Tutorial: H+ affinity diagram

Chemical Equilibrium Diagrams / Tutorials

Proton affinity diagrams

This diagram type can only be selected in SPANA with the “advanced” program level (in the menu Preferences / General options).

A proton affinity curve made with Spana will show the derivative of bound H⁺ ions with respect to the logarithm of the H⁺ activity:

d [H⁺]_bound

d (log{H⁺})

this function can, for example, be plotted against pH or [H⁺]_TOT. Remember that log{H⁺} = −pH.

Here brackets “[]” indicate concentrations, and braces “{}” indicate activities.

The amount of bound H⁺ is calculated as:

[H⁺]_bound = [H⁺]_TOT − [H⁺] + [OH⁻]

This is the amount of H⁺ bound in different species, for example in HCO₃⁻ or in Al(OH)₄⁻. The derivative is approximated numerically:

d [H⁺]_bound

d (log a_H⁺)

=

Δ [H⁺]_bound

Δ (−pH)

If a value for the ionic strenght is not given in Spana when making the diagram, then pH = −log [H⁺].

The resulting diagram shows a peak for each protonation reaction, and it can be more useful than the corresponding titration curve. Unfortunately peaks may overlap, and a diagram’s interpretation is never unique.

Citric acid

Select citrate (cit³⁻) and H⁺ as components in DATABASE. In SPANA make sure you have selected the “advanced” program level (in the menu Preferences / General options).

Make and compare the titration curves without and with citrate:

It is difficult to tell what kind of ligand is present only by looking at these curves. By taking the derivative, making a proton affinity diagram, it becomes clear that there are three protonation sites:

Mixture

Select oxalate (ox²⁻), carbonate (CO₃²⁻) and H⁺ as components in DATABASE. In SPANA make sure you have selected the “advanced” program level (in the menu Preferences / General options).

When a mixture of ligands is presents (in this case ox²⁻ and CO₃²⁻) in the proton affinity diagram the height of the peaks is proportional to the concentration of the corresponding ligand. For example:

Note that the peaks are located at the pH corresponding to the protonation constant.

Al(III) hydrolysis

An example where several peaks are overlapping in a proton affinity diagram.

Select Al³⁺ and H⁺ as components in DATABASE. In SPANA make sure you have selected the “advanced” program level (in the menu Preferences / General options).

Select the menu “Run / Modify chemical system”. Double click on each of the solid phases (Al(OH)₃(cr), AlOOH(s), etc) and deactivate all of them (by adding a “*” at the beginning of the name). Save the file.

Make a proton affinity diagram for [Al(III)]_TOT = 10⁻⁶M. The diagram shows two peaks:

The corresponding logarithmic diagram:

shows that the peak at pH ≈ 7.3 corresponds to the H⁺ exange between Al(OH)₄⁻ and Al(OH)₃, while the peak at pH ≈ 5.1/nobr> corresponds to two reactions: the proton exange between Al(OH)₃, AlOH²⁺ and Al³⁺.