03 - Fit Ni Sorption¶

Two constants again, but fitted to a different kind of experiment: a pH edge. The zinc isotherm of 02 - Fit Langmuir Isotherm held pH fixed and varied the metal; this one holds the metal fixed and varies pH, and what the two constants describe is not capacity and strength but two competing surface reactions.

It is PhreePlot’s nickel sorption example: nickel on goethite, fourteen measurements between pH 4.7 and the alkaline end.

Two reactions, two constants¶

TITLE Goethite surface 1pK model, Ni sorption 1 site.

PHASES

Fix_H+

  H+ = H+

  log_k 0.

SURFACE_MASTER_SPECIES

        Fes_   Fes_OH-0.5

SURFACE_SPECIES

        Fes_OH-0.5  = Fes_OH-0.5                                               # surface charging

        log_k  0.0

        Fes_OH-0.5  + H+ = Fes_OH2+0.5

        log_k 8.50

        2Fes_OH-0.5 + Ni+2 = (Fes_OH)2Ni+                                      # bidentate model

        log_k  @{$log_k1$}@

        2Fes_OH-0.5 + Ni+2 + H2O = (Fes_OH)2NiOH + H+

        log_k @{$log_k2$}@

SURFACE 1

# -diffuse_layer

# -no_edl

  Fes_OH-0.5    1.09e-3  32.7    3.33                                          # goethite parameters

SOLUTION 1

  units mol/kgw

  Ni     0.4258e-3                                                             # NiT

  Na     0.1                                                                   # background electrolyte

  N(5)   0.1 charge

EQUILIBRIUM_PHASES

  O2(g)  -0.67   0.1

  Fix_H+ -@{$pHobs$}@ NaOH

    -force_equality true

  Ni(OH)2 0 0

END

The surface is goethite in the 1-pK formulation, with one site type carrying a half charge:

2Fes_OH-0.5 + Ni+2 = (Fes_OH)2Ni+
                     log_k  @{$log_k1$}@

2Fes_OH-0.5 + Ni+2 + H2O = (Fes_OH)2NiOH + H+
                     log_k  @{$log_k2$}@

Both are bidentate – two surface groups to one nickel – and they differ by a proton: the second releases one, the first does not. That single difference is what makes two constants fittable from a pH edge rather than one. A reaction that releases a proton is pushed forward as pH rises, so the two species dominate in different parts of the range, and the data separates them.

The surface charging reaction, Fes_OH-0.5 + H+ = Fes_OH2+0.5 with log K 8.50, is not fitted. It is a property of goethite, measured independently, and fitting it alongside the nickel constants would let the solver trade surface charge against metal binding and find an excellent fit that means nothing. Which parameters are held fixed is as much a part of a fitting problem as which are free.

The solution is 0.43 mmol/l nickel in 0.1 M NaNO3, equilibrated with oxygen, with pH imposed at each measured value. The residual compares the nickel left in solution:

#Ni_observed# - #Ni#

Both constants start at 8 and are bounded to ±100.

The result¶

Dissolved nickel against pH, showing the sorption edge, with measurements and fitted model — Dissolved nickel against pH: the sorption edge. Nickel stays in solution at low pH, then falls sharply over about two pH units as sorption takes over, and is essentially gone above the edge.¶

Edges like this are steep because the surface is deprotonating – becoming more negative and so more attractive to a cation – at the same time as the hydrolysed surface species becomes favourable. Both fitted reactions contribute, and the **position** and the **steepness** of the edge are what determine them: roughly, the position fixes the first constant and the shape fixes the second.

This is the practical reading, and it mirrors 02 - Fit Langmuir Isotherm. Measurements that do not span the edge will fit, and will not determine anything.

Try it¶

Fit only log_k1, holding log_k2 at its starting value, and see how the edge shape fails to follow the data.
Free the surface charging constant as a third parameter and watch the fit improve while the standard errors grow.
Change the nickel concentration and see the edge move, which is the signature of a sorption-controlled system rather than a precipitate.

Source¶

Kinniburgh, D. G. and Cooper, D. M. (2011). PhreePlot: Creating graphical output with PHREEQC. This is PhreePlot’s nickel sorption fit, including the 1-pK goethite surface and the bidentate model. See the PhreePlot website.
The thermodynamic data is wateq4f.dat, distributed with PHREEQC (Parkhurst and Appelo, 2013).