Environ Technc... .Sd . 1887 1187-119. ,21 3 Kinetics of Chromium(III) Oxidation to Chromium (VI) by Reaction with Manganese Dioxide L Edmond Eery* and Dhanpat Ra! BatteDe. Pacific Northwest Laboratories. Richland, Washington 99352 compares a /TTT, _ „ ..„ othe.. o d t r soils .hav) Schroede. (9 . e e , . Le d ran . . , . m The kinetics of oxidation of aqueous Cr(III) to Cr(VI) Aovm that . 8igniricant fraction of the aqueous Crail)
in industrial waste materials oxidatioe .Th aqueou f (/0nt o f ) *»**.*s * Cr(in oxidizes )wa y db Cr(ni) is not appreciably affected by dissolved oxygen, J^fff^°^Tw»r ** ?^ ^Dmff1? *^ ^ indicating that Cr(III) reacts directly with /J-Mn02(s o )t Co(II Co(IIIo )t ) (11aqueoud )an s As(III As(Vo )t ) (72). produc catalyzey eb Cr(VIt no d d) reactionan • sP»Per wit"" ° presenhe 1 ,w oxyge t nexperimenta lkie dat-th n ao at the /J-MnO8(s) surface. In acidic solutions, the oxidation netics of aqueous Cr(HI) oxidation to Cr(VI) by reaction of aqueous Cr(III) is highly nonlinear with time, possibly with pyrolusite [0-MnO2(s)], primarily for acidic environ- because strong adsorptio producee th f no d anionic Cr(VI) ments 0-MnO2(se chose .W us o et thin )i s study because species limit amoune sth Cr(IIItf o ) species abl contaceo t t it is expecte primara e b o dt y Mn-containing soli coan di l active oxidizing sites on the j9-MnO2(s) surface. The fol- fly ashes and smelter wastes that are formed at high tem- lowing expressio derives ni d fro rate m th e H p dat r afo peratures , although it doe fort soisi no m h l environments. 3.0-4.7 that empirically account for the nonlinear rate by Additionally, 0-MnO2(s) is the most chemically pure and describin reactioe gth n rat fractioterme n ei th f so f no crystalline for MnO2(sf mo ) compare soio dt l forms such Cr(VI) to total Cr, /&, remaining in solution: • as birnessite (£-Mn02(s)] or cryptomalene fo-Mn02(s)J. d/ /df (s"1) •= Consequently, 0-MnO2(s) can be expected to have a lower L/J ,inm , I/, » , %oxides. k(A/ V)[Cr Cr(IIIu J )»(1.^ T f a/cr)«<*°0 - oridize 0 Cr(VI1. o »dt £ fo reactio& r)y / b n with where * - 2.0 (±1.6) x lO"" moI-nrV, A/V is the ft- 0-MnO2(s), then it fe logical to assume that similar and Mn02(s) surface are solutioo at n volume rati m'-ln oi A P«>bably more rapid reactions with other form manf so - mola e iJ sth anr r d[C concentratio totaf no l dissolve . dCr S*11686 oudc » shkel• occwo vt ' slightln I y acidi basio ct c solutions oxidatioe ,th f no p----;.»..#- *i.~f i» i aqueous Cr(II w verlo s D limitei s e Experimentayi th slo d y dwb an l Method solubilit Cr(OH)3(s)f yo . Materials manganese .Th e oxid experiee useth n di - —————————————————————————————— ments was reagent-grade MnO2(s) and was determined to pyrolusite b e [/?-MnO2(s) powde]y b r X-ray diffraction. . Introduction 0-MnO2(s) was sieved to obtain the 0.105-0. 149-mm Chromiu presene b y aqueoumi tma h s environment n si fraction. This fractio washes nwa d repeatedl deionizeyn i d either one or both of the Cr(III) and Cr(VI) oxidation water, leached hi a 10% HC1 plus water solution for 20-30 states. The mobility of aqueous Cr(III) is expected to be min, and again repeatedly rinsed in deionized water. The limited in slightly acidic to basic waters by the low solu- purpose of the washing and preleaching of 0-Mn02(s) was bilities of Cr(OH)3(s) and (Fe,Cr)(OH)3(s) (1, 2). In con- to remove most of the dust-sized particles that commonly trast, the mobility of aqueous Cr(VI) is expected to be adhere to the surfaces of larger grains. The specific surface controlled primarily by adsorption and desorption reac- area of prepared 0-MnO2(s) was measured by N2 gas ad- available th e tionsus e dato .T precipitatio n ao - ad sorptiod nan determine d (±0.57 nan 5. e )b o m^g't dBru y b 1 - sorption reactions for predicting the geochemical behavior nauer-Emmett-Teller (BET) calculation. of Cr, quantitative data are needed for the reactions that A 10~LT4 M Cr(III) stock solution that was made by control the distributions of the aqueous Cr oxidation states. dissolving CrCls-SH^s) in 0.1 M HC1 and a similar stock The high concentrations of Cr in some fly ash transport solution of Cr(VI) that was made with K2Cr2O7(s) were waters and boiler cleaning wastes (3) indicate that leaching used as the sources of Cr in the experiments. All chemicals ofror fC m utility waste mobilitd san groundwatern yi y ama used wer reagenf eo t grade distilled-deionized ,an d water be of environmental concern. was used in all experiments. Numerous reductants that could reduce Cr(VI) to Cr- Experimental Conditions. The experiments were (III), such as ferrous iron (4), reduced sulfur species (5), conducted to determine how the rate of aqueous Cr(III) organid an c material (6)y exis,ma leachin n ti g environ- Oxidatio affectes ni dissolvey db d oxygen, Cr(IIId )an ments thesf .O e reductants, ferrous iron is ubiquitou n si Cr(VT) concentrations, 0-Mn02(s) surface. areapH d ,an both utility wastes and soils. However, with the exception Chromium(m) concentrations in the rate experiments of the manganese oxides and dissolved oxygen, there are ranged from L9 X 10* to 38.5 X 10^ M, and the /S-Mn02(s) otheo n r generally occurring inorganic oxidants that con- surface are solutioo at n volume ratios (A/V) ranged from ceivably could oxidize Cr(ni Cr(VI)o t mos71.)n o i t 4 t 7 m^L"1 rangwastH 0. p e ee. Th o f most experiments swa material soilsd san . Manganese oxides hav hige a - had limite 3.0-4.do t 7 becaus morn ei e basic solutions aqueous sorption capacity for metal ions (7), thus potentially pro- Cr(III) is constrained to very low concentrations by the viding a local surface environment in soils and solid wastes solubility of Cr(OH)3(s) (1). We expected that the presence in whic couplee hth d processe aqueousf o s Cr(m) oxidatio solubility-controllina f o n g phase would obscur factore eth s and manganese oxide reduction may take place. Bartlett ' affecting the rate of aqueous Cr(III) oxidation; thus, most and James (8) observed that Cr(IID was oxidized to Cr(VI) of the experiments were conducted in acidic solutions more readily in soils with high elemental contents of Mn where the possible complications caused by Cr(OH)a(s) 0013-936X/87/0921-1187J01.50/0 © 1987 American Chemical Society Environ. ScW^hpol^sVeJ. W III 60 - 600 Hours 600 Figur . Effecte» Initiaf so l Cr(III) concentratio ) ratee (a th f so n no Cr(VI) formation and (b) fl-MnO^s) dissolution (open symbols) for pH V «=A/ 35. d 6an Cr(VImM.'10 ) rateFigure 4. (a th f s) .o n Effect. o e formatio2 SoO H ) p df (b s o symbold nan s indicat- rat0 e f eeth o 0-MnOj(s) dissolution (open symbols) for Wto * lKr [(XIII) X MnOJs 6 8. ] « ) dissolution measure 4.0dH p I .na Cr-fre e solution. . SoliM d symbols Indicate rate /M*iO,(sf so ) absolution measured In increaset no increasiny db initiae gth l Cr(m) concentratioCr-frene solutions. but were remarkably similar in magnitude as indicated by parallel rat /J-Mn02(sf eo ) dissolution measure increasee th d durin Cr(VIn si e gth ) concentrations (Figure 3a)n I . oxidation rate experiments was markedly increased in the contrast, the overall rate of /J-MnO2(s) dissolution was lower pH solutions (Figure 2b). Also, in Figure 2b, the decreased by increasing the initial Cr(III) concentration rates of/3-Mn02(s) dissolutio Cr-containine th n i g solu- (Figure 3b) rate .acidiTh f e o c 0-Mn02(s) dissolution ni tions (open symbols comparee )ar rate e purelCr-freth a f so o d t als s i y eo 0 solutioinclude4. H p Figurt n da i . e3b acidic 0-MnO2(s) dissolution that were measured in Cr-free A comparison of this rate to those hi Cr solutions (Figure solutions (solid symbols) for comparable pH and surface 3b) shows that concentrations of Mn increase in a linear area to solution volume ratios. Murray (IS) has shown that manner in the absence of dissolved Cr species but are MnO2(s) dissolves more rapidly in low-pH solutions. Rates increased initially and then slowed hi the Cr solutions, as of 0-Mn02(s) dissolution were significantly observe s morwa e previouslrapin d i r dfo y described experiments (Figure an initial period in the Cr solutions but eventually slowed 2b). The eventual depression in the initially rapid rates with increasing time to rates that were less than those of Cr(IH) oxidation and /J-MnO2(s) dissolution may be measured hi the Cr-free solutions hi which the rates of caused by a slow rate of desorption of the produced Cr(Vl) 0-MnO2(s) dissolution were observed to be approximately species from the 0-MnO2(s) surfaces. The zero point of linear over long periods (Figure 2b). This result implies charge for 0-MnO2(s) is reported to occur at pH 7.3 (±0.2) tha initian ta l reaction between CrdH 0-MnO2(sd )an ) (16), thus the anionic Cr(VI) species (HCrO CriV'd ran ) increase rate 0-MnO2(ssf th eo ) dissolution abov likel strongle e eb ar o thayt ty adsorbe acidin di c solutionse .Th caused purely by the acidic dissolution of 0-MnO2(s). direct adsorption of Cr(VQ species onto 0-Mn02(s) was However, afte periora rapif do d reaction Cr(VIe ,th ) re- foun increasee b o dt loweres d greatlwa H dp s froya 0 m8. action product adsorptiosn resuli 0 decreasa 2. i treactivith o e t nth experimenti eh f yo reportest thano e tar d here. 0-Mn02(s) and a consequent decrease in the rates of both We speculate that the strong adsorption of the anionic Cr(III) oxidation and 0-MnO2(s) dissolution. Cr(VI) species reduces the number of active sites on the Rates of Cr(IH) oxidation at pH 4.0 and A/V« 35.0 /J-Mn02(s) surface, thus causing a decrease in the reaction m2-L'1 for a range of initial Cr(III) concentrations indicate rates for both Cr(m) oxidation and 0-MnO2(s) dissolution similaa rrat dissolve e effec/J-MnO2(se f eth o th n f to o r dC ) ove rCr(VIe timth s ea ) concentration increases. Various dissolution (Figure 3). The oxidation rates of CrQI^wCTe^ ^ ^surface reactions between Cr and Mn redox species are Environ. Scl. Technol., Vol. 21, No. 12. 1987 1189 5' Table I. Reaction Stolchlometries Calculated from Slope* o pH = 10.1 of Plot* °f Mn(II) versus Cr(VI) by Least-Square* a pH = 8 3 Regression of the Rate Data from Figure* 2 and 3 ' PH = 6 3 slope, f o . no Crflll)A/V=35.. 6 Mn(II)/ /*'. 10- M Cr(VI)% pointH p *' «0 9 3.0 9.6 x 10-* 3.17 ± 0.54 97.6 10-X 6 * 9. 2.5 30.25 ± 3. 4 1198. 9 9 4.0 9.6 X 10-* 0.69 ± 0.16 95.6 X10-6 9. * 3 0.44. 0 ±0.111 4 89.8 10 4.0 1.9 X1Q-* 5.06 ±0.74 97.9 X1Q-8 4. * 0 1.54. 3 ±0.1811 . 98.6 9 4.0 9.6 X10-1 0.69 ±0.16 95.6 9 4.0 19.2 X 10-* 0.59 ± 0.18 92.3 9 4.0 38.5 X 10-* 0.28 ± 0.20 74.4 •Error limit* indicat standaro etw d deviations. o 200 400 600 can be expressed by the following reaction, which is rele- Hours vant to the experimental pH range of 3.0-4.7 (1), i.e. Figure 4. Rates of Cr(VI) formation In solutions containing the equivalen 10-X t 6 Cr(III*oM f9. ) precipitated as CrfOHMs) wflV hA/ CrOH2 *1.5|3-MnO2(s+ )— HCrO4 ' l.SMn2+ ) (1 * • 35.6 m2-L-». Plot dissolvef so n versudM s Cr(VI HCrO4"s )(a ) were possible, and it is difficult to separate clearly their effects made with the solution data from Figures 2 and 3 in an reaction o n rates from those cause adsorptioy db n pro- attemp comparto t experimentae eth l result stoie th -o st basicessee thesth f so n s o e experiments. However, con- chiometr reactiof yo Afte. n1 initian ra l time periof do sidering the adsorption behavior of the anionic Cr(VI) nonlinearity for 20-100 h, these plots did show linear re- species under acidic conditions, we expect that adsorption lationships between dissolved Mn(II) and dissolved Cr(VI), desorptiod an n reaction importane slopesse ar th t controllin,r bu twhicfo he shoulgth indicative db reactioe th f eo n rat Cr(IIIf eo ) oxidatio experimentae th r nfo l conditions stoichiometry, varie witd witan h Cr(IIIH hp ) concen- described here. 3.5d slopee an , th 0 , tratios3. wer H p ne t (TablA . eI) Cr(III) Precipitation addition .I rat e eth expero nt - significantll mo Mn(I yf 0 o highe 1. l Qo mo t r5 tha1. e nth iments conducte acidii dh c solutions, three experiment Cr(Vf o Qs rati o predicte reactioy db (Tabln1 indicatin, eJ I) - - g a6.3,8.3H tp 10.d ,1an were also conducted equive .Th - tha acidie tth c dissolutio 0-MnO2(s)f no , i.e. alent of 9.6 x lO"6 M aqueous Cr(IID was initially added . M n M ,„«. M .+ „ o ^ ,. o . , ,„. \J to eac thf ho e solutions whitisa t ,hbu gree ^ ^Oa(aq+ \- nO solis H2 ) )d+ wa (2 0-Mn02(sn -M H 2 )+ immediately precipitated, and the aqueous Cr(IH) con- occurred as a parallel reaction at thes~e M pH values. centrations decreased to low levels. These observations, More id o^ssolution of 0-MnO2(s) was^vident in the , withg aon i the. solubditydata for Cr(OH), eq 7 gave slopes of 2.9 (±0.8) and 3.5 (±0.8) (Figure 6), and ** the value of n is taken to be the average of the two slopes, d/c,/dt * k(A/V) [Cr J"l(l - /&)" (*° •"> for /Cr ^1.0 (9) 3.2 (±0.8). In Figure 6, it is clear that there are some large errors associated with the rate data. These errors reflect where m n i .- s im- v fri i m t~^ i /x A o - . resuli ratscattea e e analyticaeth f tar dato n rd i aan l dif- ficulties encountered in determining the small changes in * - 2.0 (±1.6) X KT" mol-m »-s » (10) Cr(VI) concentrations that occurred during some of the Linear correlation coefficients, R\ are also listed in Table fractional rate experiments conducte provid o solutiont i d h I H indicatioa ea s linearit wite plote th e hf th n th o f sf o y o higher values of fc, such as 0.30 and 0.40. the left side of eq 8 versus t. The R* values range from magnitude Th 9-1r rate fo 1eth datconstantf e% o 98 determinea s o pointst wa 5 , ,7 k , indicatind - g thaem e tth frorearrange6 q me a da pirically derived rate expressio ni9 s give q generalle n ni y descriptive of the reaction rates observed in the experi- |1/(1 - /Cr)" - 1/(1 - /&r)"}/{2.2(A/ VHCrJ-1) - kt menta with acidic solutions. (8) The rate expression hi eq 9 can be used to calculate the time required to oxidize a specific amount of Cr(III) to valuA eacer fofo h r k rat e experiment conducte acidii dh c Cr(VI). Iconsidee fw hypotheticara l exampl 1.0-ka f eo g solutio determines nwa d fro slopee mth plotf so thf so e left masacidin a f so c waste material containing 0.0% t 5w versuthesd ) an (8 elistesidq , se e valuet f ar e n o dk i f s/}-MnO2(so ) wit specifiha c surface arem^g"5 a f ad o 1an Table ID. Using the average k from all of the experiments, saturated porosity of 20% , then the resulting surface area :he rate expression describing the fractional rate of Cr(VI) to volume ratio for /3-MnO2(s) is 10 m^L*1. With this value . 12 . No . T*chr.oi •j?1 Sr n * Vr < flR3Q2603 Table IV. Time Required for Fractional Conversion of a °f manganese oxides the oxidation of aqueous Cr(III) is 10-* M Cr(III) Solution to Cr(VI) for 1 kg of a 20% Porosity unlikely to occur. Soil Containing 0.05 wt % £-MnO,(s) with a Specific Surface m*»r 0 Are5. f alo Acknowledgments fc, days /& days We thank I. P. Murarka, EPRI project manager, for his „ - 9 0 01 osfl- continual suppor interestd tan e thanW . Sass. kB . ,J 0;30 31 0'J5 41^, Schramke, and two anonymous reviewers for their com- ments and discussions and Jan Baer for her editorial re- integrate e ,„,„,„„. - th , d . an drat. e for- „eth expressiof m,..„.. o . * „ _n n give y nb V16W eq 8, the times required to oxidize 10,30,50, and 90% of Re«istry No" Mn°" 1313-13'9: Cr'744 Environ. Sci. Technol.. Vol. 21. No. 12. 1987 1193 flR30260*4period hi buffered solution was nearly directly proportional to the /3-MnO2(s) solutions with pH 5.5-9.9 and in natural lake waters. From surface area (Figure Ib). The results hi Figure la are our results and those of Schroeder and Lee (9), we con- typical of the oxidation rates observed in this study in that eluded tha oxidatioe tth aqueouf no s Cr(HI ratee th s) wer solel ey initiallyb y rapid before slowing significantly dissolved oxygen was too slow to be considered a significant after 20-100 h. Schroeder and Lee (9) have also reported factor in further rate experiments with 0-MnO2(s). The a strongly nonlinear rate of Cr(III) oxidation by an un- effect of dissolved oxygen on the rate of oxidation of specified type of MnO2(s). aqueous Cr(III) by 0-MnO2(s) at pH 4.0 was further pH and Cr which is far from the zero point of charge for 0-Mn02(s) ^ 0 (76)]3 7. . H Also[p possibilite ,th y exists that _ Mn(III) rather than Mn(IV) specie0-Mn02(se th n so ) surfac€ e is the dominant oxidant under some conditionsS ° . Clearly e ,th combined processes of Cr(III) oxidation, Cr(VI6 )6. adsorption ^ , Mn redox speciation, and 0-MnO2(s) acidic dissolution f mak determinatioe eth reactioe th f no n stoichiometrief so oxidation-reduction reactions that occur at the surfaces of manganese oxides extremely difficult Our data indicate 62 that a combination of reactions is probable under acidic conditions. Empirical Rate Expression. The experimental ob- g 6 I servations of (1) highly nonlinear reaction rates, (2) the ' 3.2 3.6 4.0 4.4 4.8 lac stronf ko g dependenc Cr(inr o H )p en concentrationo , _log (Cro, depressioe th ) (3 /J-MnO2(s f nd o an ) dissolutio_ . n r ratC n ei solutions compared to Cr5ree sections indicate that the ^J slow desorptio anionif no c Cr(Vl calculate)s specie^m toast-squarey db s- p fro e mth s regression thd e,an error fcnits Intfcate Mn02(s) surfac n importana s ei t rate-limitin standaro tw gd deviationste r pfo s abou slopee tth . Cr(III) oxidatio 0-Mn02(sy nb acidii )h c solutions- .Ad sorption of Cr(VI) species was found to occur in acidic + Cr(ni)]), and n is some positive number. By describing solutions and appeared to cause eventual decreases hi the the rate in terms of the fractional rate of Cr(VI) formation Cr(III) oxidation rate possibly by limiting the generation in eq 5, the rate-limiting effects caused by the adsorption of new reactive sites on the 0-Mn02(s) surface. As a result, of the Cr(VI) products onto 0-Mn02(s) are empirically the Cr(IH) oxidation rate was apparently more dependent taken into account. The inverse dependence on [Crt] is on CrfVT) concentration than on Cr(IID concentration. An a result of describing the rate in terms of fc, but is also empirical rate expressio bees nha n derive accouno dt r tfo confirme determinatioe th y db slopa f approxino f e o - the rate-limiting effecproducee th f to d Cr(VI) specie d s logarithan e ploa matelth initiae r f to th fo f ml1 yo - fractiona l is described below. This expression is only applicabl o et rat Cr(VIf eo ) formation (d/c,/dt) versu logarithe sth f mo acidic solutions for which we have the most rate data. In the initial total Cr concentration [Cr?] (Figure 5). The neutral and basic solutions, the precipitation of Cr(OH)3(s) rates plotted in Figure 5 were derived by normalizing the and the weaker adsorption of Cr(VT) species onto ft- Cr(VI) concentration data shown hi Figure 3a to total Cr MnO2(s) would require a different approach, but the small concentration to obtain /<> at successive times. The initial amount of rate data gathered for such conditions prevents rates were determined by fitting second-order polynomials us from formulating an applicable expression. to the fc, versus time data by a least-squares method and The rates of heterogeneous reactions that involve com- taking the derivatives of those polynomials at time equal plex phenomena at mineral surfaces can be described, in to zero. some instances, by expressions that relate the reaction rate The rate expression hi eq 5 can be integrated with re- reactioe toth n affinity, practicallwhice b n hca y described givo t gpece, fc timo tt d ean differencee th y b s between steady-state reactant concen- tration actuad san l concentrations to some power (19) o .T 1/( /c,)"'1- 1 -I/O.- l)[C - /cr)"~ « r( J-'Ml- / V)kt ) (6 apply suc ratha e expressio rate Cr(VIf eth o o nt ) forma- tion, inecessars ti defino yt steady-statea e Cr(VI) con- centration. Howeverrate th el experimentsal ,n i e initia,e th th whers i l fractio, e/& Cr(VIf no tota)o t . lCr concentrations of Cr(VD continued to slowly increase, even Equation 6 expresses the relationship between fc, and the steady-statd an , h afte 0 lons r50 a es g a concentration s were time that shoul observee db rate th e n experimentdi f si never convincingly reached. To derive a rate expression, the proposed rate expression is valid. To use eq 6 to we assumed that all of the aqueous Cr(IH) in the exper- evaluate the rate of aqueous Cr(VI) formation, it is nec- imental solution would be oxidized to Cr(VI) by reaction essary to determine the value of n, the empirical order of with 0-Mn02(s), given sufficient time and /J-MnO2(s). the reaction. The value of n was determined from two sets Because the rate of Cr(IH) oxidation is dependent on the of initial rate experiments that are described below, and amount Of Cr(VI) produced, we express this assumption this value was tested against the rate data from longer term in fractioterme th f s Cr(VIo f no tota)o t l dissolve r dC experiment determino st wit6 q h accurace e eth e th f yo remainin solutionn gi followin,e /Crth y ,b g limit rate expression. The initial rate method as applied to this study involves fc, - [Cr(VI)]/[Cr(VI) + Cr(m)] -» 1.0 as t — » (4) the determination of the fractional rate of Cr(VI) forma- ,•,.', , ^_ A. , * . tion as a function of the initial ratio of Cr(VI) to total wher brackete eth s refe molao rt r concentration s i t delved san (/c,)r dC . These initial rates linearf ,e i b n ,ca tim secondsn ei . Using this assumption propose ,w e that though tangentias a f to l lines alon reactioe gth n pathway the following rate expression isf increase descriptivM rate sf e th o nonlinearl f eo y with time e assume.W d that Cr(III) oxidatio Cr(VIo nt reactioy )b n with 0-MnO2(s) anionie th c: Cr(VI ) species, which were adde solutioo dt n At i At - t(A /VUCr Hfl 0 - /„ V for /„ ^ 1 0 (5) to create specific values of fc, >" the fractional rate ex- dfc,/d t*CA/V)[Cr- J (1.0 fct) for/CrS1. } 015 s, immediately cause-liiidn a rate-limitineffec- tbe g effect be- where * is a rate constant with units of mol-nT**'1, [CrJ cause of the reduction of reaction affinity through ad- refers to the total dissolved Cr concentration (i.e., fCr(VD sorption onto 0-Mn02(s) just as if they were produced by AR302602 Environ. Scl. Technol. 198, 712 . 119.No Vol. 1.21 Table II. Summary of Initial Fractional Rate* of Cr(VI) 8 6 Formatio Functioa * na /*rf no * fa pH df'ct/dt x 10" B*. % 3.4n= 5 (±0.64) 0.0 3.0 2.7 (±0.6) 95.6 pH=4.0 0.05 3.0 2.3 (±0.2) 99.4 , A/V=71.3 '*8 = (±0.39 1. ) 0 3. 98.40.1 0 (±0.2x 9 1. ) 0 3. 96.80.2 0 0.40 3.0 0.6 (±0.2) 93.4 <$ 0 4. 3.0.2 0s (±0.6 ) 97.2 § (±0.36 2. ) 0 4. 98.90.0 5 0.10 4.0 1.9 (±0.4) 96.4 ' 2.9n= 1 (±0.84) 0.20 4.0 1.4 (±0.2) 98.2 7.8 pH =3.0 (±0.20 1. ) 0 4. 97.10.30 A/V=35.6 0.40 4.0 0.5 (±0.2) 89.7 71.* 3V m'-L'1/ 'A . 'Error limit* indicat standaro etw d devia- tions. ______7.4 I I I 0 0.08 0.16 0.24 Cr(IU) oxidation. If the initial reaction rate for fractional ' . Cr(VI) production, d/^/dt, is linear with time, n theca nn ~lo Cf' ) a ' (1° be determined from a plot of log (d/c,/dt) versus log (1 - Hgure 6. toj-tog plot of the fractional rate of Cr(VI) formation showing ft., follows )a s fro logarithmie m th stoPe» * s use i.e , *>t*n*co 5 d. t erro forq e e th r f m o »Bmft- " s Indicat standaro etw d ^ deviations abou slopese tth . (7) Table III. Summary of Experimental Condition*. Rate determines valuwa e n Th f eo d from suc log-loha g plot Conrtant* Linead .an r Correlation Coefficient* (9-11 Data by using the rate data obtained from two sets of expert- PointB °' R**"8*" Analy*e.) ment is0 n conductewhic4. d % h, an th0 R* iou x de3. H k P *a fractionaH t [Cr?* p A10 / ]V x l rate Cr(VIf so ) formation were measure separati dh - eex periment" *• s wit h* specific valuetha , ° * /£ t f rangeso d fro 0 m0. s sfoa m to 0.40 possibilite .Th ^ 35 2a(±o!8yw a exist 3 )£ s tha apparene tth J tJj rate-lim- itin (±0.52 g1. effect) Cr(VI f s4 o 82^35 decreasy 9)ma e a tm higher value0 4. s of /cn possibly because of greater saturation of adsorption sites 4.0 38.5 35.6 1.3 (±0.5) 84.6 j3-MnO2(s)n o extremele th t ,bu y slo 6 w (±0.89. reaction3 3. 35.) 8 s0 rate93.3- 0s under such conditions prevented the gathering of accurate data. *•* '•' **•* J'SJ*0'8! |J'1 The fractional rate experiments lasted a total of 6-8 h, JJ JJ ,;} SJSS 9O8 during which a total of 8-10 samples were withdrawn and 3.5 . 94 7^1 2^3 (±0/7) 904 (±0.80 3. ) l analyze7- 87.6 determino d t 8 9- change quantitee th th i e° h 4- y /CT-/C* with time. The change in /<>-/$, with time was observed *•* 9-* 7.1 2.8 (±2.0) 84.4 to be Knear for each experiment for the 6-8-h period; *•' *• " "J*1^ !" hence, the initial fractional rates were determined from JJ J-j 7Ji SSoS 877 the slope1 7 i.4(±o!5s calculate 8 )9; lineay db 83.r0 regression0 4 experie th f so - mental data of /CT-/CT at (A/ V)t and are given in Table 4.0 9J 3&6 l!2(±o!s> 8o!o The quantity A/ V was included in the independent 4.0 9.6 71.3 1.3 (±0.5) 75.'3 solution sample removede sar e assumeW . d thae tth