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Brown's Advanced A Level Chemistry Revision Notes
Theoretical–Physical
Advanced Level
Chemistry – Equilibria – Chemical Equilibrium Revision Notes PART 6.2
6.2 Indicator theory of acid–base titrations, pH curves & pKind
What is the theory behind how an acid–alkali
indicator works? Why are some weak acids good indicators in acid–base
titrations? What is the pH range of an indicator? How does the pH change
throughout an weak/strong acid–soluble weak/strong base titration?
Chemical Equilibrium Notes Parts 5 & 6 Index
6.2
Theory of acid–base titration
indicators, pH curves and pKind
selection of a suitable
indicator and how pH changes when acids react with bases e.g. in a
titration
-
All of Equilibria part 5 "pH and weak–strong
acids and bases in aqueous solution" should have been studied prior
to tackling Part 6.
-
6.2.1
Acid–base
titration indicators are quite often weak acids in which the
unionised acid (lets call it HIn) and its 'de–protonated' form,
or conjugate base, the anion (In–),
have different colours.
-
One form can be colourless e.g.
phenolphthalein in acid–neutral solutions.
-
The equilibrium
can be simply expressed as ....
-
HIn–(aq,
colour 1)
H+(aq)
+ In–(aq,
colour 2)
-
Applying Le
Chatelier's equilibrium principle:
-
Addition of acid
favours the formation of more HIn (colour 1)
-
HIn(aq)
H+(aq)
+ In–(aq)
-
Addition of
alkali favours the formation of more I– (colour 2):
-
HIn(aq)
H+(aq)
+ In–(aq)
-
The increase in
[OH–] causes a shift to right because the reaction
-
H+(aq)
+ OH–(aq) ==> H2O(l)
-
reduces the [H+]
on the right so more HIn ionises to try to increase the [H+]
i.e. minimising the change in [H+].
-
6.2.2
The colour that
is observed will depend on the ratio [HIn]/[In–],
but at pH extremes i.e. very acid, colour 1 will dominate, or in
very alkaline solution, colour 2 will dominate. Therefore the
maximum colour 'shade' change from one to the other will occur when [HIn]
= [In–], or [colour 1] = [colour 2].
-
The pH when [HIn]
= [In–] can be calculated from the dissociation
constant, Kind (ka), for the weak acid indicator.
-
Kind
= [H+(aq)] [In–(aq)]/[HIn(aq)], but when [HIn]
= [In–] the equilibrium expression simplifies to ...
-
Kind
= [H+(aq)], so at this point the pH = –log(Kind)
-
and is referred
to as the pKind value.
-
6.2.3
pH titration
curves and choice of indicator
-
A simple pH curve for an
acid–alkali is explained on one of my
GCSE acid–alkali notes
pages and is well worth reading first, before tackling all
the possibilities described and explained below.
-
The greatest
change in indicator colour (per volume of reagent added), will occur
at the equivalence point in the titration.
-
Therefore you need to
choose an indicator with a pKind close to the pH at the
equivalence point (theory above).
-
In fact acid–base titration indicators are
usually effective over a range of several pH units but it is
essential for accurate titrations that the colour change is sharp at the equivalence point
with a small addition of acidic or alkaline titration solution.
-
Universal indicator is NOT suitable for
quantitative analysis and the indicator choices tabulated below
are explained via the sets of pH graphs shown further down using
Graphs A to D.
The effective pH range of the indicator is where there is sufficient
colour change to give a good sharp end–point and can be above or below,
but close to the pKind value of the indicator. Some
effective pH ranges for selected indicators are given below.
-
|
Indicator colour change, from acid to
alkali |
pKind
|
pH range |
example of titration use |
| Methyl
orange, (red ==> yellow) |
3.7 |
3.1–4.4 |
weak base – strong acid
titration e.g. ammonia, sodium carbonate or sodium
hydrogencarbonate titrated with hydrochloric acid |
| Bromophenol blue, (yellow ==> blue) |
4.0 |
2.8–4.6 |
weak base – strong
acid titration |
| Methyl red, (red ==> yellow) |
5.1 |
4.2–6.3 |
weak base – strong
acid titration |
| Bromothymol
blue, (yellow ==> blue) |
7.0 |
6.0–7.6 |
strong acid – strong
base titration e.g. hydrochloric acid <=> sodium hydroxide
titration |
| Phenol red,
(yellow ==> red) |
7.9 |
6.8–8.4 |
strong acid – strong
base titration e.g. hydrochloric acid <=> sodium hydroxide
titration |
| Thymol blue (base form), (yellow ==>
blue) |
8.9 |
8.0–9.6 |
weak/strong acid – strong base
titration |
| Phenolphthalein, (colourless ==> pinky–red) |
9.3 |
8.3–10.0 |
weak/strong acid – strong base
titration e.g. ethanoic acid titrated with sodium hydroxide |
-
 6.2.4
The change in pH through
various titrations is illustrated and explained to extend
the idea of choosing the right indicator.
-
Below are two
graphs of sets of curves showing how the pH changes when
weak/strong alkalis are added to weak/strong acids (set A) and vice
versa (set B).
-
The curves are a bit simplified and approximate, but
show how the pH changes in titrations.
-
By putting two graph sections from
(1) to
(4) together you can construct an approximate pH curve.
-
This is done below each graph
for the four acid–base permutations and it is assumed the acids and bases
are monobasic/monoprotic.
-
Note:
-
The end–point
= equivalence point or stoichiometric point.
-
If a buffer
calibrated pH meter is used rather than an indicator,
the end–point is obtained from the graph at the mid–point of
the steepest inflexion of the titration curve.
-
The first two
graphs (A and B) assume 20cm3 of the acid/alkali is
titrated with an alkali/acid of the same concentration e.g. 0.1 or
1.0 mol dm–3.
-
For
monoprotic/monobasic acids–base titrations there is only one point of
steepest inflexion
on the pH curve.
-
However, apart
from the strong acid–strong base curves, there are one or two
other, but much less steep, points of inflexion due to the
formation of a buffer mixture (see
determination of Ka of weak acid via titration curve).
-
The formation
of this buffer mixture makes the end–point less sharp because it
resists pH change.
-
Graph A
-
6.2.5
pH curves –
Graph A: The pH change when adding soluble base (alkali) to acid
-
6.2.5a: Curve A1
(1) +
(3):
Adding a weak base to a strong acid, end point at
(i1), approx. pH
3–5.
-
6.2.5b: Curve
A2 (1) +
(4):
Adding a strong base to a strong acid, end point
(i2), approx. pH
7.
-
pH change at
end–point very sharp e.g. titrating hydrochloric acid with
sodium hydroxide.
-
Suitable
indicators: bromothymol blue (pKind 7.0, range
6.0–7.6), phenol red (pKind 7.9, range
6.8–8.4), phenolphthalein (pKind 9.3,
range 8.3–10.0, ok for any strong acid – strong base titration
because the pH change is so sharp at the end–point i.e. the point of inflexion is very sharp for 1–2
drops of alkali over pH 3–10)
-
For all for all
these four cases, in terms of H+ and OH–
ions: Initially a high/low concentration of H+, very/mildly
acid, as the OH– is steadily added, the H+
ions are neutralised to water, so the H+
concentration steadily falls and the pH rises as the solution
becomes less acid. At pH 7, neutral there are very tiny equal
concentrations of H+ and OH– (due to the
self–ionisation of water). If excess alkali is added the pH
steadily rises to around 13 as the concentration of OH–
from the alkali rises ie solution becomes more alkaline.
-
6.2.5c: Curve
A3 (2) +
(3):
Adding a weak base to a weak acid, end point
(i2), approx. pH 7.
-
pH change at
end–point not very sharp, not practical for any titration e.g.
adding ammonia to ethanoic acid.
-
Suitable
indicators: None.
-
This
titration gives the lowest rate of change of pH approaching the
end–point, hence the poorest end–point to detect with indicator.
This is due to strong buffering effect of the mixture of
a weak base, weak acid and their salt. (for more details see
buffer examples 6.3.1 and 6.3.2)
-
6.2.5d: Curve A4
(2) +
(4):
Adding a strong base to weak acid, end point
(i3), approx. pH 9.
-
pH change at
end–point reasonable sharp e.g. you can titrate weak organic
acids like ethanoic acid with sodium hydroxide.
-
Suitable
indicators: phenolphthalein (pKind 9.3,
range 8.3–10.0), Thymol blue (base, pKind 8.9,
range 8.0–9.6)
-
The lower
rate of change of pH approaching the end–point compared to curve
A2 (above) is due to the weak buffering effect of the
mixture of a weak acid and the salt of a weak acid–strong base.
(for more details see buffer example 6.3.1)
-
Using
a pH titration curve to determine the Ka
of a weak acid
-
Graph E
-
When a
weak acid (HA) is titrated with a strong base (e.g. NaOH) a buffer mixture of A– and HA exists from soon after the
titration starts to near the end–point.
-
Therefore,
half–way to the equivalence point e.g. on addition of 10 cm3
of alkali of a 20 cm3 titration (Graph E, curve
(2) above), it means in terms
of concentrations
-
[NaA(aq)]salt = [A–(aq)] = [HA(aq)]unreacted
acid
-
Now, the
equilibrium expression for a mono basic/protic weak acid is
...
-
|
Ka =
|
[H+(aq)] [A–(aq)] |
|
–––––––––––– |
|
[HA(aq)] |
-
so, at the
half–way point, when [A–] = [HA], Ka
= [H+(aq)],
-
or at
half–way point: pH = pKa and Ka
= 10–pKa.
-
In the 'fictitious'
case of the weak acid above the pH is 4.2 at
this point,
-
therefore:
[H+(aq)] = Ka = 6.3 x
10–5 mol
dm–3.
-
Graph B
-
6.2.6
pH curves –
Graph B: The pH change when adding acid to a soluble base (alkali)
-
6.2.6a: Curve B1
(1) +
(3):
Adding a weak acid to a strong base, end point
(i1), approx. pH 9.
-
6.2.6b: Curve B2
(1) +
(4):
Adding a strong acid to strong base, end point
(i2), approx. pH 7.
-
pH change at
end–point very sharp e.g. titrating
sodium hydroxide with hydrochloric acid. For more details
see A2 above.
-
For all these
four cases, in terms of H+ and OH–
ions: Initially a high/low concentration of OH–,
very/mildly alkaline, as the H+ is steadily added, the
OH– ions are neutralised to water, so the OH–
concentration steadily falls as does the pH as the solution
becomes less alkaline. At pH 7, neutral there are very tiny
equal concentrations of H+ and OH–
ions (due to the self–ionisation of water). If excess acid
is added the pH steadily falls to around 1 as the
concentration of H+ from the acid rises.
-
6.2.6c: Curve B3
(2) +
(3):
Adding a weak acid to weak base, end point
(i2), approx. pH 7.
-
6.2.6d: Curve
B4 (2) +
(4):
Adding a strong acid to weak base, end point
(i3), approx. pH 3–5
-
e.g.
titrating ammonia with hydrochloric acid.
-
Suitable
indicators: methyl orange
(pKind 3.7, range 3.1–4.0)
-
6.2.7
More
complicated pH titration curves
-
6.2.7a The titration
of a weak dibasic acid e.g. 25 cm3 of 0.1 mol dm–3 ethanedioc acid (oxalic acid)
titrated
with 0.1 mol dm–3 sodium hydroxide
-
Graph C
-
There are two
inflexion points on the pH curve corresponding to the half and
full neutralisation of the dibasic/diprotic acid..
-
HOOC–COOH(aq)
+ NaOH(aq) ==> HCOO–COO–Na+(aq)
+ H2O(l)
-
ionically:
HOOC–COOH(aq) + OH–(aq) ==>
HCOO–COO–(aq) + H2O(l)
-
HCOO–COO–Na+(aq)
+ NaOH(aq) ==> Na+–OOC–COO–Na+(aq)
+ H2O(l)
-
ionically:
HCOO–COO–(aq) + OH–(aq)
==> –OOC–COO–(aq) + H2O(l)
-
To detect the
2nd end–point, and hence the acid quantitatively, phenolphthalein
indicator (pKind 9.3,
range 8.3–10.0) is used, since it is essentially a weak
acid–strong base titration.
-
The lower rate
of change of pH approaching the end–point compared to a strong
base–strong acid titration is due to the weak buffering effect
of the mixture of a weak acid and the salt of a weak acid–strong
base. (for more details see Case study ?)
-
Other acids
like propanedioic acid (malonic acid) and butanedioic acid (succinic
acid)
behave, and be titrated, in the same way.
-
In the case of
the tribasic/triprotic phosphoric(V) acid, H3PO4,
you would get three points of inflexion on the titration curve of
added sodium hydroxide versus pH corresponding to the
formation of
-
6.2.7b The titration
of 25cm3 of 0.1
mol dm–3 sodium carbonate titrated with 0.1
mol dm–3 hydrochloric acid.
-
Graph D
-
There are two
inflexion points on the pH curve.
-
Endpoint
(1) corresponds
to the 1st stage of neutralisation, the formation of the
hydrogencarbonate ion.
-
Na2CO3(aq)
+ HCl(aq) ==> NaCl(aq) + NaHCO3(aq)
-
ionically: CO32–(aq)
+ H+(aq) ==> HCO3–(aq)
-
This end–point
at around pH 8–9 can be detected with phenolphthalein (pKind 9.3,
range 8.3–10.0) or Thymol blue – base form (pKind
8.9, range 8.0–9.6)
-
If the conical
flask is rapidly swirled on adding the acid, you don't see any gas
bubbles of carbon dioxide.
-
End–point
(2)
corresponds to the 2nd stage of neutralisation, the formation of
water and carbon dioxide.
-
NaHCO3(aq)
+ HCl(aq) ==> NaCl(aq) + H2O(l)
+ CO2(g)
-
ionically:
HCO3–(aq) + H+(aq)
==> H2O(l) + CO2(g)
-
This end–point
around pH 3–4 can be detected with methyl orange indicator
(pKind 3.7, range 3.1–4.0) or Bromophenol blue (pKind
4.0, 2.8–4.6).
-
Overall the
reaction is ...
-
Note:
-
A mixture of
sodium carbonate and sodium hydrogencarbonate can be analysed
using two separate titrations.
-
Titration (i) using phenolphthalein
indicator measures the sodium carbonate,
-
and titration (ii)
measures the sodium carbonate plus the sodium hydrogencarbonate.
So both quantities can be calculated from the titration results.
-
6.2.8 Back
titrations
-
Examples include
...
-
Where a known
excess of acid is added to a base–alkali and the unreacted acid is 'back
titrated'
with a standard alkali solution from which the actual amount of
base–alkali originally present can be calculated.
-
Where a known
excess of alkali is added to an acid and the unreacted alkali is 'back
titrated'
with a standard acid solution from which the actual amount of acid
originally present can be calculated.
-
6.2.9
Examples of
acid–base titration questions with all the answers and
working.
-
–
Equilibria
Part 6 sub–index: 6.1 Salt hydrolysis * 6.2
Acid–base indicator theory, pH curves and
titrations
6.3 Buffers – definition, formulation
and action * 6.4 Buffer calculations * 6.5
Case studies
of buffer function
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