Supporting information to. and Ruben Kretzschmar. Institute of Isotope Geochemistry and Mineral Resources, ETH Zurich, NO, 8092 Zürich, Switzerland
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1 Supportig iformatio to Iro isotope fractioatio durig proto-promoted, ligad-cotrolled, ad reductive dissolutio of goethite Ja G. Wiederhold*., Stepha M. Kraemer, Nadya Teutsch, Paul M. Borer, Alex N. Halliday, ad Rube Kretzschmar Departmet of Evirometal Scieces, ETH Zurich, CHN, 8092 Zurich, Switzerlad Istitute of Isotope Geochemistry ad Mieral Resources, ETH Zurich, NO, 8092 Zürich, Switzerlad Swiss Federal Istitute of Aquatic Sciece ad Techology (Eawag, 8600 Dübedorf, Switzerlad Departmet of Earth Scieces, Uiversity of Oxford, Parks Road, Oxford, OX1 3PR, Uited Kigdom * wiederhold@ev.ethz.ch, phoe: +41-( , fax: +41-( Joural: Evirometal Sciece ad Techology ( This supportig iformatio was prepared i April 2006 ad cotais 5 pages, 3 tables, ad 2 figures. Table S1. Experimetal desig of goethite batch dissolutio experimets. mechaism reaget goethite coditio product i solutio reactio time iitial ph proto-promoted 0.5 M HCl g/l dark Fe(III 3 mi 24 h 0.3 ligad-cotrolled 5 mm oxalate 2.5 g/l dark Fe(III-oxalate 5 mi 315 d 3 reductive 1 mm oxalate 0.5 g/l light Fe(II 5 mi 7.5 h 3 S1
2 Table S2. Summary of results for all dissolutio experimets. sample dissolutio time [mi] dissolved fractio [%] δ 57 Fe [ ] vs. IRMM-014 2SD vs. bulk goethite bulk goethite dark dark dark dark dark dark dark dark dark dark dark dark dark wash 1 (H 2 O, ph leach 1 (0.5 M HCl leach 2 (0.5 M HCl dark total residue light light light light light light light light total residue HCl HCl HCl total residue dark B dark B dark B dark B dark C dark C dark C dark C dark C dark C dark C total residue dark D1 ph dark D2 ph dark D3 ph dark D4 ph dark D5 ph dark D6 ph light B light B light B light B light B light B Samples marked B, C ad D are additioal sample series ot discussed i the text. These data complemet our mai sample series ad cofirm the reproducibility of our results. S2
3 Descriptio of kietic fractioatio model: Calculatio of total surface site pool (moolayer: [%] = SSD SA fractio of surface Fe atoms M goethite N A (1 SSD [1/m 2 ] = surface site desity of Fe atoms (4.35 sites/m 2 from ref. 34 SA [m 2 /g] = surface area of goethite determied by N 2 -BET-method (38 m 2 /g M goethite [g/mol] = molar mass of goethite (FeOOH: g/mol N A [1/mol] = Avogadro umber ( Table S3. Distributio of iro isotopes i IRMM-014 (IRMM certificate, 1999, Geel, Belgium isotope Fe fractio (X exact mass (m mass differece (md 54 Fe Fe Fe Fe ØFe mass differece of isotope Fe to ØFe ( = 54, 56, 57, 58: md m m m ØFe = (2 ØFe F = fractioatio costat for specific reactio (idepedet of isotopic mass f = md F (ote: f is egative for 54 Fe ad positive for 56 Fe, 57 Fe ad 58 Fe (3 f determies the fractioatio of isotope relative to the average mass of iro (ØFe. We use this omeclature rather tha the commoly used fractioatio factor α or erichmet factor ε because these values oly refer to fractioatio betwee two specific isotopes (e.g., ratio 57 Fe/ 54 Fe whereas f ca be used for all four isotopes. However, the coversio of F to α ad ε is show i the followig equatios: fractioatio factor α for isotopes a Fe ad b Fe (a > b: α = 1+ ( md md F (4 a b ε = α 1 10 = md md F 10 (5 erichmet factor ε for isotopes a Fe ad b 3 3 Fe (a > b: [ ] ( ( erichmet factor ε for the isotope ratio 57 Fe/ Fe: [ ] sol Our model coceptually defies the followig three compartmets: a ε = Δ Fe - Δ Fe (6 b bulk goethite o fractioatio reactive surface site pool isotope fractioatio solutio S3
4 The size of the reactive surface site pool ( is costat due to self-replicatio of reactive surface sites durig the dissolutio reactio (umber of Fe atoms dissolved equals umber of Fe atoms repleished from bulk. Whereas the dissolutio reactio differetiates betwee the differet Fe isotopes, the selfreplicatio of reactive surface sites from the bulk goethite is oly depedet o the crystallographic positio of the ew reactive site ad ot o its isotopic mass. We express our model i terms of umbers of Fe atoms i a closed system. However, it could be easily coverted ito molar cocetratio uits. [ Fe] bulk = umber of atoms of isotope Fe i bulk goethite ( = 54, 56, 57, 58 [ Fe] = umber of atoms of isotope Fe i reactive surface site pool ( = 54, 56, 57, 58 [ Fe] sol = umber of atoms of isotope Fe i solutio ( = 54, 56, 57, 58 X = fractio of isotope i bulk mieral ( = 54, 56, 57, 58 (from Table S3 [Fe] tot bulk [ Fe] + [ Fe] [ Fe] = + sol 54 [ ] [ ] sol 56 [ ] sol 57 [ ] sol 58 Fe = Fe + Fe + Fe + [ Fe] sol sol (total umber of Fe atoms i system (8 ξ = (ξ = reactio progress variable (9 dissolved fractio [%] = ξ 100 [ Fe] tot output of isotope from = ( 1 f [ Fe] (1 f [ Fe] ξ (dissolutio with isotope fractioatio iput of isotope to = X ξ (repleishmet from bulk without isotope fractioatio Differetial equatio describig the distributio of Fe isotopes i the reactive surface site pool: [ Fe] (1 f [ Fe] ξ = (1 f [ Fe] + X We developed a umerical model describig the system with 2 fittig parameters: - fractioatio costat F (ca be coverted to erichmet factor ε with equatio 5 - size of reactive surface site pool ( The two parameters have a differet ifluece o the model output. Whereas the fractioatio costat F (or erichmet factor ε is very sesitive at early dissolved fractios ad defies the iitial fractioatio step, the size of the reactive surface site pool ( iflueces the surface depletio effect ad is resposible for the shape of the curve at higher dissolved fractios. The best model fit was determied usig the Solver tool of Microsoft EXCEL. First, we approximated our experimetal data (oly early-dissolved fractios with Δ 57 Fe < 0 with simple logarithmic fuctios (R 2 = for oxalate dark ad R 2 = for oxalate light. Solver was the used to fid the best model fit by varyig simultaeously the two fittig parameters (erichmet factor ad size of reactive surface site pool ad thereby miimizig the sum of squared differeces betwee our model ad the approximated log fuctios withi the rage of dissolved fractios of our experimetal data ( % for oxalate dark ad % for oxalate light. The followig two figures S1 ad S2 show the sesitivity of our model towards the two fittig parameters i the oxalate dark experimets. (10 S4
5 0 = 2.4 % measured data model ( ε = -2.6 model ( ε = -1 model ( ε = dissolved fractio [%] Figure S1. Model output with differet erichmet factors ε ad fixed size of reactive surface site pool ( = 2.4 % 0 ε = measured data model ( = 2.4 % model ( = 1 % model ( = 5 % dissolved fractio [%] Figure S2. Model output with differet sizes of reactive surface site pool ad fixed erichmet factor (ε = S5
( ) ( ), (S3) ( ). (S4)
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