2. Kinetic reactions React, X1t, and X2t can trace several types of reactions according to kinetic rate laws: Mineral precipitation and dissolution. Redox transformations, including those associated with surfaces and enzymes. Microbial metabolism and growth. Formation and dissociation of aqueous and surface complexes. Gas transfer.

3. Kinetics of Dissolution & Precipitation The rate of mineral dissolution or precipitation can in many cases be described by a simple rate law: r is the mineral’s dissolution rate (mol s –1 ) A s is the surface area of the mineral (cm 2 ) k + is the intrinsic rate constant (in mol cm –2 s –1 ) Q and K are the activity product and equilibrium constant for the dissolution reaction

4. Reaction Powers: Albite Dissolution pH < 1.5 1.5 < pH < 8 pH > 8

5. General Form of Built-in Rate Law Promoting and inhibiting species a j, m j = activity or concentration of promoting or inhibiting species P j = species’ power (+ is promoting, – is inhibiting) Nonlinear rate laws  : keyword order1,  : keyword order2

6. Kinetic Rate Laws You can set kinetic rate laws in several ways: Use GWB’s built-in laws. Specify the form of a custom rate law. Supply a BASIC script to evaluate the law. Write and compile a C++ function.

7. Supply specific surface area (cm 2 g –1 ) and rate constant (mol cm –2 s –1 ) for each kinetic mineral. Set rate constant (k + ) directly or via activation energy E A (J mol –1 ) and pre- exponential factor A (mol cm –2 s –1 ) for Arrhenius equation where R is gas constant, T K absolute temperature. Built-in Rate Law

8. Setting a Kinetic Rate Law for a Mineral Go to Reactants pane First, “add” a “Kinetic mineral” Set either a rate constant, or a pre-exponential factor and an activation energy Hydrogen ions promote the reaction with a “power” of one You can set options for the nucleation, nonlinearity, and cross-affinity Set the mineral’s initial mass and specific surface area

9. Custom Rate Laws Simply type out the form of the rate law Alternatively, import a Basic script, or a C++ function compiled into a library Details: See “Custom Rate Laws” in the GWB Reaction Modeling Guide React contains a symbolic interpreter that can evaluate any rate law

10. Task 1 — Precipitation and Dissolution Quartz reacts with deionized water at 25°C Quartz dissolves or precipitates according to a kinetic rate law. How do saturation state and silica concentration change with time?

11. 2 4 6 8 10 12 Supersaturation Undersaturation SiO 2 (aq) (mg/kg) 0+.25+.5+.75+1 0.5 1 1.5 2 Supersaturation Undersaturation Time (years) Quartz saturation (Q/K) Quartz solubility Quartz saturation

12. Mineral Nucleation In order for a new mineral to precipitate, it must have nuclei on which to grow. React uses a simple description of nucleation. The user specifies: A nucleus density (keyword nucleus; the surface area on which the mineral can grow, in cm 2 per cm 3 of fluid). A critical saturation index (keyword critSI ; log Q/K = 0, by default) above which the nuclei are available.

13. Fig. 1. Comparison of measured and computed Eh values in 30 ground waters as a function of pH. Symbols and couples are summarized in Table 1. Points connected by a vertical line are derived from a single water sample. Table 1. Redox couples and plotting symbols used in the construction of Fig. 1 + x MField-measured Eh value Fe 3+ /Fe 2+ O 2 /H 2 O Fe 2+ /Fe(OH) 3 (s) HS - /SO 4 2- HS - /S(rhombic) NH 4 + /NO 3 - NO 2 - /NO 3 - CH 4 /HCO 3 - NH 4 + /N 2 Lindberg and Runnells, 1984, Science, 225, 925–927. NH 4 + /NO 2 -

14. Fe 3+, FeCl 2+, Fe(OH) 3, … Cu 2+, CuCl 2, CuNH 3 2+, … SO 4, HSO 4 −, … Fe 2+, FeCl +, Fe(OH) 2, … Cu +, CuCl 2 −, CuNH 3 +, … HS −, H 2 S, S 2−, … Master Eh Equilibrium Approach 2−

15. Fe 3+, FeCl 2+, Fe(OH) 3, … Cu 2+, CuCl 2, CuNH 3 2+, … SO 4, HSO 4 −, … Fe 2+, FeCl +, Fe(OH) 2, … Cu +, CuCl 2 −, CuNH 3 +, … HS −, H 2 S, S 2−, … 2− Disequilibrium: Disable redox coupling reaction(s) Master Eh Eh S

16. Fe 3+, FeCl 2+, Fe(OH) 3, … Cu 2+, CuCl 2, CuNH 3 2+, … SO 4, HSO 4 −, … Fe 2+, FeCl +, Fe(OH) 2, … Cu +, CuCl 2 −, CuNH 3 +, … HS −, H 2 S, S 2−, … 2− Eh S Disequilibrium: Each disabled couple has distinct Nernst Eh Eh Fe Eh Cu

17. Redox Kinetics – Homogeneous Catalysis m j = concentration of promoting or inhibiting species P j = species’ power (+ is promoting, – is inhibiting) Q and K are the reaction’s activity product and equilibrium constant

18. Example – Fe 2+ oxidation

19. Task 2 — Homogeneous Catalysis Oxidation of ferrous iron by dioxygen. Decouple Fe +++ / Fe ++ redox pair. Fix pH, O 2 fugacity.

20. 0+5+10+15+20 0 10 20 30 Fe 2+ Fe 3+ Component concentration (mmolal) Time (days)

21. Redox Kinetics – Catalysis on Mineral Surfaces A s is the catalyzing surface area. Choose a specific mineral as a catalyst (A s will be calculated from its mass), or set a total area. Possible to set parallel pathways for same redox reaction (absence or presence of a catalyst). Total reaction rate would be sum of rates.

22. Task 3 — Catalysis on Mineral Surfaces Catalytic oxidation of Mn 2+ on ferric iron surface. Decouple various oxidation states of Mn and Fe. Fix pH, oxidation state.

23. 0+2+4+6+8+10 0 5 10 15 20 Mn(II) concentration (umolal) Time (days)

24. Modeling Strategy It is neither practical nor possible to describe all chemical reactions with kinetics. Chemical reactions may be divided into three groups Reactions that proceed quickly over the time span of the calculation  equilibrium model. Reactions that proceed negligibly over the calculation  suppressed reaction. Reactions that proceed slowly but measurably  kinetic law.

25. Craig M. Bethke and Brian Farrell © Copyright 2016 Aqueous Solutions LLC. This document may be reproduced and modified freely to support any licensed use of The Geochemist’s Workbench® software, provided that any derived materials acknowledge original authorship.