09 - Kinetic Oxidation¶

Dissolved ferrous iron meeting oxygen. Thermodynamically the answer is immediate – Fe(II) is not stable in oxygenated water – so an equilibrium calculation says all the iron is Fe(III) and stops there.

The useful question is how long, and that needs a rate.

A rate law in the input¶

TITLE Example 9.--Kinetically controlled oxidation of ferrous

                  iron. Decoupled valence states of iron.

SOLUTION_MASTER_SPECIES

Fe_di              Fe_di+2    0.0     Fe_di              55.847

Fe_tri             Fe_tri+3   0.0     Fe_tri             55.847

SOLUTION_SPECIES

Fe_di+2 = Fe_di+2

        log_k   0.0

Fe_tri+3 = Fe_tri+3

        log_k   0.0

# Fe+2 species

Fe_di+2 + H2O = Fe_diOH+ + H+

        log_k   -9.5

        delta_h 13.20   kcal

#... and also other Fe+2 species

Fe_di+2 + Cl- = Fe_diCl+

        log_k   0.14

Fe_di+2 + CO3-2 = Fe_diCO3

        log_k   4.38

Fe_di+2 + HCO3- = Fe_diHCO3+

        log_k   2.0

Fe_di+2 + SO4-2 = Fe_diSO4

        log_k   2.25

        delta_h 3.230   kcal

Fe_di+2 + HSO4- = Fe_diHSO4+

        log_k   1.08

Fe_di+2 + 2HS- = Fe_di(HS)2

        log_k   8.95

Fe_di+2 + 3HS- = Fe_di(HS)3-

        log_k   10.987

Fe_di+2 + HPO4-2 = Fe_diHPO4

        log_k   3.6

Fe_di+2 + H2PO4- = Fe_diH2PO4+

        log_k   2.7

Fe_di+2 + F- = Fe_diF+

        log_k   1.0

# Fe+3 species

Fe_tri+3 + H2O = Fe_triOH+2 + H+

        log_k   -2.19

        delta_h 10.4    kcal

#... and also other Fe+3 species

Fe_tri+3 + 2 H2O = Fe_tri(OH)2+ + 2 H+

        log_k   -5.67

        delta_h 17.1    kcal

Fe_tri+3 + 3 H2O = Fe_tri(OH)3 + 3 H+

        log_k   -12.56

        delta_h 24.8    kcal

Fe_tri+3 + 4 H2O = Fe_tri(OH)4- + 4 H+

        log_k   -21.6

        delta_h 31.9    kcal

2 Fe_tri+3 + 2 H2O = Fe_tri2(OH)2+4 + 2 H+

        log_k   -2.95

        delta_h 13.5    kcal

3 Fe_tri+3 + 4 H2O = Fe_tri3(OH)4+5 + 4 H+

        log_k   -6.3

        delta_h 14.3    kcal

Fe_tri+3 + Cl- = Fe_triCl+2

        log_k   1.48

        delta_h 5.6     kcal

Fe_tri+3 + 2 Cl- = Fe_triCl2+

        log_k   2.13

Fe_tri+3 + 3 Cl- = Fe_triCl3

        log_k   1.13

Fe_tri+3 + SO4-2 = Fe_triSO4+

        log_k   4.04

        delta_h 3.91    kcal

Fe_tri+3 + HSO4- = Fe_triHSO4+2

        log_k   2.48

Fe_tri+3 + 2 SO4-2 = Fe_tri(SO4)2-

        log_k   5.38

        delta_h 4.60    kcal

Fe_tri+3 + HPO4-2 = Fe_triHPO4+

        log_k   5.43

        delta_h 5.76    kcal

Fe_tri+3 + H2PO4- = Fe_triH2PO4+2

        log_k   5.43

Fe_tri+3 + F- = Fe_triF+2

        log_k   6.2

        delta_h 2.7     kcal

Fe_tri+3 + 2 F- = Fe_triF2+

        log_k   10.8

        delta_h 4.8     kcal

Fe_tri+3 + 3 F- = Fe_triF3

        log_k   14.0

        delta_h 5.4     kcal

PHASES

Goethite

        Fe_triOOH + 3 H+ = Fe_tri+3 + 2 H2O

        log_k   -1.0

END

SOLUTION 1

        pH  7.0

        pe 10.0  O2(g) -0.67

        Fe_di  0.1

        Na  10.

        Cl  10.  charge

EQUILIBRIUM_PHASES 1

        O2(g)           -0.67

RATES

Fe_di_ox

  -start

  10  Fe_di = TOT("Fe_di")

  20  if (Fe_di <= 0) then goto 200

  30  p_o2 = SR("O2(g)")

  40  moles = (2.91e-9 + 1.33e12 * (ACT("OH-"))^2 * p_o2) * Fe_di * TIME

  200 SAVE moles

  -end

KINETICS 1

Fe_di_ox

        -formula  Fe_di  -1.0  Fe_tri  1.0

        -steps 100 400 3100 10800 21600 5.04e4 8.64e4 1.728e5 1.728e5 1.728e5 1.728e5

        -step_divide 1e-4

INCREMENTAL_REACTIONS true

END

The oxidation rate of ferrous iron is strongly dependent on pH – it goes as the square of the hydroxide activity, so a unit of pH is a hundredfold in rate – and on the oxygen partial pressure. That law is written into a RATES block as BASIC, and a KINETICS block integrates it over time.

This is the general shape of a kinetic model in PHREEQC: the equilibrium calculation gives the speciation at each instant, and the rate law says how fast the irreversible step proceeds. The two are solved together at every step, so the rate sees the current pH and the current speciation rather than the starting ones.

The result¶

Fe(2) falling and Fe(3) rising over days, with pH on the same axes — Fe(II) falling and Fe(III) rising over several days, with pH on the same axes.¶

The pH curve is the one to watch, and it is why the two species are not simple mirror images. Oxidising ferrous iron and precipitating the ferric product releases acid, so the pH falls as the reaction proceeds – and since the rate depends on the square of the hydroxide activity, the reaction slows itself down. The system is self-limiting through its own product.

An equilibrium model gives none of this. It gives the endpoint, which was never in doubt.

What it shows¶

That kinetics is required whenever the rate is comparable with the timescale of interest, and that a rate law coupled to a speciation calculation can show feedback that neither would show alone.

The practical case is iron removal from groundwater: the time to oxidise the iron, and therefore the size of the plant, depends on a pH that the reaction itself is changing.

Source¶

Parkhurst, D. L. and Appelo, C. A. J. (2013). Description of input and examples for PHREEQC version 3. U.S. Geological Survey Techniques and Methods, book 6, chapter A43. This is Example 9 of that manual.
Singer, P. C. and Stumm, W. (1970). Acidic mine drainage: the rate- determining step. Science 167, 1121-1123, for the rate law’s form.