acid, necessary for change of
colouring of the indicator, should be very small
 Change of colouring of the indicator must to be reversible
1894 – the ionic theory of indicators
 Indicators of an acid-base titration method
are weak acids or the bases at which not
ionised molecules and ions have different
colouring
HInd
red
Lacmus
Phenolphthalein colourless
↔
H+
+
Indblue
rose
Ind: - one-colour (phenolphthalein )
- two-colour (methyl orange , lacmus)
Limitation of ionic theory of indicators :
 Ascertaining of different colouring of acidic
and basic forms, but is not present an
explanation of presence and colouring change.
 The structure and colouring are not connected.
 Colouring change is ionic process but why it
often is long in time?
Advantages of the ionic theory: possibility of
quantitative interpretation of results of change
of colouring.
The theory of chromophore – colouring of
organic compounds is connected with presence of
a chromophore groups at molecules of indicators :
- N=N-; -N=O; =C=S; -N=NO
Auxochrome groups haven’t colouring, but with
a chromophore groups strengthen action of the
last, causing deeper intensity of colouring.
C2H5
CH3
-OH; -NH2; -OCH3;
;
N
CH3
N
C2H5
Colouring change is a consequence of isomeric
transformation which changes an indicator
structure
O
N
O
OH
The colourless form
O N-O-H
O
The yellow form
Limitation of chromophore theory of
indicators
 Does not give an explanation why tautomeric
transformations and change of colouring of a
solution of indicators occurs at change рН a
solution.
 Colouring changes instant, where as intramolecular transformations generally long
processes is frequent.
 Does not give a quantitative estimation of
connection of colouring change with change рН.
The ionic- chromophore theory
 The acid-base indicators are weak acids and the
bases, and the neutral molecule of the indicator
and its ionised form contain different
chromophore groups
O
N
O
O N-O-H
N-O
O
+ H+
OH
colourless
O
yellow
O
yellow
The ionic- chromophore theory
1
2
НInd0 ↔ HInd ↔ H+ + Indthe acid
the base
form
form
Сacid . form
pH  pK  lg
Сbase. form
pH  pK  1
 рТ of most often used indicators in the acid-base
titration:
 Methyl orange
4,0
 Methyl red
5,5
 Lacmus
7,0
 Phenolphthalein
9,0
 pT of the indicator is value of рН at which colour
of the indicator sharply changes and stop to add
titrant (there is end point of titration)




Factors which influence the indicator
indication.
At increase tо the temperature indicator becomes
less sensitive to Н+ -ions for indicators-bases
Presence of organic solvent (alcohol, acetone),
albuminous molecules, salts changes рК of the
indicator
It is necessary to define titre a working solution
in the same conditions at which the test analysis
is conducted
it isn’t recommended to take a lot quantity of
indicator
2. Indicator
choice, calculation of errors
of titration in a method protolytometry.
Indicator choice spend two methods:
 On reaction products
 On titration curves
Titration curve for 0,1 mol/L hydrochloric acid by
0,1 mol/L sodium hydroxide
Dependence of inflection points on
concentration of defined substance
(0,1 mol/L and 0,01 mol/L)
Dependence of inflection points
on force of acid
Dependence of inflection points
on force of acid
Titration curve for weak acid (CH3COOH) by
weak base (NH4OH)
Titration curve for H3PO4 by NaOH
Factors which influence on
inflection points
 constants of acid or base
 temperatura of solutions
 concentration of defined substances
 concentration of used titrants
Choice of the indicator:
The pT of indicator (interval of transition of
colouring - pH range) should be in limit of
inflection points on a titration curve
Choice of the indicator:
The pT of indicator (interval of transition of
colouring - pH range) should be in limit of
inflection points on a titration curve
Titration curve of 0.100 M HCl
with 0.200 M NaOH
Titration curve of 0,1 М CH3COOH
by 0,2 M NaOH
Titration curve of 0,1 М NH3
by 0,1 M HCl
Titration curve of weak acid by weak base
Titration curve for 50.00 mL of 0.100 M
CH3COOH with 0.100 M NaOH showing the
range of pHs (or pT) and volumes of titrant over
which the indicators bromothymol blue and
phenolphthalein are expected to change color.
Titration curve of mix
0,1 M HCl + 0,1 M CH3COOH
by 0,1 М NaOH
Acetic acid
Ка=1,74·10-5
Titration curve of mix
acetic and malatic acids
Malatic acid
Ка=1,50·10-4
Acetic acid
Ка=1,74·10-5
К1:К2<104
Titration curve of maleinic acid
Titration curve 0,1 М oxalic acid
by 0,1 М NaOH
Determinate the end-point by potentiometric way
Titration error - the determinate error in a
titration due to the difference between the end
point and the equivalence point.
Indicator’s error
 “+” – if have excess of base when define
acid
 “-” – if have rest of acid when define acid
Hydroxonium error
 pT
10 V2
x
 100%
C k Vk
Indicator’s error :
pT 14
Hydroxyl error
Acidic error
Bases error
10
V2
x
 100%
Ck Vk
рК a рТ
x HA  10
xMeOH  10
 100%
рК b рТ 14
 100%
7. NONAQUEOUS ACID–BASE TITRATION.
Titration in water solutions is limited by factors:
 It is impossible to titrate for a mix of acids or the
bases if constants of dissociation differ less, than
on four order
 It is impossible to titrate for a mix of strong and
weak acids (bases)
 It is impossible to titrate very weak acids (bases)
 It is impossible to titrate separately for a mix of
acids (bases) with near constants of dissociation
 It is impossible to define substances which are
insoluble in water.
Choice of solvents:
 The constant of autoprotolysis solvent should be
as small as possible
 For titration of the weak bases should be to take
a solvent with the expressed progenic properties
(the acid nature of solvent)
 For titration of weak acids should be to take a
solvent with expressed protophilic properties,
(the basis nature of solvent)
 Dielectric inductivity of solvent should be as it is
possible above
The weak bases often are titrated in the acetic
acid medium
(strengthening of force of the bases)
 Titrant: perchlorate acid HClO4
 Standardization: on potassium hydrogenphthalate, or
on sodium salicylate if have solution of HClO4 in
CH3OH
Nonaqueous acid–base titration of weak bases
by perchlorate acid
 Indicators: crystal violet (violet – blue or
green),
thymol dark blue (yellow – rose).
The weak acids often are titrated in the
medium dimethyl formamide, ethylene diamine,
butylamine, pyridine
(strengthening of force of the acids)
 Titrant: sodium hydroxide NaOH in the
solution of benzene with methanol
sodium
methylate
CH3ONa
in
methanol or in the solution of benzene with
methanol.
Standardization of NaOH and CH3ONa on
benzoic acid
Nonaqueous acid–base titration of weak
acids by NaOH or CH3ONa
 Indicators: thymol blue (red-yellow and
yellow-blue) or physico-chemical methods
(potentiometry).
In nonaqueous acid–base titration determinate
the end-point by potenthiometric way
In nonaqueous acid–base titration determinate
the end-point by potenthiometric way
Thanks for your attention!