The document details the principles of titration, including types of titrations such as precipitation, acid-base, complexation, and redox reactions, emphasizing the importance of accurate measurements and standardization. It also discusses methods for determining the equivalence point, endpoint detection technologies, and the necessary properties for indicators and standards used in titrations. Additionally, it addresses potential errors in titration methods and best practices for using volumetric apparatus.

1. Principles of Titration and errors
By Dr. A. Amsavel

2. Introduction
Volumetric analysis
 Simple and easy
 Fast and can be done on site
 Less expensive
 Estimation of content or Assay
 Precise and accurate
 Depends on method and specificity

3. Requirements of a Titration Reaction
Reaction must complete by 99.9 %
so that < 0.1 % (or 1 ppt) remains unreacted
Rxn must be rapid
Titration needs to be performed in a
reasonable time period
The stoichiometry must be well defined, and
known
It can be predicted from equilibrium constants
A method must be available to determine the
equivalence point

4. Types of Titration
1) Precipitation
– A(aq) + B(aq) = AB(s)
2) Acid-Base rxn
– H+ + OH¯ = H2O (strong acids or bases)
– HA + OH¯ = H2O + A¯ (weak acids)
– A¯ + H+ = H2O + HA (weak bases)
3) Complexation rxn
– Zn2+ + 4NH3 = Zn(NH3)42+
4) Redox rxn (oxidation-reduction)
– Fe2+ + Ce4+ = Fe3+ + Ce3+

5. Standards
• Measurements are made with reference to standards
– The accuracy of a result is only as good as the quality
and accuracy of the standards used
– A standard is a reference material whose purity and
composition are well known and well defined
• Primary Standards
– Used as titrants or used to standardize titrants
– Requirements
• Usually solid to make it easier to weigh
• Easy to obtain, purify and store, and easy to dry
• Inert in the atmosphere
• High formula weight so that it can be weighed with high precision

6. Endpoint Detection
It is critical, to know the completion of reaction /
determination
1) Visual indicators:
• Observe a colour change or precipitation at the endpoint.
– Rxn progress checked by addition of external or self indicator
2) Photometry:
• Use an instrument to follow the colour change or
precipitation
3) Electrochemistry:
• Potentiometry - measure voltage change ( pH electrode)
• Amperometry - measure change in current between electrodes in
solution
• Conductance – measure conductivity changes of solution
Later two used for coloured, turbid, end point accurate

7. Acid-base titration
 Neutralization titration

Neutralization Indicators
 Indicators & mixed indicators
 Neutralization curve
 Non-aqueous titration

8. Acids & Bases
Acids:
 Arrhenius acid: Any substance that, when
dissolved in water, increases the concentration of
hydronium ion (H3O+)

Bronsted-Lowry acid: A proton donor
conjugate base

Lewis acid: An electron acceptor
Bases:

Arrhenius base: Any substance that, when
dissolved in water, increases the concentration of
hydroxide ion (OH-)

Bronsted-Lowery base: A proton acceptor
conjugate acid

Lewis acid: An electron donor

9. Brønsted-Lowry Theory of Acids & Bases
The conjugate acid of a base is the base plus the
attached proton and the conjugate base of an acid is
the acid minus the proton
p. 507

10. Lewis Theory of Acids & Bases
p. 506

11. pH calculation
Q1: Calculate the pH of a solution if [H+] = 2.7 x 10-4 M
pH = -log[H+] pH = -log(2.7 x 10-4) = 3.57
Q2: Find the hydrogen ion concentration of a solution if its
pH is 11.62.
[H+] = 10-pH [H+] = 10-11.62 = 2.4 x 10-12M
Q3: Find the pOH and the pH of a solution if its hydroxide
ion concentration is 7.9 x 10-5M
pOH = -log[OH-] pOH = -log(7.9 x 10-5) = 4.10
pH + pOH = 14 pH = 14 - 4.10 pH = 9.9

12. A solution with a pH of 1 has [H+] of 0.1 mol/L or 10-1
A solution with a pH of 3 has [H+] of 0.001 mol/L or 10-3

13. pH of solutions
Stomach juice: pH = 1.0 – 3.0 Human blood: pH = 7.3 – 7.5
Lemon juice: pH = 2.2 – 2.4 Seawater: pH = 7.8 – 8.3
Vinegar: pH = 2.4 – 3.4 Ammonia: pH = 10.5 – 11.5
Carbonated drinks: pH = 2.0 – 4.0 0.1M Na2CO3: pH = 11.7
Orange juice: pH = 3.0 – 4.0 1.0M NaOH: pH = 14.0

14. ENDPOINT = POINT OF NEUTRALIZATION =
EQUIVALENCE POINT
MOLES OF ACID = MOLES OF BASE

15. Ka and Kb
The equilibrium constant for a Brønsted acid is
represented by Ka, and base is represented by Kb.
CH3COOH(aq) + H2O(l) H3O+(aq) + CH3COO–(aq)
[H3O+][CH3COO–]
Notice that H2O is not Ka = –––––––––––––––––
included in either [CH3COOH]
equilibrium expression.
NH3(aq) + H2O(l) NH4+(aq) + OH–(aq)
[NH4+][OH–]
Kb = –––––––––––––
pH of 1M AcoH =2.4 [NH3]

17. NaOH
Titration curve: HCl Vs NaOH solution
1 M Sol 0.1M sol
14.0
Vol ml pH pH
0.0 0.0 1.0
12.0
50.0 0.5 1.5
75.0 0.8 1.8
10.0
90.0 1.3 2.3
98.0 2.0 3.0
8.0
99.0 2.3 3.3
99.5 2.6 3.6
6.0
99.8 3.0 4.0
99.9 3.3 4.3
4.0
100.0 7.0 7.0
100.1 10.7 9.7 2.0
100.2 11.0 10.0
100.5 11.4 10.4 0.0
0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0
101.0 11.7 10.7
Series1 Series2
102.0 12.0 11.0
110.0 12.7 11.7
150.0 13.3 12.3

18. Titration curve
NaOH 1 M Sol 0.1M sol
Vol ml pH pH
98.0 2.0 3.0
99.0 2.3 3.3
99.5 2.6 3.6
99.8 3.0 4.0
99.9 3.3 4.3
100.0 7.0 7.0
100.1 10.7 9.7
100.2 11.0 10.0
100.5 11.4 10.4
101.0 11.7 10.7
102.0 12.0 11.0

19. Titration Curve: Strong Acid with Strong Base
At the equivalence point
in an acid–base titration,
the acid and base have
been brought together in
precise stoichiometric
proportions.
(Endpoint)
Bromphenol blue,
bromthymol blue, and
phenolphthalein all
change color at very
nearly 20.0 mL
At about what volume
would we see a color
change if we used methyl
violet as the indicator?

20. Titration Curve: Weak Acid with Strong Base
The equivalence-point
pH is NOT 7.00 here.
Why not??
Bromphenol blue was ok
for the strong acid/strong
base titration, but it
changes color far too early
to be useful here.

22. Acid–Base Indicators
 An acid–base indicator is a weak acid or
base.
 The acid form (HA) of the indicator has one
color, the conjugate base (A–) has a different
color. One of the “colors” may be colorless.
 In an acidic solution, [H3O+] is high. Because
H3O+ is a common ion, it suppresses the
ionization of the indicator acid, and we see
the color of HA.
 In a basic solution, [OH–] is high, and it reacts
with HA, forming the color of A–.

23. Function of Indicators
Example: phenolphthalein
 Near pH 8, Indicator dissociates and gives red base
Human eye can detect it as a pink tinge at that pH
 Indicators must be carefully chosen so that their
colour changes take place at the pH values expected
for an aqueous solution of the salt produced in the
titration.

24. Basis of Indicator selection
Indicator colour change, from acid pH
pKind example of titration use
to alkali range
weak base - strong acid
Methyl orange, (red ==> yellow) 3.7 3.1-4.4 titration e.g. ammonia titrated
with hydrochloric acid
Bromophenol blue, (yellow ==> weak base - strong acid
4.0 2.8-4.6
blue) titration
weak base - strong acid
Methyl red, (red ==> yellow) 5.1 4.2-6.3
titration
strong acid - strong base
Bromothymol blue, (yellow ==>
7.0 6.0-7.6 titration e.g. hydrochloric acid
blue)
<=> sodium hydroxide titration
strong acid - strong base
Phenol red, (yellow ==> red) 7.9 6.8-8.4 titration e.g. hydrochloric acid
<=> sodium hydroxide titration
Thymol blue (base form), (yellow weak/strong acid - strong base
8.9 8.0-9.6
==> blue) titration
weak acid - strong base
Phenolphthalein, (colourless ==> 8.3-
9.3 titration e.g. ethanoic acid
pinky-red) 10.0
titrated with sodium hydroxide

25. Colours of indicator at different pH

26. Indicators: Color changes against pH

27. Non-Aqueous Titration
 Theory is same as acid-Base titration
 Reaction carry out in non-aqueous
medium
 Applied where

Material which are not soluble in water
 Week acid and bases are titrated
 Poor end point in water medium
Principle based on Brønsted-Lowry Theory

28. Brønsted-Lowry Theory
The conjugate acid of a base is the base plus the
attached proton and the conjugate base of an acid is
the acid minus the proton
p. 507

29. Solvents used in NAT
Solvents used can be classified as four types:
 Aprotic solvents: Chemically neutral

Eg. Toluene, carbon tetrachloride
 Protogenic solvents: Acidic nature readily donate
protons,
 Eg. Anhyd. HF, H2SO4
 Amphiprotic solvent: Which are sly ionize and donate
and accept protons,
 Eg Alcohols, weak organic acids.

Acetic acid makes weak acid into storing base
 Protophilc solvents: Posses high affinity for protons.

Eg. Liq ammonia, Amine, Ketones

Increases the acidic strength

30. Selection of Solvents for NAT
Acetic acid used for titration of weak bases,
Nitrogen containing compounds
Acetonitrile / with ACOH: Metal ethanoates
Alcohols (IPA, nBA) : Soaps and salts of
organic acids,
DMF: Benzoic acid, amides etc

31. Titrants for NAT
 Perchloric acid in acetic acid
 Amines, amine salts, amino acids, salts of
acids
 Potassium Methoxide in Toluene-
Methanol
 Quan ammonium hydroxide in Acetonitrile-
pyridine
 Acids, enols, imides & sulphonamides

32. Indicators for NAT
 Principle is similar to acid base titration
Indicators:
 Crystal violet, Methyl red, Thymol blue, &
1-Naphthaol benzein

33. Calculation
o Normality: Eq.wt/1000ml or meq/mL
o Morality: Mole/1000ml
o V1 N1 = V2N2
o N1 = V2N2/V1
 Normality = Wt of sample x 1000 / Eq. Wt x V
 Wt of sample (mg) = V x N x Eq. wt
 Assay = Qty estimated in sample x 100/ wt of sample
 Assay = V x N x Eq. wt x 100/ wt of sample x 1000

34.  1 ml of 1N HCl = 0.04g of NaOH (40/1000)
 1 ml of 0.1N HCl = 0.004g of NaOH

35. Titration Error
Error in methods:
The endpoint method may not show a change
exactly at the equivalence point due to the
reactions involved
Titration Error = Vol at endpoint - Vol at
equivalence point
• Negative error & Positive error means endpoint is
early - before equiv point or late after equiv point

36. Errors in Volume and weight:
 10 ml titre volume = 100 %
 If difference is 0.1ml error is 1%; 0.2ml = 2%
 5ml titre volume = 100 %

0.1ml = 2% error
 Optimum level is about 25ml
 25 ml titre volume = 100 %

0.1ml = 0.4% error

37. Volumetric apparatus
USP:
 Burette selection:
 NLT 30% nominal volume (15ml in 50ml burette)
 Micro burette for < 10ml
 Limit of error:
 Volumetric flask: 25ml, 50ml, 100ml is 0.03, 0.05&
0.08ml
 Pipets:5, 10, 25 ml is 0.01, 0.02 &0.03ml
 Burets:10, 25, 50ml is 0.02, 0.1&0.1ml
Tips: out flow NMT 500uL per second

38. Operational & personal error
List several of the variables involved in correctly using a
10mL volumetric pipette.
 drain time;
 possible beads on the inner surface
 temperature;
 bringing meniscus to the proper level;
 angle of drain;
 touching off last drop;
 rinsing of the pipet with the solution used;
 Pipet calibration; etc.

39. Error in weighing can occur.
• Misreading of the balance,
• Balance not level,
• Not cleaning the surface of the balance first,
• Touching the weighed object with moist hands,
• Leaving the balance doors open during weighing,
• Using a miscalibrated balance,
• Not cooling the sample down to near room temperature,
• Not removing a static charge from the sample,
• Excess vibration or air currents from people or nearby
equipment, and
• Prolonged time sample left on pan adds/loses moisture.

40. Possible contamination
An analyst could
 contaminate a sample during weighing by placing a
contaminated spatula
 placing the sample on or into a contaminated holder
during weighing,
 dropping some lint/hair/skin or sneeze into the sample
while weighing,
 opening up a bottle of chemicals near the sample being
weighed.
 When performing trace analysis, it is possible for just a
microgram even massive fingerprint!

41. Units of measurement
Name Defining Units
Molarity moles of solute/liter (solutions), or
(e.g. 0.1200 M) millimoles/milliliter (solutions)
(grams of substance/grams of sample) x
Percent
100%, or
(e.g. 23.45 %)
centigrams/gram (seldom used)
milligrams/liter (solutions), or
Parts per million
micrograms/milliliter (solutions)
(e.g 2.34 ppm, 2.34
milligrams/kilogram (solids), or
mg/L)
micrograms/gram (solids)
Parts per billion
micrograms/liter (solutions), or
(e.g. 0.45 ppb, 0.45
nanograms/gram (solids)
ug/L)

42. Oxidation- reduction titration
 Oxidation-reduction reaction
 Reduction potential is calculated by
 Nernst equation
• E1= E’ + 0.591/n log (ox)/(red)
• E=(E1+E2)/2
 Equivalence point by redox potential Vs
Volume
 Indicator selection

43. Precipitation titration
 Reagents used id based on Solubility
products of precipitate
 Titration curve: -log Conc. Of ion Vs Volume
 Concentration of ions

Eg. Ksol(Agcl) = Ag + Cl
 Indicator:
 Formation of coloured compound (ppt/complex)
 Adsorption indicators

44. Complexation titration
 M + EDTA M(EDTA)
 Complex formation depend on Stability
constant, pH,
 titration curve pM Vs, Vol of EDTA
 Indicators (Metal / metal ion indicators):
 M-ln + EDTA M(EDTA) + In

45. Types of Complexation titration
 Back titration
 Masking
 Selective de-masking
 Separation by ppt and solvent extraction
 Application, almost metals,

46. An Equation for Buffer
Solutions
 In certain applications, there is a need to repeat the
calculations of the pH of buffer solutions many times.
This can be done with a single, simple equation, but
there are some limitations.
 The Henderson–Hasselbalch equation:
[conjugate base]
pH = pKa + log ––––––––––––––
[weak acid]
• To use this equation, the ratio [conjugate base]/[weak acid]
must have a value between 0.10–10 and both concentrations
must exceed Ka by a factor of 100 or more.

47. The Common Ion Effect
 Consider a solution of acetic acid.
 If we add acetate ion as a second solute (i.e., sodium
acetate), the pH of the solution increases:
LeChâtelier’s principle: What
happens to [H3O+] when the
equilibrium shifts to the left?