Titration curves
Titration curves are only of interest
to explore under what conditions a titration can be made.
For example to find out what are the lower limits
for the reagent concentrations.
Acid-base titrations
Acid-base titration curves are plots of calculated pH as a funtion of added
acid (H+) or base (OH−).
Because the components in the DATABASE database
are the un-protonated ligands, you might need to
exchange a component for a complex in
Spana if you
wish to simulate the titration of an acid (a protonated ligand) with a base.
For example: titration of acetic acid with NaOH. In order to have
OH− as the component in
the X-axis it is necessary to set the hydroxide ion as a chemical component.
This is achieved by exchanging a component
with a reaction. In this case the original component H+
is exchanged for the complex OH−.
Acetate
(CH3COO−) is also exchanged with acetic
acid (CH3COOH).
Now it is possible to calculate a titration curve of acetic acid:
In this example the X-axis starts at [OH−]TOT =
−5 mM to simulate an initial solution
containing a strong acid, [HCl]initial = 5 mM,
and 10 mM acetic acid. Compare
the diagram above with a titration curve without acetic acid
(titration of a strong acid with
a strong base).
You can simulate a tritration of a smaller amount of acetic acid, but
remember to decrease the X-axis range in the same proportion. For example,
for a titration of 1 mM of acid, the [OH−]
concentration should be between zero and ≈2 mM.
What is the minimum initial acid concentration required to “see” a pH
change? Is it possible, for example, to titrate a 1 μM solution?
Titration of Mg with edta
|
edta (ethylenediaminetetraacetate) is a is widely used
hexadentate (“six-toothed”) ligand and chelating agent:
Organic ligands like edta are linked to the element carbon
in DATABASE. |
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|
Magnesium can be titrated with edta using a pH 10 buffer and
Calmagite as metal-indicator.
This is a tri-protic acid, H3ind, and its colour changes
with protonation: H2ind− is bright red
(pH < 9),
Hind2− is clear blue (pH 9 to 12), and
ind3− is reddish orange (pH > 12).
Complexation with Ca or Mg also induces a colour change (at pH 10):
| |
Mg2+ |
+ Hind2−
blue |
 |
Mg(ind)−
red
|
+ H+ |
Equilibrium constants: because Calmagite is not included in the DATABASE
database you must add the new data for this indicator.
The original reference contains
some approximate equilibrium constants
(at ionic strength I = 0.1 M):
| |
ind3− + H+
Hind2− |
|
logK1,H = 12.35 |
| |
ind3− + 2H+
H2ind− |
|
logβ2,H = 20.49 |
| |
ind3− + Mg2+
Mg(ind)− |
|
logK1,Mg = 5.7 |
The last equilibrium constant, K1,Mg, was
estimated in the reference from a meassured 25% “extent of dissociation
of the compound” at I = 0.1, pH = 10 and
Calmagite and Mg concentrations equal to 2.5×10−5
M. Simulations made with Spana show that
to obtain such a degree of complex formation, logK1,Mg
must instead be ≈7.4,
and we will use this value here.
Extrapolation to zero ionic strength using
Davies eqn. gives
logK°1,H ≈13.02,
logβ°2,H ≈21.60,
and
logK°1,Mg ≈8.7.
Add these data in DATABASE.
Titration curve: to simulate a Mg-edta tritration start by selecting in DATABASE
the following components: H+, Mg2+,
EDTA4−, NH3 and
Ind3− (which you just added).
Note that edta is found among the order organic ligands, linked to the element carbon.
Then use the menu “File / Save and Exit” to make an input file for Spana.
When simulating a titration it is important to keep track of the proton balance.
Edta solutions are normally prepared from the di-sodium salt
Na2edta·2H2O.
In Spana select the menu “Run /
Modify chemical system”
to exchange EDTA4− for
H2EDTA2−.
Exchange also Ind3− for HInd2−
and H+ for NH4+
(to simulate a NH4+/NH3 pH≈10 buffer).
The components are now: Mg2+, H2EDTA2−,
HInd2−, NH4+
and NH3.
Now a diagram can be made. Select H2EDTA2−
for the X-axis, [NH4+]T = 0.001 and
[NH3]T = 0.02 (to keep pH ≈10),
[Mg2+]T = 0.001 and
[HInd2−]T = 5×10−6.
The following fraction diagram for Calmagite is obtained:
(the colours of the curves may be changed using the menu “Preferences /
Diagram windows”, see also
“make it pretty: change the diagram”)
The end point is reached when the solution is blue
without a trace of purple colour. By varying the
the concentration of the buffer (NH3) it is seen that
if pH is decreased below 10 then the fraction of H2ind−
increases, the final colour becomes less blue,
and the titration’s end point is more difficult to see.
It may be shown, by making a fraction diagram for Mg2+,
that the initial solution is slightly oversaturated with Mg(OH)2(cr),
and precipitation might occur at higher pH, or higher Mg-concentrations.
This would make the colour change sluggish and the end point difficult to see.
In conclusion: the buffering of pH is fundamental
in this titration.
