WOLFRAM|DEMONSTRATIONS PROJECT

H
4
A

​
fractional composition diagram
fractional composition bar chart
k
1
0.05
k
2
0.001
k
3
1.×
-8
10
k
4
1.×
-12
10
pH
0
α
H
4
A
α
H
3
-
A
α
H
2
2-
A
α
3-
HA
α
4-
A
This Demonstration shows the chemical equilibria in a polyprotic acid dissociation reaction at a given pH:
H
4
A
k
1
⇌
H
3
-
A
+
+
H
,
H
3
-
A
k
2
⇌
H
2
2-
A
+
+
H
,
H
2
2-
A
k
3
⇌
3-
HA
+
+
H
,
3-
HA
k
4
⇌
4-
A
+
+
H
.
The expressions for the fraction of an acid in each form (
H
4
A
,
H
3
-
A
,
H
2
2-
A
,
3-
HA
,
4-
A
) as a function of pH are obtained by taking account of the equilibrium constant and the mass balance. The fraction of molecules in a certain species is called
α
H
n-x
x-
A
, where
n
is the number of hydrogens on the undissociated acid molecule and
x
is the number of dissociated hydrogen ions. These are calculated as follows:
α
H
4
A
=
4
[
+
H
]
Δ
,
α
H
3
-
A
=
k
1
*
3
[
+
H
]
Δ
,…,
α
4-
A
=
k
1
k
2
k
3
k
4
Δ
where
Δ=
4
[
+
H
]
+
3
k
1
[
+
H
]
+⋯+
k
1
k
2
k
3
k
4
and
[
+
H
]=
-pH
10
.
Moreover, the concentration (M) of the generic species
H
n-x
x-
A
is given by:
[
H
n-x
x-
A
]=
C
T
α
H
n-x
x-
A
,
where
C
T
is the total concentration of the undissociated acid set to 0.1.
When "fractional composition diagram" is selected, you can change the
k
1
,
k
2
,
k
3
and
k
4
controls to observe the variation of the
α
values as a function of pH. By changing the pH control, you will obtain the individual
α
values, as highlighted by the dots on the diagram.
When "fractional composition bar chart" is selected, you can change the
k
1
,
k
2
,
k
3
,
k
4
and pH controls to see the resultant species concentration variations at equilibrium, where the sum of the species concentrations equals
C
T
. Further, we show the
wt%
of the different addends in
Δ
, which accounts for the approximations often used in calculations [1].