Theory of Acid-base Indicators and Acid-base Titration Curves

Acid base indicators &
pH Titration Curves
Dr. Sajjad Ullah
Institute of Chemical Sciences, University of Peshawar

IV. Acid-Base Indicators
A. Finding the equivalence point of a titration
1) Use a pH meter
a) Plot pH versus titrant volume
b) Center vertical region = equivalence point
2) Use an Acid-Base Indicator
a) Acid-Base Indicator = molecule that changes color based on pH
b) Choose an indicator that changes color at the equivalence point
c) End Point = when the indicator changes color. If you have chosen
the wrong indicator, the end point will be different than the eq. pt.
d) Indicators are often Weak Acids that lose a proton (causing the color
change) when [OH-] reaches a certain concentration
HIn + OH- In- + H2O

Indicator : An indicator is a compound having a physical property (usually
color) that changes abruptly near the equivalence point of a chemical reaction.
The completion of the titration is detected by some physical change
(such as colour of the indicator).
End point (observed): The point of titration
at which this change (in colour or some other
physical property) occurs is called the End
Point which occurs just after the equivalence
point.
Equivalence point (Theoretical): The point of titration at
which number of moles of titrant = titrand
Titration error : The difference in volume of standard solution in terms of the
difference in End point and Equivalence point.
(phenolphthalein)
For Ideal Titration, the visible End point = Equivalence point, and titration
error ~ 0 (Instrumental methods such as using a pH meter)
Basic terms in Titrimetric analysis
The goal is for the end point to coincide with the equivalence point.
A convenient way is to add an indicator to the solution and visually detect the end point.

Acid-base indicators (Ostwald theory)
General Many indicators are weak acids and partially dissociate in aqueous solution
HIn(aq) H+
(aq) + In¯(aq)
The un-ionised form (HIn) is a different colour to the anionic form (In¯).
Apply Le Chatelier’s Principle to predict any colour change
In acid - increase of [H+]
- equilibrium moves to the left to give red undissociated form
In alkali - increase of [OH¯]
- OH¯ ions remove H+ ions to form water; H+(aq) + OH¯(aq) H2O(l)
- equilibrium will move to the right to produce a blue colour
Summary In acidic solution pH = pKin±1
HIn(aq) H+
(aq) + In¯(aq)
In alkaline solution
Acid-base indicators are weak acids or weak bases that are highly coloured due to
highly conjugated organic constituents.

5
HIn(aq) H+
(aq) + In¯(aq)
pH = pKa + log [In-]/[HIn]
pH = pKa ± 1 (02 pH unit change)
pH = pKa + log(1/10) = pKa - 1
pH = pKa + log(10/1) = pKa + 1
Most indicators require a transition range of about 02 pH units.
The pKa of the indicator should be close to the pH of the equivalence point.
Phenolphthalein is most widely used for strong acid-base titrations since its transition is
between colorless and pink. It is not usable at lower concertation of acid and bases since
it falls outside the steep portion of the titration curve and bromothymol blue is generally
used instead.
Generally two drops (0.1 mL)
of 0.01M (~0.1%) indicator are
used

COLOUR CHANGES OF SOME COMMON INDICATORS
Must have an easily observed colour change.
Must change immediately in the required pH range
over the addition of ‘half’ a drop of reagent.
Acid-base indicators
PHENOLPHTHALEIN
LITMUS
METHYL ORANGE
1 2 3 4 5 6 7 8 9 10 11 12 13 14
CHANGE
CHANGE
CHANGE
pH

The simple Ostwald theory of the colour change of indicators has
been revised, and the colour changes are believed to be due to
structural changes, including the production of quinonoid and
resonance forms;
Quinonoid Theory
Triphenyl carbinol form RedColourless
Vogel's TEXTBOOK OF QUANTITATIVE CHEMICAL ANALYSIS 5th ed, pp. 263

To be useful, an indicator must
change over the “vertical” section
of the curve where there is a large
change in pH for the addition of a
very small volume of alkali.
The indicator used depends on
the pH changes around the end
point - the indicator must change
during the ‘vertical’ portion of the
curve.
In the example, the only suitable
indicator is PHENOLPHTHALEIN.
Must have an easily observed colour change.
Must change immediately in the required pH range
over the addition of ‘half’ a drop of reagent.
Acid-base indicators
PHENOLPHTHALEIN
LITMUS
METHYL ORANGE

Acid-Base Titration Curves
A. Titration = addition of a measurable volume of a known solution (titrant) to an
unknown solution until the reaction is seen to be completed
B. Use the stoichiometry of the reaction of the known and unknown to calculate
the concentration of the unknown solution
C. A pH curve or titration curve shows the change in pH versus volume of
titrant as the titration proceeds
1) pH meter can be used to monitor
pH during the titration
2) An acid-base indicator can be used
to signal reaching the equivalence point
First Derivative Curve
Shows where change is greatest

Types of pH curves
Types There are four types of acid-base titration; each has a characteristic curve.
strong acid (HCl) v. strong base (NaOH)
weak acid (CH3COOH) v. strong alkali (NaOH)
strong acid (HCl) v. weak base (NH3)
weak acid (CH3COOH) v. weak base (NH3)

11
HCl + NaOH NaCl + H2O
Strong acid vs. strong base
II. Before the end point:
[H+] = [H3O+]=[HCl]unreacted
pH = – log [HCl]unreacted
III. At the end point:
[H+] ≡ [OH–]
KW = 10–14 pH ≡ 7
IV. After the end point:
[OH–] = [NaOH]excess
pOH = – log [NaOH]excess
I. At the start:
[H+] = [H3O+]=[HCl]0
pH = – log [HCl]0

12
G.D Christian, Analytical Chemistry, 6 ed, Chapter 8

Adding 0.1M NaOH
to 25 mL of 0.1M HCl

pH 1 at the start
due to 0.1M HCl
(strong
monoprotic acid)
Adding 0.1M NaOH

Very little pH change
during the initial 20 mL
pH 1 at the start
due to 0.1M HCl
(strong
monoprotic acid)
Adding 0.1M NaOH

during the initial 20cm3
Very sharp change in pH
over the addition of less
than half a drop of NaOH
pH 1 at the start
due to 0.1M HCl
(strong
monoprotic acid)

Very sharp change in pH
over the addition of less
than half a drop of NaOH
Curve levels off at pH 13
due to excess 0.1M NaOH
(a strong alkali)
pH 1 at the start
due to 0.1M HCl
(strong
monoprotic acid)

Any of the indicators listed will be suitable - they all change in the ‘vertical’ portion
PHENOLPHTHALEIN
LITMUS
METHYL ORANGE

Important points:
a) pH increases slowly far from the equivalence point
b) pH changes quickly near the equivalence point
c) The equivalence point of a strong acid—strong base titration = 7.00
The titration of a strong base with a strong acid is almost identical

strong base (0.1M NaOH) Vs. strong acid (0.1M HCl) Effect of Concentration of End-point break
Selection of the indicator becomes more criticle in
case of dilute solutions (e.g, 0.001M HCl vs 0.001M
NaOH in the above example
The magnitude of End-point break (vertical part of the
titration curve depends on concentration of acid and
base.
G.D Christian, Analytical Chemistry, 6 ed, Chapter 8
Phenolphthalein is most widely used for strong
acid-base titrations since its transition is between
colorless and pink. It is not usable at lower
concertation of acid and bases since it falls
outside the steep portion of the titration curve
and bromothymol blue is generally used instead.

I. At the start:
Weak acid    COOHCHKH a 3
Excess of strong base [OH–] = [NaOH]excess
II. Before the end point:
Buffer (acid / salt)    
 


COOCH
COOHCHK
H
3
3a  
 COOHCH
COOCH
PKpH a
3
3log


or
III. At the end point:
Hydrolysing salt    
 COOCHKOH 3b or  
 COOCHPKPKpH aw 3log2/12/12/1
Weak acid (CH3COOH) vs. strong base (NaOH)
Vogel's TEXTBOOK OF QUANTITATIVE CHEMICAL ANALYSIS 5th ed, pp. 28 G.D Christian, ANALYTICAL CHEMISTRY, 6 ed, Chapter 8, Table 8.2

Steady pH change
(Buffer)
Sharp change in pH over
the addition of less than
half a drop of NaOH
due to excess 0.1M NaOH
(a strong alkali)
pH 4 due to 0.1M
CH3COOH (weak
monoprotic acid)
weak acid (CH3COOH) v. strong base (NaOH)
pH=pKa = 4.76
Hydrolysis of CH3COO-
at end point, pH above 7
End point pH 7-10

Titration of a Weak Acid with a Strong Base
A. Addition of a strong base to a weak acid forms a Buffer Solution
1) HA + OH- A- + H2O
2) If not enough base has been added to complete the reaction: HA/A- buffer
B. Important Points
1) pH increases more rapidly at the start than for a strong acid
2) pH levels off near pKa due to HA/A- buffering effect
pH = pKa + log([A-]/[HA]) = pKa + log(1) = pKa (when [A-] = [HA])
3) Curve is steepest near equivalence point. Equivalence Point > 7.0
4) Curve is similar to strong acid—strong base after eq. pt. due to excess OH-
12.5
½ Equivalence Pt.
pH = pKa

PHENOLPHTHALEIN
LITMUS
METHYL ORANGE
Only phenolphthalein is suitable - it is the only one to change in the ‘vertical’ portion
weak acid (CH3COOH) v. strong base (NaOH)

Effect of Concentration of End-point break
Curve 1= 0.1M CH3COOH vs 0.1 M NaOH
 Hydrolysis of CH3COO- at end
point, pH is above 7
 The greater the concentration of
CH3COO- , the greater the pH
 Hydrolysis of CH3COO- is negligible
after the equivalenc epoint due to
excess OH-.
 Phenolphthalein serves as suitable
indicator in this case but only
above 0.001M concentration of
CH3COOH and NaOH
 pH meter ay be used for titration of
very dilute solutions or when Ka
value of the weak acid is less than
10-8

Titration curves for 100 mL of 0.1M Weak acids
of diffrent Ka values versus 0.1M NaOH
The weaker the acid (small Ka), the stronger is
its conjugate base (salt with higher Kb), and
the more alakline is the equivalence point.
pH meter may be used for titration weak acid
(Ka <10-8)
Titration curves for 100 mL of 0.1M Weak
base of different Kb values versus 0.1M HCl
The weaker the base (small Kb), the stronger is its
conjugate acid (salt with higher Ka), and the more
acidic is the equivalence point
G.D Christian, ANALYTICAL CHEMISTRY, 6 ed, Chapter 8

I. At the start:
Weak base
  basebCKOH 
   OHNHKOH 4b
II. Before the end point: Buffer (base / salt)
 
salt
base
b
C
C
KOH 
   
 


4
4b
NH
OHNHK
OH
III. At the end point: Hydrolysing salt (Brönsted acid)
[H+] = Cexcess acid
[H+] = [HClexcess
Excess of strong acid
  salta CKH     
 4a NHKH
 
 base
saltPKpOH b log
 ClNHPKbPKpH w 4log2/12/12/1 
Weak base (NH3) vs. strong acid (HCl)
Vogel's TEXTBOOK OF QUANTITATIVE CHEMICAL ANALYSIS 5th ed, pp. 28 G.D Christian, ANALYTICAL CHEMISTRY, 6 ed, Chapter 8, Table 8.2
pKb (NH4OH) = 4.751, Kb= 1.75X10-5 at 25 deg C
pKa (NH4
+)= 9.24, Ka = 5.7 x10-10

Weak base (NH3) vs. strong acid (HCl)
Titration curves for 100 mL of 0.1M NH3
versus 0.1M HCl
End point pH 4-7

Types
Steady pH change
pH 4 due to 0.1M
CH3COOH (weak
monoprotic acid)
NO SHARP
CHANGE IN pH
due to excess 0.1M NH3
(a weak alkali)

PHENOLPHTHALEIN
LITMUS
METHYL ORANGE
NOTHING SUITABLE
There is no suitable indicator- none change in the ‘vertical’ portion.
The end point can be detected by plotting a curve using a pH meter.

Other pH curves - acid v. carbonate
Sodium carbonate reacts with hydrochloric acid in two steps...
Step 1 Na2CO3 + HCl ——> NaHCO3 + NaCl
Step 2 NaHCO3 + HCl ——> NaCl + H2O + CO2
Overall Na2CO3 + 2HCl ——> 2NaCl + H2O + CO2

Step 1 Na2CO3 + HCl ——> NaHCO3 + NaCl KH1=Kb1=KW/Ka2 = 2.1x10-4
Step 2 NaHCO3 + HCl ——> NaCl + H2O + CO2 KH2=Kb2=KW/Ka1 = 2.3x10-8
There are two sharp pH changes
The second addition of HCl is exactly
the same as the first because the
number of moles of HCl which react
with the NaHCO3 is the same as that
reacting with the Na2CO3.
17.50cm3 35.00cm3
CO3
2-/HCO3
-
HCO3
- /CO2

First rapid pH change around pH = 8.5
due to the formation of NaHCO3 .
Can be detected using phenolphthalein
There are two sharp pH changes

phenolphthalein
methyl orange
First rapid pH change around pH = 8.5
due to the formation of NaHCO3 .
Can be detected using phenolphthalein
Second rapid pH change around pH = 4
due to the formation of acidic CO2 .
Can be detected using methyl orange.
There are two moderately sharp
pH changes
Methy red

If we boil the solution, it removes CO2 and hence the buffer system
(HCO3
-/CO2), leaving only HCO3
- in solution, and a sharp end point
can be obtained with methyl red
Modified methyl orange (MO+xylene cyanole FF) can be used which gives a sharp
Gray colour at the end point to detect it.

Other pH curves - polyprotic acids (H3PO4)
Phosphoric acid is triprotic; it reacts with sodium hydroxide in three steps...
Step 1 H3PO4 + NaOH ——> NaH2PO4 + H2O
Step 2 NaH2PO4 + NaOH ——> Na2HPO4 + H2O
Step 3 Na2HPO4 + NaOH ——> Na3PO4 + H2O

There are three sharp pH changes
Each successive addition of
NaOH is the same as equal
number of moles are involved.

pH of H3PO4 = 1.5

pH of NaH2PO4 = 4.4
pH of H3PO4 = 1.5

pH of Na2HPO4 = 9.6
pH of NaH2PO4 = 4.4
pH of H3PO4 = 1.5

pH of Na3PO4 = 12
pH of Na2HPO4 = 9.6
pH of NaH2PO4 = 4.4
pH of H3PO4 = 1.5

Sharp change in pH over
the addition of less than
half a drop of NH3
due to excess 0.1M NH3
(a weak alkali)
pH 1 at the start
due to 0.1M HCl
strong acid (HCl) v. weak base (NH3)

PHENOLPHTHALEIN
LITMUS
METHYL ORANGE
strong acid (HCl) v. weak base (NH4OH as titrant)
Only methyl orange is suitable - it is the only one to change in the ‘vertical’ portion

Theory of Acid-base Indicators and Acid-base Titration Curves

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