Quantitative analysis
It deals with the determination of
the quantity of the substance to be
analyzed.
1
Classification according to the process of
measurement
1- Volumetric analysis (titration)
depends on measuring the volume of the analyzed sample and the volume of
standard solution used for complete reaction,
OR measuring the capacity of the sample to combine with the standard
quantitatively
2- Instrumental method of analysis (physico-chemical methods)
depends on measuring optical or electrical properties which are quantitatively
related to the analyzed sample concentration.
3- Gravimetric analysis
depends on weighing the final product of reaction after its isolation in pure and
stable form of definite chemical structure.
2
Requirements of titrimetric reactions:
1. The reaction must be simple and expressed by
a chemical equation.
2. A single reaction must occur between the
sample and titrant as described by a chemical
equation.
3. The reaction must be instantaneous (rapid).
4. Suitable standard solution must be available.
5. The end point should be easily detected.
3
N.B.
• A quantitative reaction
reaction that proceeds forward to produce stable
product(s) such as weakly ionizable compounds,
e.g. H2O, weak acid, weak base, sparingly soluble
salts (precipitate), complex ion, …
I- Ionic combination reactions:- The reaction goes to completion due to formation of slightly ionizable
or slightly insoluble products.
a- Neutralization reaction :
In which acid reacts with base to form slightly ionized water.
H+ + OHH2O
b- Formation of precipitate :
Ag+ + ClAgCl ↓
Ba+2 + SO42BaSO4 ↓
4
c- Formation of slightly ionizable complex :
Ag+ + 2 CN[Ag(CN)2]Ca+2 + H2Y-2 [EDTA]
2H+ + CaY-2 [Ca-EDTA complex]
II- Electron transfer reactions :
In which electron transfer from one reactant to another.
It is called (oxidation -reduction reactions)
Ce+4 + Fe+2
Ce+3 + Fe+3
i.e. Fe+2
Fe+3 + e oxidation (loss of e.)
Ce+4 + e
Ce+3 reduction (gain of e)
Standard Solutions
They are solutions of exact, known
concentration. They are classified according to
the type of concentration into molar, normal
and empirical solutions.
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1. Molar solution (M)
It is a solution of known concentration, each liter
contains the gram molecular weight or its
fractions or multiples.
e.g.
• Molecular weight (M.wt) / liter (L), it is expressed
as 1M or M
• ½ M.wt /L, it is expressed as M/2 or 0.5M.
• 4 M.wt/L, it is expressed as 4M.
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2. Normal solution (N)
It is a solution of known concentration, each liter
contain the gram equivalent weight (eq.wt) or its
fractions or multiples.
e.g.
• eq.wt/L, it is expressed as 1N or N solution.
• 0.1eq.wt/L, it is expressed as 0.1N or N/10 solution.
• 3 eq.wt/L, it is expressed as 3N solution.
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How to Calculate the equivalent weight ?
• Acids
Eq.wt = (M.wt )/ number of replaceable hydrogen
HCl
eq.wt = M.wt / 1
H2SO4
eq.wt = M.wt / 2
• Bases
Eq.wt = (M.wt )/ number of replaceable hydroxyl ion
NaOH
eq.wt = M.wt / 1
Ba(OH)2
eq.wt = M.wt / 2
• Salts
Eq.wt = M.wt / number of cations x its valency
• Or =M.wt / number of anions x its valency
Na2SO4 eq.wt = M.wt / 2 x 1 or M.wt / 1 x 2
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3. Emperical solution
It is a solution of known concentration, prepared in such a
way that 1ml of it reacts with a definite amount of the
analyzed substance. It is used for determination of one
substance only. (used for routine analysis)
e.g. empirical standard AgNO3, 1ml of it reacts with 0.001 g.
NaCl.
• AgNO3 + NaCl  AgCl + NaNO3
M.wt AgNO3 = M.wt NaCl
170 gm AgNO3 = 58.5 gm. NaCl
x
= 0.001 gm NaCl
x = 0.001 x 170 / 58.5 = 0.0029 gm AgNO3
i.e. each 1ml empirical AgNO3 should contain 0.0029 gm
AgNO3 to be equivalent to 0.001 gm NaCl.
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Standard solution is classified into:
1- Primary standard chemicals
Primary standard chemicals are substances of definitely known composition
and high purity.
They must fulfill the following requirements:
1. Easily available in high purity and known composition.
2. Easily tested for impurity.
3. Stable, i.e. not absorbing water or CO2 from air, non volatile and
withstand drying at 110-120 oC.
4. Must react with other substances quantitatively according to a
balanced chemical equation (react stoichiometrically).
5. Readily soluble in the solvent.
6. Having high equivalent weight to minimize error during weighing.
Examples of primary standard chemicals:
Potassium hydrogen phthalate (KHC8H4O4),
benzoic acid (HC7H5O2),
constant-boiling-point hydrochloric acid,
anhydrous sodium carbonate (Na2CO3),
anhydrous potassium bicarbonate (KHCO3) and
mercuric oxide (HgO).
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2- Secondary standard chemicals:
• Secondary standard chemicals are substances which
may be used for standardization and whose content
have been found by comparison against primary
standard.
e.g.
HCl,
NaOH,
borax (Na2B4O7.10H2O) and
oxalic acid (H2C2O4.2H2O).
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Preparation of standard solutions
a. Direct method:
An accurately weighed amount of the solute is
transferred into a volumetric flask, dissolved in
the solvent then completed to the required
volume and mixed well. The solute must be a
chemical of primary standard quality.
b. Indirect method:
If the solute is not primary standard, prepare
solution of approximate concentration
(approximate standard), which must be
standardized against primary standard solution.
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The standardization factor (f)
f = volume of exact standard / volume of approximate
standard
• It ranges from 0.95-1.05, out this range the solution is
not of expected strength.
• The volume of secondary standard must be multiplied by
its standardization factor (f) to obtain the volume of exact
normality or molarity.
Calculation of equivalent factor (F)
It is how much of sample substance is equivalent to 1ml
standard.
Finally, calculation of sample concentration
- Concentration of sample solutions in gm/L
= Volume of exact standard consumed x f x Equivalent factor (F) x 1000
Volume of the Sample
In case of powdered sample (solid), - Concentration of sample g %
= Volume of exact standard consumed x f x Equivalent factor (F) x100
wt. of sample
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I-Volumetric (Titrimetric)
Methods of Analysis
I-1- Acid-Base Titrations
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I-1-A. Acid-Base titrations in aqueous medium
• Electrolytic dissociation theory
Electrolyte in water
cations + anions
• Degree of dissociation: ()
 = No. of molecule dissociated / total No. of molecules
• When dissociation is complete, “ “ will be unity
and the electrolyte is strong, if it is far from unity
it is called a weak electrolyte.
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ACID- BASE THEORIES
1-Electrolytic dissociation theory (Arrhenius theory)
• When an electrolyte dissolves in water, it will dissociate to
a certain extent to give cations and anions.
• The acid is the electrolyte dissociates to give (H+), while,
the base is the electrolyte dissociates to give OH-.
• acid-base reaction (neutralization reaction),
is a combination between hydrogen ions and hydroxyl ions
to form water.
(H+ + OH- = H2O).
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Points of weakness in electrolytic dissociation
theory
1. HCl gas has no acidic properties on dry litmus
paper.
2. Ammonia and amines, which are known bases,
although they contain no hydroxyl groups.
3. The basic character of solution of sodium metal
(Nao) in ethanol is due to the formation of
sodium ethoxide.
4. H+ is very small in size, its electric charge is
very intense, therefore, it can’t exist
independently in solution
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2. Bronsted-Lowry Theory
• An acid is any substance that produces proton(s), while
a base accepts proton(s).
• Acid
proton + conjugate base
• Base + proton
conjugate acid
The stronger the acid, the weaker its conjugate base
and vice versa.
e.g.
• Acid
Base
conj-Acid conj-Base
• HCl
+ H2O
H3O+
+
Cl• H2O
+ NH3
NH4+
+
OH18
3. Lewis Theory:
•
•
•
an acid is the substance that accepts electron-pair.
A base is electron-pair donner.
Compounds containing no OH- and yet reacts alkaline,
e.g., ammonia:
H
H
H N: + HCl
H N:
Cl -
H
H
•
H
b- Compounds containing no H-atoms, yet they react
as acids, e.g., boron trichloride with triethylamine
Cl
Cl
Et
Et
B
Et N:
Et N
Cl
Et
Et
Cl
B Cl
Cl
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THE LAW OF MASS ACTION
"The velocity of a chemical reaction is proportional to the
product of the active masses of the reacting substances“
(f)
A+B
C+D
(b)
At equilibrium
K "equilibrium constant“ = [C] [D] / [A] [B]
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ACID-BASE EQUILIBRIA IN WATER
e.g. monobasic weak acid (acetic a.)
HAc
H+ + AcApplying the law of mass action
[H+] [Ac-]
[HAc]
• "K" is the ionization constant or dissociation constant of the acid,
usually written Ka.
K(acetic acid) =
For polybasic acid
H 2A
HAK1 = [H+] [HA-]/[H2A]
K2 = [H+] [A2-]/[HA-]
H+ + HAH+ + A2-
• K1 and K2 are the primary and secondary dissociation constants,
respectively. (always K1 > K2)
21
The dissociation of water
H2O
H+ + OHKeq = [H+] [OH-] / [H2O]
Kw = [H+] [OH-] = 10-14
at 25 oC [H+] = [OH-] = 10-7
• when [H+] =[OH-] ; it is a neutral solution
• when [H+] >[OH-] ; it is an acidic solution
• when [H+] <[OH-] ; it is a basic solution
22
Hydrogen ion exponent “pH”
•
•
•
•
pH= - log [H+], while pOH= - log [OH-]
As Kw = [H+] [OH-] = 10-14
- log Kw = - log [H+] - log [OH-] = - log10-14
pKw = pH + pOH = 14
when pH = 7 ; it is a neutral solution
when pH > 7 ; it is a basic solution
when pH < 7 ; it is an acidic solution
A pH increase of one unit corresponds to a
tenfold decrease of [H+].
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pH of acids and bases
1. pH of strong acid (s.a.) or strong base (s.b.)
pH= -log[H+] for s.a. while pOH= -log[OH-] for s.b.
e.g.
0.1N HCl
gives
[H+] = 10-1
pH of 0.1N HCl = -log 10-1 = 1
Also, 0.1 N NaOH (pOH=1) has a pH value of:
pKw = pH + pOH
14 = pH + 1; so, pH = 13
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2. pH of weak acid (w.a.)
• HAc
H+ + AcKa = [H+] [Ac-]/[HAc]
as Ca= acid concentration i.e. [HAc] & [H+]=[Ac-]
So ka = [H+]2 / Ca
[H+]2 = Ka. Ca
[H+] = (Ka. Ca)½
-log [H+] = ½ (-log Ka - log Ca)
pH = ½ p Ka + ½ p Ca
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3. pH of weak base (w.b.)
• BOH
B+ +OH-
Kb = [B+] [OH-]/[BOH]
as Cb= base concentration i.e. [BOH] & [B+]=[OH-]
So kb = [OH-]2 / Cb
…..
pOH = ½ p Kb + ½ p Cb
pH = 14 - pOH
pH = 14 - ½ p Kb - ½ p Cb
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4. pH of salt solutions
1. S (s.a-s.b): NaCl, KCl,…
pH  7
2. S (w.a-s.b): CH3COONa
pH = 7 + ½pKa - ½pCs
3. S (s.a-w.b): NH4Cl
pH = 7 - ½pKb + ½pCs
4. S (w.a-w.b): CH3COONH4
pH= 7 + ½pKa- ½pKb
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BUFFER SOLUTIONS
These are solutions that resist changes in
the pH, upon addition of small amounts of
acids or alkalies.
They consist of:
• weak acid and its salt e.g., acetic acidsodium acetate.
• OR
• weak base and its salt e.g., ammonium
hydroxide-ammonium chloride
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The buffer action
The pH doesn’t change upon
• Addition of strong acid
H+ + AcHAc (weak acid)
• Addition of strong base
OH- + HAc
H2O + Ac-(salt)
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pH of buffer solution
Henderson equation
Buffers from weak acids and their salts,
e.g., CH3COOH/CH3COONa:
Ka = [H+] [A-] / [HA]
log Ka = log [H+] + log [A-] / [HA]
-log [H+] = -log Ka + log [A-] / [HA]
pH = pKa + log [A-]/[HA]
pH = pKa + log [salt]/[acid]
•
[Salt]/[Acid] is known as buffer ratio.
•
•
When, [Salt] = [Acid], so, pH=pka.
Buffers of different pH values are prepared by varying
the buffer ratio. However, this ratio should be10/1 or
1/10, i.e., pH = pKa + 1
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The buffer capacity
• It is the magnitude of the resistance of a buffer
to change in the pH.
• OR, it is the ratio of strong acid or base added,
to the small changes in the pH brought about:
Buffer capacity   =  B/pH
• The higher the buffer capacity, the more efficient
is the buffer.
• High buffer capacity occurs when
1. the concentration of the two components is high
2. the two components are present in equal
concentration.
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Buffers from weak bases and their salts;
e.g., NH4OH/NH4Cl
• pOH = pKb + log [salt] / [base]
• pH = pKw - pKb - log [salt] / [base]
• pH = pKw - pKb + log [base] / [salt]
Q.
1.
Calculate the pH of a buffer solution containing 0.1M
sodium acetate and 0.1M acetic acid (pKa = 4.76).
2.
Calculate the pH of a solution containing 0.07 M
ammonia and 0.28 M ammonium chloride (pKb = 4.76).
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Neutralization Indicators
They are substances added during titration to
determine the equivalence point.
1- COLOR INDICATIORS
• Substance which change color in accordance
with pH are used as neutralization indicators,
e.g., methyl orange (M.O) (two color
indicator) and phenolphthalein (ph.ph.) (one
color indicator).
• They are weak acids or weak bases, which
change color with change of pH of the
medium. Used to detect the end point in an
acid-base titration.
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Theories of color indicator
1- Ostwald –Arrhenious theory
Acidic indicators. e.g., ph.ph.:
H Ind
H+ + Ind“colorless"
“red“
Basic indicators. e.g., M.O.
Ind OH
“yellow“
Ind+ + OH“red“
Addition of an acid or base will shift equilibrium, so the indicator will
change its color.
1.
2.
3.
Objections to Ostwald theory;
When a small quantity of alkali is added to ph.ph. solution, it turns
red, but addition of more alkali a colorless solution.
Slow color change, while ionic reactions are rapid.
A number of acid- base indicators show their color changes in
non-aqueous media, where ionization is depressed.
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Chromophoric Theory
• A color change occurs as a result of some intra-molecular
rearrangement, which changes the structure of the indicator.
• The color change of indicators is due to the presence of
unsaturated groups called chromophores in the indicator
molecule. e.g. of such gps are N=N, C=C-C=C, etc.
• Auxochromes can’t by themselves confer color to a compound
but when present together with chromophores they augment
the action of the latter and deepen the color. e.g. of such gps
are -OH and –NH2.
• By the chromphore theory the color change of an indicator is
the result of an isomeric change, i.e., an intra-molecular
rearrangement which changes the structure of the indicator
leading to formation, or disappearance, of chromophores so,
the color changes.
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Some common indicators
phenolphthalein (ph.ph.)
HO
OH
C
O
Free ph. ph., "benzenoid"
Colorless, pH below 7.
CO
OH, pH 8-10
O
O
O
O
C
C
COO
COO
Ouinonoid ph.ph, resonance hybrid
of the two tautomeric forms.
Red in colour, pH 8-10
excess
OH
-
O
O
C
OH
COO
Tribasic salt of Ph.Ph., devoid of
quinonoid chromophore,
Colorless, pH above 12
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Methyl Orange (M.O.)
N
N
Benzenoid structure (orange)
pH 3.3-4.2
SO3H
H
N
CH3
+
OH-(H2O)
N
CH3
-OH
H+
H
N
N
N
Yellow
(salt formation)
SO3
CH3
N
CH3
Red (inner salt)
pH 3.3
SO3
CH3
N
CH3
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Effective range of an indicator
For an acid indicator
H Ind
Ind- + H+
Unionized, (acidic color)
ionized,(basic color)
Kind =[H+][Ind-]/[H Ind]
pH = pKind + log [Ind-]/[HInd]
pH = pKind + log [basic color]/[acidic color]
When the concentration of the basic color is equal to that of acidic color, so
pH = pKind
The color change of an indicator depends on the ratio [basic color]/[acidic
color], which should not exceed 1/10 or 10/1, so that :
pH = pKind + 1 (The effective range of an indicator)
The effective range of an indicator is the pH units over which it change its
color, for a good indicator this should not exceed two pH units, e.g.
phenolphthalein: (8-10), methyl orange: (3.3-4.4) and methyl red (4-6).
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Screened Indictors
With some indicators, e.g., methyl orange, the color change is not
easily detectable. A sharper color change may be obtained by
using a mixture of the indicator and a dye, e.g., methyl orange
with indigocarmine. The color change from yellowish green
"alkaline" to violet "acid“
Mixed Indicators
A sharper color change may be obtained by using a mixture of two
indicators having similar pH but showing contrasting color,
e.g. thymol blue and cresol red.
Universal or Multirange Indicators
By suitably mixing certain indicators, the color change extends over
a considerable pH range. Such mixtures are usually called
universal indicators. They are not suitable for quantitative
titration but may be used for the rough determination of pH
of solutions.
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2‐ TURBIDITY INDICATORS
• Many higher organic acids or bases form colloidal solutions
which, at certain pH, from flocculent precipitates.
• Their use is limited only to case when the use of color indicator
is not practical, e.g. when titrating a dark colored solution.
3‐FLUORESCENCE INDICATORS
• Certain compounds emit visible radiation when exposed to
ultraviolet light. This property may stop, or intensify, when
certain pH is reached.
• Fluorescence indicators, e.g. umbelliferone, are used to
detect end point when color or turbid solutions are titrated.
40
Neutralization titration curves
• It is a plot of pH versus the volume of
titrant.
• Used to study the feasibility of the titration,
and to select a suitable indicator.
41
1. Strong acid-strong base titration
e.g., HCl against NaOH
Before and during titration
pH = pCa
at the equivalence point
pH = pOH = ½pKw = 7 (neutral)
after the equivalence point, excess NaOH
pH = pKw - pCb
42
2. Weak acid-strong base titration,
e.g. CH3COOH and NaOH
The initial pH
pH = ½pKa + ½PCa
During titration
pH=pKa + log [salt]/[acid]
At the equivalence point
pH = 7 + ½pKa - ½pCs
After the equivalence point, excess NaOH
pH = pKw - pCb
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Weak base-strong acid titration
e.g. NH3 and HCl
At the start pH of weak base
pH = 14 - ½pKb - ½pCb
During the titration
pH = 14 - pKb + log [base]/[salt]
At the equivalence point
pH = 7 - ½pKb + ½pCs
After the equivalence point
pH = -log [H+]
44
Weak acid-weak base titration,
e.g. NH3 and CH3COOH
The titration curve is smooth and the pH
change at the vicinity of the e.p. is very
small.
Such titration is not feasible and should be
avoided
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