Chem.Eq.Diagr  Chemical Equilibrium Diagrams / Tutorials

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 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:

Titration_acetic

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?


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Titration of Mg with edta

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+

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 logK1,Mg must instead be ≈7.4 to obtain such degree of complex formation, and we will use this corrected value.

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.

After that, to simulate a Mg-edta tritration start by selecting in DATABASE the following components: H+, Mg2+, EDTA4−, NH3 and Ind3− (which you have just added as a component). 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).

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 species is obtained:

Titration_Mg-edta

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, and perhaps at 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.

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