Supporting Information. Hydroxyl Radical Production by H 2 O 2 -Mediated. Conditions

Transcription

1 Supportng Informaton Hydroxyl Radcal Producton by H 2 O 2 -Medated Oxdaton of Fe(II) Complexed by Suwannee Rver Fulvc Acd Under Crcumneutral Frehwater Condton Chrtopher J. Mller, Andrew L. Roe, T. Davd Wate* School of Cvl and Envronmental Engneerng, The Unverty of New South Wale, Sydney, New South Wale 2052, Autrala Southern Cro GeoScence, Southern Cro Unverty, Lmore, New South Wale 2480, Autrala Supportng Informaton contan detal of the knetc model parameter fttng procedure, a table of addtonal reacton n the preence of t-butanol and four fgure contanng further expermental data and knetc model output. S1

2 S1. Addtonal Reacton n the Preence of t-utanol Table S1. Addtonal reacton n the preence of t-butanol Reacton HO + (CH 3 ) 3 COH H 2 O + CH 2 C(CH 3 ) 2 OH Rate Contant (M 1 1 ) a 2 CH 2 C(CH 3 ) 2 OH HO(CH 3 ) 2 CH 2 CH 2 C(CH 3 ) 2 OH 2k = b Fe(II)L + CH 2 C(CH 3 ) 2 OH Fe(III)L + [ CH 2 (CH 3 ) 3 COH] CH 2 C(CH 3 ) 2 OH + O 2 OOCH 2 C(CH 3 ) 2 OH Fe(II)L + OOCH 2 C(CH 3 ) 2 OH Fe(III)L + HOC(CH 3 ) 2 CH 2 OO c d e 2 OOCH 2 C(CH 3 ) 2 OH [HOC(CH 3 ) 2 CH 2 OO] 2 2k = (8 ± 2) 10 8 b [HOC(CH 3 ) 2 CH 2 OO] 2 O 2 + HOC(CH 3 ) 2 CH 2 OH + HOC(CH 3 ) 2 CHO [HOC(CH 3 ) 2 CH 2 OO] 2 H 2 O HOC(CH 3 ) 2 CHO [HOC(CH 3 ) 2 CH 2 OO] 2 O CH 2 O + 2 C(CH 3 ) 2 OH [HOC(CH 3 ) 2 CH 2 OO] 2 O 2 + HO(CH 3 ) 2 CCH 2 OOCH 2 C(CH 3 ) 2 OH C(CH 3 ) 2 OH + O 2 OOC(CH 3 ) 2 OH OOC(CH 3 ) 2 OH (CH 3 ) 2 C=O + HO 2 R = f R = f R = f R = f d d a uxton et al. 1 b Smc et al. 2 c rate contant for Fe(II)EDTA from Croft et al. 3, aumed the ame for Fe(II)L 1 ; although Rahhal and Rchter 4 ugget the reacton doen t occur for Fe(II)DTPA, th reacton wll only be a mnor pathway for the organc radcal and wll not trongly nfluence the model predcton at the Fe(II) concentraton ued here. d Rez et al. 5 e etmate from Khakn et al. 6 f decay of tetroxde ntermedate aumed to be rapd; a value of R wa adopted, wth the proporton (R) taken from Rez et al. 5 S2

3 S2. Model Fttng Procedure The model wa ft by determnng the parameter bet able to reproduce the fnal oberved Phth- OH concentraton () and alo the peudo-frt order rate contant for Phth-OH formaton (k ). Thee parameter were determned for both the expermental data and knetc model output by fttng a functon of the form t ( e k ) [ Phth OH] = 1 (S1) ung a non-lnear leat-quare algorthm. In th way the fnal model wa able to well-contran both the magntude and formaton rate of HO producton. A the two obervable ( and k ) were of dfferent order of magntude a unt dtance calng wa appled to each obervable to enure they were both of equal mportance n the fttng proce. 7 The calng wa appled to both the expermental data and the knetc model output ung calng parameter derved from the expermental data, a outlned below. = n k, k = n (S2) d = ( ) 2, d ( = k k k ) 2 (S3) In thee equaton n the total number of condton examned and and k are value of and k at condton. The caled value were determned a below, where and k are the caled parameter. d = (S4) k k = (S5) d k k S3

4 To determne the model value of and k the knetc model wa run n Kntecu, then a nonlnear leat-quare fttng routne appled to ft eq S1 to the model output. In th way, by runnng the model at varyng rate contant value, numercal etmate of the partal dervatve of and k could be evaluated ung the formula below. ((1+ ) k ) ( (1 ) k ) 2 k (S6) k ((1+ ) k ) k ((1 ) k ) 2 k (S7) where (( 1+ ) and (( 1+ ) )k k )k are the value of and k, repectvely, when the model evaluated for k = (1 + )k. Thee dervatve are requred to form the Jacoban matrx n the parameter fttng proce, however, due to the unt calng appled to the data thee dervatve alo requred calng. ( ) = k d (S8) = 1 (S9) d k mlarly, = 1 d k (S10) The model wa ft ung a non-lnear leat quare approach by adjutng rate contant k 4r and k 9 (number refer to reacton n the man paper), a uch, dervatve wth repect to thee rate contant were determned and the Jacoban formed a below. J J = J k (S11) S4

5 where: J = M 4r 1 4r n 9 M 1 9 n (S12) J k 4r = M 4r 1 n 9 M 1 9 n (S13) A weghtng matrx wa alo requred n the model fttng proce, contructed ung the nvere of the varance of and k (after accountng for calng). Under ome condton the value of k could not be relably determned due to the rapdty of the reacton and nablty to ample fat enough to obtan data able to determne th parameter accurately. In thee cae the value of the tandard error of k wa et to an arbtrarly hgh value of 10 1 to enure that th data pont dd not unduly nfluence the fttng proce. Fnally, the weghtng matrx (W) wa further caled uch that the um of weght for wa equvalent to the um of weght for k, enurng both parameter had equal mpact upon the fttng proce. The fttng proce wa conducted followng Manthey, 8 wth an adjutment matrx X calculated ung the formula below, where X a column vector contanng the parameter that are beng ftted (.e., k 4r and k 9 ). A new etmate for X wa obtaned from X + X and the proce repeated untl convergence. T 1 T ( J WJ) J WK X= (S14) After convergence, the varance-covarance matrx (Q xx ) wa computed and the value of the tandard error for the ftted parameter determned by takng the quare root of the dagonal entre of the approprately caled varance-covarance matrx (Q xx ) S5

6 xx T ( J ) 1 Q = WJ (S15) Q Q xx = (S16) S xx 2 0 where: 2 K T WK S0 = (S17) n p n = number of datapont p = number of parameter beng ftted S6

7 S3. Plot of Knetc Model Output and Expermental Data Fgure S1. Comparon of expermental data and knetc model output for [SRFA] = 10 mg L 1. In all panel [Fe(II)] 0 wa 2 µm, H 2 O 2 concentraton were a labeled, ymbol repreent expermental data (from at leat two eparate experment), error bar are one tandard error from the calbraton and old lne how the knetc model output. S7

8 S8 Fgure S2. Comparon of expermental data and knetc model output for [SRFA] = 20 mg L 1. In all panel [Fe(II)] 0 wa 2 µm, H 2 O 2 concentraton were a labeled, ymbol repreent expermental data (from at leat two eparate experment), error bar are one tandard error from the calbraton and old lne how the knetc model output.

9 S9 Fgure S3. Comparon of expermental data and knetc model output for [SRFA] = 30 mg L 1. In all panel [Fe(II)] 0 wa 2 µm, H 2 O 2 concentraton were a labeled, ymbol repreent expermental data (from three eparate experment), error bar are one tandard error from the calbraton and old lne how the knetc model output.

10 S10 Fgure S4. Comparon of expermental data and knetc model output for [SRFA] = 40 mg L 1. In all panel [Fe(II)] 0 wa 2 µm, H 2 O 2 concentraton were a labeled, ymbol repreent expermental data (from at leat two eparate experment), error bar are one tandard error from the calbraton and old lne how the knetc model output.

11 S4. Reference (1) uxton, G. V.; Greentock, C. L.; Helman, W. P.; Ro, A.. Crtcal revew of rate contant for reacton of hydrated electron, hydrogen atom and hydroxyl radcal ( OH/ O ) n aqueou oluton. J. Phy. Chem. Ref. Data 1988, 17 (2), (2) Smc, M.; Neta, P.; Hayon, E. Pule radoly tudy of alcohol n aqueou oluton. J. Phy. Chem. 1969, 73 (11), (3) Croft, S.; Glbert,. C.; Smth, J. R. L.; Whtwood, A. C. An E.S.R. nvetgaton of the reactve ntermedate generated n the reacton between Fe II and H 2 O 2 n aqueou oluton. Drect evdence for the formaton of the hydroxyl radcal. Free Radcal Re. 1992, 17 (1), (4) Rahhal, S.; Rchter, H. W. Reacton of hydroxyl radcal wth the ferrou and ferrc ron chelate of dethylenetramne-n,n,n',n'',n''-pentaacetate. Free Radcal Re. 1989, 6 (6), (5) Rez, E.; Schmdt, W.; Schuchmann, H. P.; von Sonntag, C. Photoly of ozone n aqueou oluton n the preence of tertary butanol. Envron. Sc. Technol. 2003, 37 (9), (6) Khakn, G. I.; Alfa, Z..; Hue, R. E.; Neta, P. Oxdaton of ferrou and ferrocyande on by peroxyl radcal. J. Phy. Chem. 1996, 100 (17), (7) Gunt, R. F.; Maon, R. L. Regreon Analy and t Applcaton: A Data-Orented Approach. Marcel Dekker, nc.: New York and ael, S11

12 (8) Manthey, D. General Leat-Square Drect Soluton and undle Adjutment. S12