Speciation and α-Values
• Speciation - the relative concentration of each of
the related species in a solution.
• α-Value can be defined as:
• αX = Molar concentration of species X
Total molar concentration of all related species
where species X is the species of interest.
There are no units for α because it is a
fraction.
1
Eg. acetic acid
• Dissociation of acetic acid:
• CH3COOH → CH3COO- + H+
• α CH3COOH =
[CH3COOH]
[CH3COOH] + [CH3COO-]
It is the CH3COOH and CH3COO- (the
conjugate pair) that are the “related
species”.
2
Tutorial
1. When ammonia is added to an aqueous
solution of Zn2+ the following species can
exist:
Zn2+, Zn(NH3)2+, Zn(NH3)22+, Zn(NH3)32+,
Zn(NH3)42+, NH3, NH4+, H+, OH-, H2O
Write down an expression for α Zn2+
in terms of the concentrations of the
relevant species.
3
Calculating α-Values
• how do we find the α-values?
– Calculate from the relevant equilibrium
constants and the concentrations of other
relevant species.
– For example, to calculate α0 for acetic acid,
use Ka for acetic acid and [H+]
4
• there’s a pattern for an acid that can
donate n protons:
(See your textbook for how it’s done…)
• What about α1, α2 etc? All the α
expressions have the same denominator.
• The numerator for α1 is the same as for
the 2nd term of the denominator, the
numerator for α2 is the same as the 3rd
term and so on… (Can you see that the
numerator for αo is the same as the 1st
term in the denominator?)
5
Calculating α-Values
The sum of the values for a system must equal
unity; i.e.
0 + 1 + 2 + 3 = 1
For an acid that can donate n protons we get:
HnA =
[H+]n
[H+]n +Ka1 [H+]n-1 + Ka1 Ka2 [H+]n-2 +…+ Ka1....Kan
6
Tutorial
2. What is the value of α1 in a solution
which has [CH3COOH] = 0.025 M and
[CH3COO-] = 0.050 M?
α CH3COOH = α 0
α CH3COO- = α 1
3. Calculate α1 for acetic acid at pH 7.00
7
α-Plots
• Also known as speciation diagrams
• Graphical representations of α-values.
• It is a plot of the α-value vs pH.
• Information about the composition of solutions
can be found.
• eg. pH speciation diagram for a monoprotic
acid.
8
Alpha plot for a monoprotic acid
Speciation Diagram for Acetic Acid
1.0
0.8
0.6
α0
0.4
α1
α
0.2
0.0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14
pH
9
Dissociation of acetic acid
• Eg. Acetic acid
• CH3COOH → CH3COO- + H+
• below about pH 5, the dominant species is HA
(CH3COOH).
• above about pH 5, the dominant species is A(CH COO-).
3
• at just below pH 5, α0 = α1 = 0.5 and so
[CH3COOH] = [CH3COO-]
10
Tutorial
4. Write down the expression for Ka for
acetic acid and use it to calculate the pH
at which [CH3COOH] = [CH3COO-].
Compare your answer with the
speciation diagram for acetic acid.
11
1.0
H2A
alpha
0.8
0.6
HA-
H2A
0.4
H2A ↔ H+ + HApKa = 7.0
0.2
HA-
0.0
5
6
7
8
9 10
pH
Alpha plot for first dissociation of
a diprotic acid
12
1.0
HA
H2-A
alpha
0.8
0.6
HHA
2A
2-AA
0.4
HA- ↔ H+ + A2pKa = 12.3
0.2
HA
A2--
0.0
10 11 12 13 14
Alpha plot for second dissociation
of a diprotic acid
13
1.0
HA-
H2A
alpha
0.8
0.6
HA-
H2A
A2-
0.4
0.2
HA-
A2-
0.0
5
6
7
8
9 10
10 11 12 13 14
pH
Alpha plot for a diprotic acid
14
DISSOCIATION of H3PO4
H3PO4 + H2O ⇔ H3O+ + H2PO4-
-3
Ka1 = 7.11 X 10
H2PO4- + H2O ⇔ H3O+ + HPO42-
-8
Ka2 = 6.32 X 10
HPO42- + H2O ⇔ H3O+ + PO43-
-13
Ka3 = 4.5 X 10
15
1.0
H3PO4
H2PO4-
HPO42-
0.6
H3PO4
alpha
0.8
0.4
H2PO4-
HPO42-
0.2
H2PO4-
PO43-
PO43-
HPO42-
0.0
1
2
3
4
5
6
7
8
9 10
10 11 12 13 14
pH
Alpha Plot for Phosphoric Acid (triprotic acid)
16
•
The line with the largest value of α at the
lowest pH must correspond to the fully
protonated form and
•
the line with the largest value of α at the
highest pH must belong to the fully
deprotonated form.
Tutorial
5. Write down an expression for α H3PO4 in a
solution of phosphoric acid.
17
Fractions of dissociating
species at a given pH
For a given total concentration of phosphoric
acid, C H3PO4, we can write
C H3PO4 = [PO43-] + [HPO42-] + [H2PO4-] +
[H3PO4]
α 0 = [H3PO4]
α 2 = [HPO42-]
C H3PO4
C H3PO4
18
Tutorial
6. Calculate the equilibrium concentrations
of the different species in a 0.10 M
phosphoric acid solution at pH 3.00.
19
Tutorial
7. These questions are based on the speciation
diagram for phosphoric acid.
a) Which phosphate species is present at the
greatest concentration at pH 5?
b) Determine the values for the three acid
dissociation constants (Ka values) for
phosphoric acid.
8. Calculate:
• α0 for phosphoric acid at pH 7.00
• α2 for phosphoric acid at pH 7.00
20
Neutralisation Reactions
• Certain indicators undergo a colour change when only
the first of the three protons in phosphoric acid has been
neutralised;
neutralised; i.e
H3PO4
+ OH-
→
H2PO4- + H2O
• Certain other indicators change colour after 2 hydrogen
ions have reacted:
H3PO4 +2OH- →
HPO42-
+ 2H2O
• It is not practical to titrate the third proton; thus the
equivalent that is 1/3 of the formula weight for H3PO4 is
not encountered in the context of a neutralisation
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reaction.
• H3PO4
• Ka1 = 7.11 X 10-3
•
•
Ka2 = 6.32 X 10
Ka3 = 4.5 X 10
-8
-13
pKa1
= 2.148
pKa2
= 7.199
pKa3 = 12.35
The first stoichiometric endpoint is given approx.
by
pH = ½ (pKa1 + pKa2)
The second stoichiometric endpoint is given
approx. by
pH = ½ (pKa2 + pKa3)
22
Tutorial
9. These questions are based on the speciation
diagram for phosphoric acid.
a) A buffer solution was prepared by making
an equimolar mixture of KH2PO4 and K2HPO4,
what is the pH of the solution?
b) If you were titrating H3PO4 with NaOH, what
would you expect to be the pH at the first
equivalence point?
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Transitional Metal complexes
Fractional Composition diagram for Zn/OH in
Aqueous Solution
1.0
0.9
Zn
0.8
2+
Zn(OH)4
0.7
2-
0.6
α 0.5
0.4
Zn(OH)2(aq)
0.3
0.2
Zn(OH)
Zn(OH)3
+
-
0.1
0.0
4
5
6
7
8
pH
9
10
11
12
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Tutorial
10. From the zinc/hydroxide speciation diagram:
Which are the important zinc species
a)
below pH 7
b)
above pH 12
c)
at pH 9.5
11. A saturated solution of zinc hydroxide,
buffered to pH 8.0 has a total zinc
concentration of 3.0x10-4 M. Calculate the
molar concentrations of all the zinc species
present in that solution.
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speciation diagrams - not
dependent on pH
• E.g. In aqueous solution, the Hg2+ ion can
become complexed by Cl- ions – in other
words, the Cl- ions form a (coordinate)
covalent bond with Hg2+ . The relevant
equilibria are:
• Hg2+ + Cl- → HgCl+
• HgCl+ + Cl- → Hg(Cl)2
• Hg(Cl)2 + Cl- → Hg(Cl)3• Hg(Cl)3- + Cl- → Hg(Cl)4226
Speciation Diagram for Hg(Cl)n
(2-n)+
1.0
0.9
0.8
α
0.7
α0
0.6
α1
0.5
α2
0.4
α3
α4
0.3
0.2
0.1
0.0
1E-07
0.000001 0.00001
0.0001
0.001
0.01
0.1
1
10
[Cl-] (M)
αn refers to the species with n Clattached to the Hg2+
27
Tutorial
12. This question is based on the Hg(Cl) diagram.
a) Under what conditions will Hg(Cl)42- be
the major mercury species in solution?
b) Under what conditions will Hg2+ be present
in solution?
c) You are told in first year Chemistry that
“when salts dissolve in water they dissociate
completely”. What does this diagram tell you
about the behaviour of HgCl2?
28
α-Plots and Titrations
• Consider the titration of a solution of CH3COOH
with NaOH.
• The equation for the titration reaction is:
•
CH3COOH(aq) + NaOH(aq) → CH3COONa(aq) + H2O(l)
• At the equivalence point:
• all the CH3COOH will have just been converted
to CH3COONa and so α0 = 0 and α1 = 1.
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• For some polyprotic acids, the conditions
of α0 = 0 and α1 = 1 are not satisfied. In
this case you will not be able to find an
endpoint for the titration of the first proton
of the acid.
• Consider the example of another triprotic
acid, citric acid:
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F ra ct io nal C o mpo s it io n o f C it rat e So lut io n a s a F unc tio n o f pH
K1 = 7.45x10-4; K2 = 1.73x10-5; K3 = 4.02x10-7
1.0
0.8
α0
α1
α2
α3
0.6
α
0.4
0.2
0.0
0
1
2
3
4
5
6
7
8
9
10
pH
31
• the second reaction starts before the first one
has finished and α1 never reaches a value of 1
– in other words, the H2Cit- ion is never the only
one in solution.
• Does this mean that citric acid cannot be titrated
successfully with sodium hydroxide? No – if
enough sodium hydroxide is added, the only
species in solution will be the Cit3- anion and the
reaction:
H3Cit(aq) + 3NaOH(aq) → Na3Cit(aq) + 3H2O(l)
will have gone to completion.
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Dissociation of Citric acid
• H3Cit + H2O
⇌ H2Cit- + H3O+
• H2Cit-
+ H2O
⇌ HCit2- + H3O+
• HCit2-
+ H2O
⇌ Cit3- + H3O+
33
Tutorial
13. Use the α-plot for phosphoric acid to estimate
the pH at the equivalence point for:
H3PO4(aq) + 2NaOH(aq) → Na2HPO4(aq) + 2H2O(l)
14. Use the α-plot for citric to answer the
following questions.
What citrate species will be in solution at:
a)
b)
pH = 1.0
pH = 5.0
c)
pH = 9.0
34
Tutorial
15. What would be the pH at the
equivalence point for the titration of
citric acid with sodium hydroxide?
16. For the titration of citric acid with
sodium hydroxide, list all the species
that would be in solution:
a) half way through the titration,
b) at the equivalence point.
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