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Brown's Chemistry Clinic
Equilibria Part 6
"Acid-base titrations, indicators, buffers and non-aqueous media"
GCE-AS-A2-IB Advanced Level Theoretical-Physical Chemistry revision notes
GCSE
Notes on reversible reactions-equilibrium *
Advanced Part 1. Equilibrium,
Le Chatelier's Principle-rules * Part 2.
Kc and Kp equilibrium expressions and
calculations
* Part 3. Equilibria and industrial processes *
Part 4.
Partition,
solubility product and ion-exchange *
Part 5. pH, weak-strong acid-base theory and calculations * Part 6 sub-index: 6.1
Salt hydrolysis * 6.2 Acid-base indicators and
titrations * 6.3 Buffers - definition, formulation
and action * 6.4 Buffer calculations * 6.5
Case studies
of buffer function * 6.6 Acids-bases in non-aqueous media *
Part 7. Redox equilibria, half-cell electrode potentials,
electrolysis and electrochemical series
*
Part 8 Phase equilibria-vapour
pressure, boiling point and intermolecular forces
* The K and ΔS-ΔG connection with EØcell
will be dealt with via new thermodynamics pages later, but an
example of a ΔS-ΔG calculation is given at the end of
the advanced kinetics pages and ΔG for cells is
mentioned in Equilibria Part 7.
M = old fashioned shorthand for mol dm-3
*
EMAIL
query?comment
6.1
Salt Hydrolysis
-
Despite being
taught at lower academic levels that salts e.g. sodium chloride,
dissolve in water to form neutral solutions of pH 7.
-
In reality, and
looking at a wider variety of 'salts', the picture is much more complicated
and a 'salt' solution may be acid, neutral or alkaline
depending on the nature of the interaction of the salt ions with water.
-
The reasons are
quite clear when you consider the possible Bronsted-Lowry interactions
that can take place between the ions of the salt and water.
-
6.1.1
Examples of
acidic salt solutions: pH <7
-
6.1.2
Examples of
nearly neutral salt solutions: pH approx. 7
-
6.1.3
Examples of
alkaline salt solutions: pH>7
-
6.1.3a: Salts of a
weak acid and a strong base e.g. sodium ethanoate
-
The hydrated
sodium ion shows no acidic character but the ethanoate ion is a
strong conjugate base of a the weak ethanoic acid (pKa
= 4.76, Ka = 1.74 x 10-5
mol dm-3), so an acid-base
hydrolysis reaction occurs to generate hydroxide ions to raise the
pH to about pH 9.
-
6.1.3b: Potassium
cyanide: is the salt of the very strong base potassium hydroxide
and the very weak hydrocyanic acid (pKa = 9.31, Ka =
4.9 x 10-10 mol dm-3). The hydrated potassium ion shows
no acidic behaviour, but the cyanide ion is a strong conjugate base
of the very weak hydrocyanic acid (HCN) which interacts with water to generate
hydroxide ions. Hydrocyanic acid (pKa = 9.4) is weaker
than ethanoic acid (pKa = 4.76) , so the equilibrium is
more on the right, more OH-, and so the pH is more
alkaline, i.e. over 9.
-
6.1.3c: Sodium carbonate
is the 'salt' of the strong base sodium hydroxide and the very weak
'carbonic acid'
-
Again the
hydrated sodium ion shows no acidic character but the carbonate
ion is a strong conjugate base of a the weak 'carbonic' acid, so
an acid-base hydrolysis reaction occurs to generate hydroxide ions
to raise the pH.
-
CO32-(aq)
+ H2O(l)  HCO3-(aq)
+ OH-(aq)
6.2
The theory of acid-base
indicators and pKind
-
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
-
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 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 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)
-
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 'ficticious'
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.
-
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 'backtitrated'
with a standard alkali solution,
-
Where a known
excess of alkali is added to an acid and the unreacted alkali is 'backtitrated'
with a standard acid solution.
-
6.2.9
Examples of
acid-base titration questions with all the answers and
working.
6.3
Buffers - definition, formulation and
action
-
6.3.1 A buffer is a
solution that minimises pH change on the addition of small amounts
of acid or alkali.
-
Buffers and
their chemical reactions must obey Le Chatelier's Equilibrium
Concentration Principle, and act in a way to remove H+
and OH- ions. BUT, they cannot theoretically
prevent the pH being lowered/raised by the addition of acid/alkali,
however small the change. Any buffer will eventually be 'used up' if
large quantities of acid or alkali are added to the solution.
-
6.3.2 Typical
buffers and their action.
-
Buffering
action example 6.3.2a
-
A mixture of
a weak acid and the salt of the weak acid with a strong base.
-
Organic acids
like methanoic, ethanoic, propanoic, citric, benzenedicarboxylic
etc. are frequently used in buffer mixtures i.e. those with the
carboxylic acid functional group -COOH
-
The salts are
usually those of the strong base-alkalis sodium and potassium
hydroxide.
-
e.g. ethanoic
acid CH3COOH and sodium ethanoate CH3COO-Na+
gives buffers in the range pH 3.7-5.6
-
CH3COOH
and CH3COO- constitute a conjugate
acid-base pair.
-
In solution
most of the weak acid is NOT ionised and the relatively high
concentration of the CH3COO- ion actually
inhibits ionisation.
-
The salt is
fully ionised in solution to give a relatively high concentration of
the ethanoate ions.
-
Buffering
action example 6.3.2b
-
A mixture of
a weak base and the salt of the weak base with a strong acid.
-
e.g. ammonia NH3
and ammonium chloride NH4+Cl-
-
NH4+
and NH3 constitute a conjugate acid-base pair.
-
In solution most
of the ammonia is NOT ionised (and even suppressed by the ammonium
ions from the salt).
-
The salt is
fully ionised in solution giving relatively high concentrations of
the ammonium ion.
-
?
-
6.3.3 Preparing
buffer solutions.
-
Quite often
several solutions of salts, weak acids/bases are prepared and then
mixed in different ratios to provide buffers of a wide pH range.
-
Sometimes a
single salt will do to give a single accurate pH value for calibrating a pH
meter. (see Case study 6.5.1)
6.4
Buffer calculations
6.5
Case studies of the function and
uses of
buffers in aqueous media
-
Case study 6.5.1 Other common
buffer solutions and their use in the laboratory.
-
 Potassium
hydrogen benzene-1,2-dicarboxylate is an 'all in one'
buffer solution of pH 4.0
-
(i) H+(aq)
+ -OOC-C6H4-COOH(aq)
HOOC-C6H4-COOH(aq)
-
(ii) -OOC-C6H4-COOH(aq)
+ OH-(aq) -OOC-C6H4-COO-(aq)
+ H2O(l)
-
(i) removes hydrogen ions
and (ii) removes hydroxide ions.
-
Buffers can be
made by mixing the salt with the original benzene-1,2-dicarboxylic
acid to give buffers in the range 2.2-3.8
-
A mixture of
salts of a polybasic/polyprotic acid e.g. the salts KH2PO4, Na2HPO4
and Na3PO4 from phosphoric(V) acid (a
tribasic/triprotic acid) can give
buffer solutions in the range pH 6-12 e.g.
-
from Na2HPO4: HPO42-(aq)
+ H+(aq)
H2PO4-(aq)
(removes hydrogen ions)
-
from Na3PO4:
PO43-(aq)
+ H+(aq)
HPO42-(aq)
+ H2O(l) (removes hydrogen ions)
-
from KH2PO4: H2PO4-(aq)
+ OH-(aq)
HPO42-(aq)
+ H2O(l) (removes hydroxide ions)
-
from Na2HPO4:
HPO42-(aq)
+ OH-(aq)
PO43-(aq)
+ H2O(l) (removes hydroxide ions)
-
The HPO42-
ion is amphoteric, acting both as a proton donor and acceptor
and phosphate(V) ions are important in the buffering of intracellular
fluids in living organisms (see Case study 6.5.2 below).
-
Buffer
solutions are used to accurately calibrate pH meters.
-
Case study 6.5.2 The
importance of buffering in
biological systems
-
6.5.2b Inside cells
hydrogenphosphate(V) ions act as the major intracellular buffer
system, with contributions from organic phosphates such as
glucose-6-phosphate and ATP.
-
6.5.2c The major
extracellular buffer is the 'carbonic acid'-'bicarbonate' or hydrogencarbonate system
which enables e.g. blood, to function as an extraordinary effective
buffer operating at about pH 7.
-
(i) CO2(g,
lungs)
+ aq
(ii) CO2(aq*) + H2O(l)
(iii) H2CO3(aq)
(iv) HCO3-(aq)
+ H+(aq)
-
(v) H2CO3(aq)
+ OH-(aq)
(vi) HCO3-(aq)
+ H2O(l) *(aq) =
intra/extracellular fluids
-
(iv) to (iii)
removes hydrogen ions and (v) to (vi) removes hydroxide ions.
-
The effectiveness
of the system depends on the reservoir of dissolved carbon dioxide in
the blood plasma and the gas in the lungs.
-
If hydroxide
ions are removed via reaction (v) to (iv), the depleted H2CO3
is readily replaced via the reaction sequence (i) to (ii) and (ii)
to (iii).
-
If hydrogen ions
are removed via (iv) to (iii) the reverse sequence of 1. can restore
the system to the original pH.
-
The ability of
mammals to maintain a fairly constant [HCO3-]/[H2CO3]
ratio in blood plasma is reflected in the rate of CO2
production in the cell oxidation reactions of respiration and the rate
of CO2 loss by expiration.
-
The blood plasma
of man is about 7.4 and any deviation below 7.0, or above 7.8, as can
happen in disease, can cause irreparable damage.
-
Intracellular and
extracellular systems are very pH sensitive and small changes in pH
can produce ill-effects in living organisms, hence, e.g. the bodies
irritation by all except the very weakest of acids and alkalis in
contact with the skin.
-
Case study 6.5.3
Shampoos
-
Case study 6.5.4:
*
6.6
Acid and bases in non-aqueous
media
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[Al(H2O)5(OH)]2+(aq)
+ H3O+(aq)
The importance of
a stable pH cannot be over emphasised for the efficient function of
enzyme-proteins which control most of the chemistry of life. Most
enzymes can only operate at their maximum catalytic capacity over
a narrow range of pH and three examples are shown. Examples
of conjugate acid-base pairs that fulfil this important buffering operation are described below.