Acid Base Titration

1. 1
ACID-BASE TITRATIONS
Ashraf M. Mahmoud, Ph.D.

2.  Introduction
 Acid-base theories: Definition and limitations.
 Law of mass action & acid-base equilibrium in water.
 Buffer solutions: definition, types & importance in
pharmacy.
 Neutralization indicators
 Neutralization titration curves
 Applications of acid-base titration in aqueous medium.
 Acid-base titrations in non-aqueous medium.
Contents

3. 3
Introduction
Aim: is to determine the quantity of the substance under analysis
Classification of quntitative analysis
According to method of analysis:
I- Volumetric analysis
II- Gravimetric analysis : Analysis by weight
III- Instrumental analysis: HPLC, IR, UV-VIS spectrophotometry

4. Introduction
Volumetric analysis:
Standard ≠ Sample complete reaction
Solution of exact known conc. Substance to be determined
A. Ionic combination reactions:
1. Neutralization (H2O formation) H+ + OH- H2O
2. Precipitation Ag+ + Cl- AgCl ppt
3. Complex formation Ag+ + 2CN- [Ag(CN)2]-
B. Redox (electron-transfer) reactions:
Involve change in the O.N. of the substance
Ce4+ + Fe2+ Ce3+ + Fe3+

5. 5
Requirements for a titrimetric reaction:
1. Simple reaction expressed by a chemical equation
2. No side reaction
3. Very rapid
4. Availability of a suitable standard solution
5. Ease of detection of the end point
Sources of errors in titrimetry:
1. Loss of sample 2. Contaminations 3. Non proper mixing
4. Weighing errors 5. dilution errors 6. reading errors
7. Use of wrong indicators 8. Personal errors
Requirements for the titration reactions

6. 6
Standard solutions
Standard solutions (St. soln):
1. Emperical St. soln : No. of ml that react with substance
2. Molar St. soln : gm. M.wt of sub./ 1L
3. Normal St. soln : gm. eq.wt / 1L = M.wt / No of H+ or OH-
4. Formal St. soln : gm. Formula wt / 1L
5. Molal St soln : gm. M.wt of sub./ 1Kg
6. % W/V : gm/100 ml
7. % W/W : gm/100 gm
8. % V/V : ml / 100 ml
9. Ppm : mg / Kg

7. 7
Primary Standards
Primary Standards:
Substances of definite known composition and high purity
1. Easily obtained in a very pure form
2. Easily tested for impurities
3. Stable, non hygroscopic, non volatile
4. Readily soluble
5. Should have a high eq. wt to decrease the weighing errors
6. React stoichiometrically with other sub.
Examples: Pot. Acid phathalate, anhyd. Na2CO3 , KHCO3

8. Acid-Base Theories
1. Arrhenious Theory: Acid is the substance, which ionises into
H+, while bases give OH-. This theory did not discuss the role of
solvent in the ionisation.
2. Brönsted-Lowry Theory: Acid is the substance, which produces
or donates H+, a base accept H+.
Acid  Proton + Conjugate base
HCl  H+ + Cl-
H2O  H+ + OH-
The solvent in this theory, is involved in the reaction as acid or base,
e.g. HCl + H2O  H3O+ + Cl- NH3 + H2O  NH4
+
+ OH-
3. Lewis Theory: Base is the substance that contains an atom with
unshared pair of electrons (e.g. N, O, S, P), while an acid which
accepts to share this electronic pair. HCl + :NH3  NH4
+ + Cl-
Neutralization is the formation of a co-ordinate bond between acid and base.
Compounds with no OH- are alkaline (NH3): HCl + :NH3  NH4
+ + Cl-
Compounds with no H+ are acids (BCl3): BCl3 + :NEt3  Cl3B NEt3

9. Law of Mass Action & Acid-Base Equilibrium in Water
1. Law of Mass Action:
The velocity of a chemical reaction is proportional to the
product of the active masses of the reacting substances.
Vf = Kf [A][B] Vb = Kb [C][D]
Vf is the velocity of forward reaction, Vb is the velocity of
backward reaction,
Kf and Kb are the proportionality constants.
At equilibrium: Vf = Vb and Kf [A][B] = Kb [C][D]
A + B C
+ D
f
b
[C] [D] Kf
[A] [B] Kb
= = K (Equilibrium constant)

10. 2. Acid-Base Equilibrium in Water:
HOAC H+ + O
Ka
[H+] [OAC —
]
[HOAC]
= Ka (Ionization or dissociation constant)
H2A H+ + HA—
K1 [H+] [HA —
]
[H2A]
K1 =
Dibasic acid
K1 =1 ry DC
HA- H+ + A2—
K2 [H+] [A2 —
]
[HA —
]
K2 = K2= 2ry DC
Tribasic acid, H3PO4:
H3PO4 H++ H2PO4
— H+ + HPO4
2—
H+ + PO4
3—
K1 K2 K3
K1 = 1.1  102
K2 = 2.0  107
K3 = 3.6  1013

11. 3. Dissociation of Water:
H2O H+ + OH
Kw [H+] [OH ]
[H2O]
Kw =
Since water is slightly ionised, the value of [H2O] may be
regarded as unity, hence: [H+][OH ] = KW (ionic product of
water = 1 1014  at 25 °C).
In pure water, [H+] = [OH ] = 1  107-
Solution
pH
[H+] > [OH ] [H+] = [OH ] [H+] < [OH ]
Acidic Neutral Alkaline
< 7 7 > 7
0 7 14
pH Scale

12. pH = —log [H+] pOH = —log [OH-] [H+][OH ] = KW = 1014
pH + pOH = 14
Hydrogen ion exponent “pH”
Acid
Neutral
Alkaline
Solution pH [H+] mole/L [OH ] mole/L
0
1.0
2.0
3.0
4.0
5.0
6.0
1.0
0.1
0.01
0.001
0.0001
0.00001
0.000001
0.00000000000001
0.0000000000001
0.000000000001
0.00000000001
0.0000000001
0.000000001
0.00000001
7.0 0.0000001 0.0000001
8.0
9.0
10.0
11.0
12.0
13.0
14.0
0.00000001
0.000000001
0.0000000001
0.00000000001
0.000000000001
0.0000000000001
0.00000000000001
0.000001
0.00001
0.0001
0.001
0.01
0.1
1.0

13. pH of Acids, Bases, and Solutions
1. pH of Strong Acid or Bases:
Strong acids or bases are completely dissociated, the [H+] or [OH-]:
0.1 N HCl gives [H+] = 1/10, pH = — log 101— = 1.0
0.1 N NaOH, pKW = pH + pOH, 14 = pH + 1 pH =13
2. pH of Weak Acids:
HOAC H+ + OAC
Ka
Ka = [H+] [OAC ] / [HOAC]
Since [H+] = [OAC-] and the degree of dissociation is very low
Ka = [H+]2 / Ca ( Ca is total acid concentration).
[H+]2 = Ca  Ka [H+] = Ca  Ka pH = ½ pCa + ½

3. pH of Weak Bases:
pH = pKW– ½ pCb – ½ pKb
Base concentration is Cb .
Dissociation constant of base is Kb.

14. 1. Salts of Strong Acids and Strong Bases (KCl) :
Neutral, pH = 7.
pH of Salt Solutions
2. Salts of Strong Acids and Weak Bases (NH4Cl) :
Acidic, pH  7.
NH4Cl + H2O NH4OH + HCl
pH = ½ pKW – ½ pKb +
½ pCs
3. Salts of Weak Acids and Strong Bases (NaOAC) :
Alkaline, pH  7.
CH3COONa + H2O CH3COOH + NaOH
pH = ½ pkW + ½ pka – ½
pCs
4. Salts of Weak Acids and Weak Bases (NH4OAC) :
Acidic or alkaline ?. It depends on the dissociation
constant of the acid or base.
AB + H2O AH + BOH pH = ½ pKW + ½ pKa –
½ pKb

15. 1. Definition: Solutions that resist change in pH, upon the
addition of small amounts of acids or alkalies.
Buffer Solutions
2. Types:
1 - Weak acid and its salt: Example: acetic acid and
sodium acetate.
pH = pKa + log [A ]/[HA] [A ] = salt
concentration
pH = pKa + log [salt]/[Acid] [salt]/[acid] is the
buffer ratio
When [salt] = [acid], pH = pKa
2- Weak base and its salt: Example : ammonia and
ammonia chloride
pOH = pKb + log [salt] / [base]
pH = pKw - pOH
pH = pKW – pKb – log [salt] / [base]
Henderson Equations for Buffer Solutions

16. 4. Mechanism of Buffer Action:
a. First Type of Buffer
H+ + OAC HOAC
OH + HOAC OAC + H2O
b. Second Type of Buffer
H+ + NH4OH NH4
+ + H2O
OH + NH4Cl NH4OH + Cl
Buffer Solutions

17. - The number of gm equivalent of strong acid or strong
base required to change the pH of 1 L of buffer solution
by one pH unit.
Buffer Capacity
Definition:
In general, the buffer capacity is maintained within the range
1:10 - 10:1.
Buffers show maximum buffering action when:
pH = pKa ± 1.
a- Control of pH of liquid formulations (syrups, pH of 2.0 – 8.0),
parenteral, (pH 4.0 – 9.0), eye drops (pH of 7.4, optimize
stability, solubility or biological compatibility of the dissolved
drug).
b- The pH of blood is very well buffered.
c- Common pharmaceutical buffer is Sorenson’s phosphate
buffer which is composed of disodium hydrogen phosphate
3. Importance of buffer solutions in pharmacy

18. Neutralization Indicators
1. Definition: Weak acid or weak base which changes colour
with the change in pH. Phenolphthalein and methyl orange
are the most used.
2. Theories of Colour
Changes:
a. Ostwald Theory: indicators are either weak organic acids or
bases, in which undissociated molecules differ in colour from
their ions.
HIn H+ + In (Acidic indicator as
phenolphthalein)
InOH OH + In+ (Basic indicator
as methyl orange)
b. Chromophore Theory: colour change depends on the
presence of unsaturated chromophoric group in the indicator
molecule (e.g. NO2, NO, N=N, C=C, etc. ).
Higher max (colour)
Auxochromes (OH or NH2 ) with chromophore  colour
intensity.
Protons donating-accepting leads to structural arra

19. 3. Indicator Constant: Weak acid or weak base which
changes colour with the change in pH.
pH = PKIn + log [basic colour]/ [acidic colour]
When [basic colour] = [acidic colour]
pH = PKIn
Middle tint of an indicator
HIn H+ +
In
Unionized ionized
(acidic) (basic
colour)
Neutralization Indicators

20. acidiccolour %
99.99 99 91 70 60 50 40 30 9 1 0.1 0.01
0.01 1 9 30 40 50 60 70 91 99 99.9 99.99
pK - 1 pK pK +1
basiccolour % Red Blue
Redder
Useful range
Bluer
4. Effective Range of an Indicator: pH = PKIn  1
Ratio =1:10 & 10:1
Neutralization Indicators

21. Indicator
Phenolphthalein
o-Cresolphthalein
Thymolphthalein
Thymol blue (acid range)
Thymol blue (basic
range)
Bromophenol blue
Bromophenol red
Bromothymol blue
Phenol red
Cresol red
Methyl yellow
Methyl
orange
Methyl red
Alizarin
pH
range
Acidic
colour
Colourless
Colourless
Red
Pink
Blue
Yellow
Red
Yellow
Yellow
Yellow
Yellow
Yellow
Yellow
Yellow
Blue
Blue-
violet
Red
Blue
Red
Red
Red
Red
Red
Yellow
Yellow
Yellow
Yellow
Violet
Basic
colour
8.2 – 10.0
9.3 – 10.5
3.3 – 4.4
1.2 – 2.8
8.0 – 9.6
3.0 – 4.6
4.8 – 6.4
6.0 – 7.0
6.4 – 8.0
7.2 – 8.8
2.9-4.0
3.1-4.4
4.2-6.2
10.1-12.0

22. Screened Indicators. A mixture of an indicator + dye
Give more sharper colour change
Example: (methyl orange & indigo
carmine)
6. Screened, Mixed and Universal
Indicators
Mixed indicators. A mixture of two indicators having similar pH
range but showing contrasting colour.
Universal (multi-range) indicators. A mixture of indicators, its colour
change extends over a considerable pH
range.
Used for rough determination of pH, but not suitable for
titration.
Neutralization Indicators

23. Neutralization (Acid-Base) Titration Curves
- The titration curve is a plot of pH values versus the volume of
titrant.
- They are constructed to study the feasibility of the titration and
to help in choosing an indicator for the titration.

24. 1. Strong Acid – Strong Base (HCl – NaOH) 40.0
mL of 0.1 M HCl
 Before addition of any NaOH:
pH = pCa = — log [H+] = — log 0.1 = 1
 After addition of 40 mL of NaOH (at the equivalence
point):
pH = pOH = ½ pKW =7.0
 After addition of 10 mL of NaOH:
pH = pCa = — log [H+] = — log (0.1 30 / 50) = —
log 0.06 = 1.22
 After addition of 20 mL of NaOH:
pH = pCa = — log [H+] = — log (0.1 20 / 60) = — log
0.033 = 1.48
 After addition of 30 mL of NaOH:
pH = pCa = — log [H+] = — log (0.1 10 / 70) = — log
0.014 = 1.85
 After the equivalence point (after addition of 50 mL
NaOH):
pH = pKW – pCb = 14 – ( — log 0.110/90)

25. Titration Curve for Strong Acid – Strong Base
(HCl – NaOH)
PR
MO
PP
AY
MR

26. 2. Weak Acid – Strong Base (HOAC – NaOH) 40.0
mL of 0.1 M HOAC
 Before addition of any NaOH:
pH = ½ pKa + ½ pCa = ½ (4.74) + ½ ( — log 0.1) =
2.37 + 0.5 = 2.87
 After addition of 40 mL of NaOH (at the equivalence
point):
pH = ½ pKW + ½ pKa – ½ pCs = 7 + 2.37 –
½(1.3) = 8.72
 After addition of 20 mL of NaOH (Buffer):
pH = pKa + log [salt] / [acid] = 4.74 + log 1 = 4.74 +
0 = 4.74
 After the equivalence point (after addition of 50 mL
NaOH):
pH = pKW – pOH = 14 – (- log 0.110/90)
pH = 14 – ( — log 0.01) = 14 – 1.95) = 12.05

27. Titration Curves for Strong Acid ( – ) or Weak acid ( – )
with Strong Base
pKa

28. Titration Curve for Weak Base – Strong Acid (NH4
OH – NaOH)
pKb

29. Titration of 100 mL of diprotic acid (H2A) with NaOH
 pH at 1 st E.P. = ½ (pK1 + pK2 ) = ½ (2.12 + 7.12) = 4.66
(M.O.)
 pH at 2 st E.P. = ½ pK + ½ pK — ½ pC = 9.94

30. APPLICATIONS
ACID-BASE TITRATIONS
(NEUTRALIZATION REACTIONS)

31. Direct Titration Methods
1. Determination of Acids &
Bases
Strong acids are titrated with standard alkaline: MO or Ph.Ph.
Weak acids are titrated with standard alkaline: Ph. Ph. not M.O.
Acids which are insoluble in water (as benzoic acid) should be
first dissolve in neutralized ethanol and then titrated with NaOH:
Ph. Ph.
Acid salts (KH-phthalate, KHSO4 & KH-tartarate) are titrated with
NaOH: Ph.Ph.
Boric acid as a weak monobasic acid (K2 = 5.8  1010-), is titrated
with standard NaOH after addition of polyhydroxy compounds
(e.g. glycerol): Ph.Ph.
Strong base are titrated with standard acid: MO or Ph.Ph.
Weak bases are titrated with standard acid: M.O. not. Ph. Ph.
CH2
CH2
CH
OH
OH
OH
+
OH OH
OH
B
OH
CH
CH2
CH2
O
O
B O H + H2O

32. 2. Double-Indicator Titrations
 Direct titration of a mixture of two monobasic acids to determine
the quantity of each acid by the use of two indicators.
 The difference in the ionization constants of the two acids must be
at least 104. Thus, it is possible to titrate HCl in the presence of
boric acid (Ka = 5.5 1010 ) or HCl in the presence of acetic acid
(Ka = 1.8 105 ).
 H+ of HCl  ionization of
HOAC by common ion
effect; NaOH
neutralizes HCl first.
After completion of the
reaction, NaOH neutralizes
AOAC.

33. These salts are formed from either:
– A strong base & a very weak acid (borax & Na2CO3). or
– Strong acid & a very weak base (FeCl3 & AlCl3).
3. Titration of Easily Hydrolysable Salts
(Displacement Titration)
b. Titration of Borax (Na2B4O7)
Na2B4O7 + 7 H2O  2 NaOH + 4
H3BO3
2 NaOH + 2 HCl  2 NaCl + 2 H2O
( M.O. )
4H3BO3 + 4NaOH 4NaBO2 + 8H2O
glycerol
( Ph.Ph )
Titration of a Mixture of Borax & Boric Acid ?.

34. b. Titration of Sodium Carbonate
(Na2CO3)
Na2CO3 + HCl  NaHCO3 + NaCl pH = 8.35 Ph. P
K1= 4.2107
NaHCO3 + HCl  CO2 + H2O + NaCl pH = 3.8 M.
K2 = 4.8  1011
Kb1  106 (required for a sharp
E.P.), the pH break is
decreased by the formation of
CO2, beyond the first E.P.
Kb2  106 : the second E.P. is
not very sharp. It can be
sharpened by boiling off the
CO2 .
Boiled solution
– Titration of a Mixture of Na2CO3 & NaHCO3 ?.
– Titration of a Mixture of Na2CO3 & NaOH ?.
– Titration of a Mixture of Na2CO3 & Na2B4O7 ?.

35. Used when direct titration is not suitable as in:
– Volatile substance as ammonia or formic acid (loss).
– Substance, which require heating with standard reagent.
– Insoluble substance as ZnO, CaO, and BaCO3.
– Substance needed excess reagent for rapid quantitative reaction
(lactic acid).
Indirect (Back or Residual) Titration Methods
Carried out as
follow:
A known excess standard solution is first added and allowed to
react completely with the sample. The residual quantity of the
added standard is then determined.
ZnO + 2HCl  ZnCl2 + H2O
A known weight of ZnO is treated with a known excess standard
HCl, the excess HCl is then back titrated with standard NaOH
1. Determination of insoluble oxides and Carbonates (ZnO
, CaO & CaCO3)

36. Determination of mixture of CaO and CaCO3
– Total by adding known excess standard HCl and back titration
with standard NaOH (M.O.)
– CaO by adding 10% neutral sucrose , alcohol, and titrating with
standard acid (Ph.Ph.).
The indicator losses its colour before [H+] is not strong enough
to attack the insoluble CaCO3.
2. Determination of Esters (Aspirin: acetylsalicylic
acid)
R—COOR + NaOH
R—COONa + ROH
Reflux / Heat
A known weight of the ester is refluxed with a known excess of
standard NaOH.
The residual NaOH is back titrated with standard acid (Ph.Ph.).