Mole balance and saturation concentrations

[Charlie]

I'm having difficulty understanding a result and want to check if this is due to the model or my understanding.   I am simulating the addition of smithsonite (ZnCO3) to a solution, with and without the presence of a mineral surface to which Zn can complex with.  I am trying to see how the surface takes up Zn (and lowers the dissolved concentration) and also assess the 'breakthrough' of Zn once the sites are full.

When I plot the results for the final dissolved total concentration of Zn, I find that the saturation concentration is greater than compared to the simulation without the surface included (controlled by precipitation of Zn(OH)2).  I'm not sure that I understand how this would be possible? Surely the solubility of Zn(OH)2 is the control and this will not change?  I have checked to see if this is possibly due to moles/molality conversions but I don't think that it is.

When I have tried this with Pb in exactly the same fashion, the total dissolved Pb concentrations are limited by the saturation concentration for Pb(OH)2 as expected. 

This is the input script (for Zn):

SURFACE_MASTER_SPECIES
        Vac_ Vac_O3-2
SURFACE_SPECIES
        Vac_O3-2 = Vac_O3-2;         log_k 0.0
        -cd music 0 0 0 0 0
        Vac_O3-2 + H+  = Vac_O3H-;   log_k 2.3
        -cd_music 1 0 0 0 0
        Vac_O3-2 + 2H+ = Vac_O3H2;   log_k 4.6
        -cd_music 2 0 0 0 0
        Vac_O3-2 + 3H+ = Vac_O3H3+;  log_k 6.9
        -cd_music 3 0 0 0 0
   Vac_O3-2 + Zn+2 = Vac_O3Zn;  log_k 4.56
        -cd_music  1 0 1 0 0    #This is a fit to experimental data

PHASES
Fix_pe   
e- = e-
log_k 0.0

SELECTED_OUTPUT
-file Zn_sorb.xls
-totals Zn
-molalities Vac_O3Zn
-equilibrium_phases smithsonite Zn(OH)2(e)
-saturation_indices smithsonite Zn(OH)2(e)
-reset false
-pH true
-pe true
-reaction true

USER_PUNCH
-heading Zn(ppb)
-start
10 PUNCH Tot("Zn")*65.409*1000*1000
-end

SOLUTION 1
pH 8

EQUILIBRIUM_PHASES 1
CO2(g) -3.5 1000  # atmospheric
Calcite 0.0 10
Dolomite 0.0 10
Smithsonite 0.0 0.0
Zn(OH)2(e) 0.0 0.0
Hematite 0.0 10
Goethite 0.0 10
#Gypsum 0.0 0.0
Fix_pe -7  O2(g)

REACTION 1
Smithsonite
0.1 moles in 100 steps

SURFACE 1
Vac_       0.0165 892   3.3
        -capacitances   0.5
        -cd_music
END

#Compare to the case without the surface included:

USE solution 1
USE reaction 1
USE equilibrium_phases 1

END

[dlparkhurst]

Not sure if this is the complete story, but consider this explanation. Zn(OH)2 is more soluble at lower pH. If you compare the pH generated by adding smithsonite with and without the surface, you find that the pH is lower when Zn is allowed to sorb. Thus, Zn(OH)2 tends to dissolve more and you end up with a higher total Zn when Zn sorption is present.


SURFACE_MASTER_SPECIES
        Vac_ Vac_O3-2
SURFACE_SPECIES
        Vac_O3-2 = Vac_O3-2;        log_k 0.0
        -cd music 0 0 0 0 0
        Vac_O3-2 + H+  = Vac_O3H-;  log_k 2.3
        -cd_music 1 0 0 0 0
        Vac_O3-2 + 2H+ = Vac_O3H2;  log_k 4.6
        -cd_music 2 0 0 0 0
        Vac_O3-2 + 3H+ = Vac_O3H3+;  log_k 6.9
        -cd_music 3 0 0 0 0
Vac_O3-2 + Zn+2 = Vac_O3Zn;  log_k 4.56
        -cd_music  1 0 1 0 0    #This is a fit to experimental data

SOLUTION 1
units ppm
pH 8
END
USE solution 1
REACTION 1
Smithsonite
0.1 moles
END
USE solution 1
USE REACTION 1
SURFACE 1
Vac_O3-2      0.0165 892  3.3
        -capacitances  0.5
        -cd_music
END

[Charlie]

Thanks David for your thoughts.  That makes sense and I think that is partly the answer. 

However, using my script I see that the pH rises from 8.16 to ~8.8 (with sorption ) and remains at pH 8.8 at site saturation, and Zn(OH)2 precipitation, with a total dissolved Zn concentration of 3932 ppb.  For the case without the surface, the pH is constant at ~8.357 and the total dissolved Zn concentration is relatively lower, at 2132 ppb (please see my earlier attachment).  This seems contrary to your explanation above.

Is it possible that after the sites reach saturation the total dissolved Zn concentration is a sum of the Zn from being in equilibrium with both the surface and the Zn(OH)2 ?

[dlparkhurst]

Sorry I didn't work all the way through your problem. Here is explanation number 2. Consider the calculation (below) where you perform the reaction without the surface, save the results, then add the surface. (Note, if the surface is not defined in equilibrium with a solution, it is a good idea to use an uncharged form of the surface in the SURFACE definition, in this case Vac_O3H2 or Vac_O2.)

As you add the surface, you can use the following sequence to describe the results:
(1) the surface sorbs Zn, which causes (2) Zn(OH)2 to dissolve. (3) The dissolution of Zn(OH)2 increases the pH (CO3/HCO3 ratio), which causes calcite and dolomite to precipitate, and (4) CO2 to dissolve. (5) there is a net increase in carbon in the system, which forms Zn-carbonate aqueous complexes that increase the solubility of Zn(OH)2.

The simulations isolate the effect of adding the surface. The effect of adding the surface changes can be seen in the mole transfers of the last simulation in this input file and by comparison to the aqueous composition of the previous simulation (excluding the surface) although the sequence I've presented is somewhat arbitrary.


SURFACE_MASTER_SPECIES
        Vac_ Vac_O3-2
SURFACE_SPECIES
        Vac_O3-2 = Vac_O3-2;        log_k 0.0
        -cd music 0 0 0 0 0
        Vac_O3-2 + H+  = Vac_O3H-;  log_k 2.3
        -cd_music 1 0 0 0 0
        Vac_O3-2 + 2H+ = Vac_O3H2;  log_k 4.6
        -cd_music 2 0 0 0 0
        Vac_O3-2 + 3H+ = Vac_O3H3+;  log_k 6.9
        -cd_music 3 0 0 0 0
Vac_O3-2 + Zn+2 = Vac_O3Zn;  log_k 4.56
        -cd_music  1 0 1 0 0    #This is a fit to experimental data

PHASES
Fix_pe   
e- = e-
log_k 0.0

SOLUTION 1
pH 8
END
EQUILIBRIUM_PHASES 1
CO2(g) -3.5 1000  # atmospheric
Calcite 0.0 10
Dolomite 0.0 10
Smithsonite 0.0 0.0
Zn(OH)2(e) 0.0 0.0
Hematite 0.0 10
Goethite 0.0 10
#Gypsum 0.0 0.0
Fix_pe -7  O2(g)
END
REACTION 1
Smithsonite
0.1 moles in 1 steps

SURFACE 1
Vac_O3H2      0.0165 892  3.3
        -capacitances  0.5
        -cd_music
END

#Compare to the case without the surface included:

USE solution 1
USE reaction 1
USE equilibrium_phases 1
SAVE solution 2
SAVE equilibrium_phases 2
END

USE surface 1
USE solution 2
USE equilibrium_phases 2
END

[Charlie]

Thanks David.  It seems that there are more subtleties in this than I had first expected.  I am going to try omitting equilibrium phases and assessing the results.  It is good to consider/realise that surface complexation reactions can modify the overall solution conditions and therefore affect solubilities in different ways.