cinetica landolt

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by affectess of anent pro-lculationhe major

l N . Thed regionsntitativee modelimentallycesses.parentlyon. Rateerimentsntainingcter ized,~4too rapider studyS1

ormationwer rate.odel N.however,scillationin deter-D can beran ce oflfite. Inarily de-reaction

Table 111. Detailed MechanismProcess A

10,- + I- + 2H' H,I,O,H,I,O, - O I + H I 0 2H,I,O, + 1-- HOI + 01-01- + H HOI1- + H I O , + H' F- 2HOI1- + H O I + H' 2 + H 2 0I, + I- ,-13- - + I,HS0,- + I , S031+ I-H S 0 3 - + 13- S 0 3 1+ 21-H S 0 3 1 + H,O - S 0 4 -+ 1- + 2H'1,- - + I,Fe(CN)64-+ I, e(CN),'- + 12-Fe(CN)64-+ 1,- e(CN),3- + 21-10,- + H S O c - IO, + SO4,-HIO, + HS0,- - O I + H S 0 4 -H O I + H S O < - - + H S 0 4 - + H'H2S03 ' + H S O CH S 0 3 - H' + SO3,-HS0, - ' + SO4,-

1)(2)( 3 )4 )5 )6)( 7 )

- 7 )(8)9 )10)- 7 )1 1)(12)13)(14 )

Process B

Process C

Process D

1 5 )Buffer System

16)(17)18)

dependence in iodide. Brays2 proposed a reaction scheme in 1930tha t accounted for the fou rth- and fifth-order, two-term r ate law.His convincing arg um en t called for preequilibrium 1 followed bythe rate-determining steps 2 and 3. The critical intermediate

lculationhe majorl N. Thed regionsntitativeseems in-he modelimentallycesses.parentlyon. Rateerimentsntainingcter ized,~(Figure 4too rapider studyS1formationwer rate.model N.however,scillationin deter-D can bearan ce ofulfite. Inarily de-reactionnd of theavior canscillatory

, , ,H,I,O, + 1-- HOI + 01-01- + H H O I1- + H I O , + H' F- 2HOI1- + H O I + H' 2 + H 2 0I, + I- ,-13- - + I,HS0,- + I , S 0 3 1 + I-H S 0 3 - + 13- S 0 3 1+ 21-H S 0 3 1 + H,O - S 0 4 - + 1- + 2H'1,- - + I,Fe(CN)64-+ I, e(CN),'- + 12-Fe(CN)64-+ 1,- e(CN),3- + 21-10,- + H S O c - IO, + SO4,-HIO, + HS0,- - O I + H S 0 4 -H O I + H S O < - - + H S 0 4 - + H'H2S03 ' + H S O CH S 0 3 - H' + SO3,-H S 0 , - ' + SO4,-

( 3 )4)5 )6)( 7 )

- 7 )(8)9 )10)

- 7 )1 1)(12)13)(14 )

Process B

Process C

Process D

1 5 )Buffer System

16)(17 )18)

dependence in iodide. Brays2 proposed a reaction scheme in 1930tha t accounted for the fourth- and fifth-order, two-term r ate law.His convincing arg um en t called for preequilibrium 1 followed bythe rate-determining steps 2 and 3. The critical intermediatespecies in this scheme is H,1 20 3 or 1202 , he m ixed anhy dride ofH O I and HIO ,. Decomposition of the intermediate in step 2 leadsto the fourth-order term and bimolecular reaction with I- in step3 leads to the f if th-order term. The result ing H OI and H I 0 2Wednesday, October 17, 2012


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species constitute a buffer system that must be included in an E R Ldescription of the oscillatory behavior.Iodate Oxidation of Iodide. Th e major pathway for the re-duction of iodate is the Du shm an reaction2s given by process A.IO,- 81- 6H+ = 31,- 3H20

Th e stoichiometry of process A is written in terms of the prod uct1 - rather than I2 since, as shown in F igure 1 I- is always presentin relatively high concen tration. W hile both I, and I,- ap pe ara s react ant species in othe r processes, they a re in rapid equilib-rium26an d th e stoichiometry of each process is written in term sof the pred ominan t species I,-.Process A has been the subject of many investigations sinceDushmans 190 4 study.2s Liebhafsky a nd Roe2 have reviewedthe empirical rate laws tha t have appeared over the years. Ma nystudies have found tha t a two-term rat e law is necessary for ana cc ur at e d esc rip tio n of t he r e a c t i ~ n . ~ * - ~ ~term first-order iniodide is domin ant a t low iodide concentrations; a t higher iodideconcentrations a second term second-order in iodide becomesdom inant. Th e first-order term is difficult to characterize becausein typical experiments even the iodide contaminan t in the iodatereagent provides sufficient concentration to m ake the second-orderterm dom inant. T h e second-order term , however, is well-estab-lished and was even reported in Dushmans originalLiebhafsky an d Roe2 concluded that rat e law s most consistentwith the known experimental behavior. Ra te law Y has been an

-d [IO3-]R , = - - k,,[IO,-][I-] [I2 ka 2[I0 3-] I-I2 [H +l2d ta )

essential component in the descript ions of bi~tabil i ty~-~nd

W e neglect the protonatireaction according to pr2Fe(CN)6

A detailed investigatiothe ra te of oxidation of FI,- depends inversely on thwith I2 and not with I -.and reverse reactions canemploying con servation-d[I,-] k,[I,-] [R , = - - dt K[I-] [

k-? [

The reverse reaction betmore extensively th an thto be comparatively sloReynolds studied procpH dependence; howeveof I2 with no added I- shslower a t pH 1.48. W hileby 1 is apparently slow er,involving th e oxidation bacidities as th e c harge onprotonations.Uncatalyzed Iodate Odirect reaction between boxygen ato m transfers wasa n d E gg ert a n d S ~ h a r niodate and arsenous acidWednesday, October 17, 2012


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the acidities of the oscillatory Landolt reaction, and process Ais therefore considered to be irreversible.Bisulfite Reduction of Iodine and Triiodide. Iodine and triiodidegenerated in process A react with bisulfite to generate iodide an dbisulfate. Wh ile both HS03-and S032 re stoichiometricallysignificant in typical experiments reported here and in thosereported by EO E,I5 only HS03- eacts with I2 and I - accordingto a study by Bunau and Eigen.,, Th e net reaction is written

(25) D ushman, S. J Phys. Chem. 1904, 8 453.(26) M yers, 0 E. J Chem. Phys. 1958, 28, 1027.(27) Liebhafsky, H. A.; Roe G. M. Int. J Chem. Kinet. 1979, 11 693.28) Abel, E.; Hilferding, K . Z . Phys. Chem. 1928, 136, 186.(29) Beran, P.; Bruckenstein, S. J Phys. Chem. 1968, 72, 3630.(30) Schildcrout, S. M.; Fortunato, F. A. J . Phys. Chem. 1975, 79 , 31.(31) Biinau, G. V.; Eigen, M. Z. Phys. Chem. N.F. 1962, 32, 27.

is impo rtant with bisthe observation t hatand iodate react faisolutions containingth e course of days.Ithe sam e as that oftwo distinct reactio1 0 3 -

(32) Jordan, J.; Ewi(33) Reynolds, W .(34) Adamson, A.(35) Indelli, A.; Gu(36) Majid, Y. A.;(37) Sorum, C. H.;Chem. SOC. 952, 7 4 , 2

de o f the pHncentration ofmost constanteriod almosttremes of theranch at highracketing thef steady statescillation. There 1 occurs ate .

clude iodate,sulfuric acid.t processes oftions betweenr intermediatesimilar to thetion-reductioncant oxysulfurded in an ER L

J . Am . Chem. SOC.Vol. 109, No 16 1987 4871in terms of triiodide ion according to process B

HS03- 1 - H 2 0= HS04- 31- 2H + (B)Biinau and Eigen3I studied the sulfite reduction of iodine atdifferent acidities and varying concentrations of iodide and

chloride. Th ree reaction pathways were found, two correspondingto the bisulfite reductions of I, an d 1,- and the third correspondingto th e reduction of I,Cl-. R at e law @, with the term for thereduction of 12C1- om itted, is relevant to th e expe riments repo rtedhere. Th e second term includes the formation constant K for

I,-. R a te law /3 indicates that H O I from th e hydrolysis of I, isunimportant in the reaction; bisulfite is apparently sufficientlyreactive to directly attac k I and I,-. Bunau and Eigen found noevidence for significant reverse reaction a nd process B is therefo reregarded as irreversible.Ferrocyanide Reduction of Iodine. The iodine product of processA m ay also be reduced by ferrocyanide. The protonated complexHFe(CN),,- (pK, = 4.2)3 2 is significant only briefly in th eoscillatory Landolt reaction as th e p H reaches its lowest values.

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+l2a )

- ~ndThet a ts A

dideandallyoseingtten

693., 31.

.Uncatalyzed Iodate Oxidation of Bisulfite. An uncatalyzeddirect reaction between bisulfite an d iod ate involving successiveoxygen atom transfers was proposed in the ea rly studies of Landolt,a nd E ggert an d S ~ h a r n o w . ~ hile the direct reaction betweeniodate an d arsenous acid is very slow4an d often considered to benegligible,6-10*2isulfite is apparen tly sufficiently reactive tha tthis pathway becomes significant. Evidence that the direct reactionis impo rtant w ith bisulfite an d not with arsenous acid comes fromthe observation t ha t slightly basic solutions containing bisulfitea n d iod ate r ea ct f a ir ly ra pid ly to c o m p l e t i ~ n ~ ~ ~ hile similarsolutions containing arsenous acid and iodate do not react overthe course of days.I4 Th e stoichiometry of th e direct reaction isthe sam e as th at of (A ) 3(B); however, th e processes involvetwo distinct reaction pathways.

D)0 3 - 3HSO3- = 1- 4- 3HS04-(32) Jordan, J .; Ewing, G. J. Inorg. Chem . 1962, I 587.(33) Reynolds, W . L. J Am . Chem. SOC. 958, 80 830.(34) Adamson, A. W . J Phys. Chem. 1952, 56 858.(35) Indelli, A.; Guaraldi, G. C. J Chem. SOC 964, 36.(36) Majid, Y. A.; How lett, K. E. J Chem. SOC. 1968, 679.(37) Sorum, C. H.; Charlton, F. S.; eptune, J. A,; Edwards, J. 0 J A m .Chem. SOC. 952, 7 4 , 219.

4872 J . A m . Chem. SOC.Vol 109 No. 16 1987Table 11. Rate and Eauilibrium Constants for Model N

k = 9.2 IO M-) s I ka2 = 8.1 IO M4 s Ik n = 2.2 O M-I SK k = 2.3 x 109 M-1 s-1rk: = 1 . 3 x 103 M-1 s-I) k = 6.1 lo- M-2 s-I 1k Y b= 8.5 I O M-I s-Ikb = 0.25 M- s-lkel = 3.4 x 106 s-Ike2= 8.1 x 103 s - ~k,, = 2.5 x 109 s ~K = 539 M-

k e 2.0 I O 8 M- s Ik_ 2 = 5.0 1 O l o M-I s-IkE 1.0 10 M-l s-I

Values used in Figure 4. bValue used in Figures 3 and 5Rate measurements of process D ar e difficult because th ealternate autocatalytic pathway A) 3 B) is usually dom inant.Th us, while process D is usually included in descriptions of theLando lt reaction, the form of the rate law and corresponding rate

constant@ ) have not been experimentally determin ed. An earlystudy by Skr aba l and Zahorka 3* reported a high-order two-termra te law; however, the re is considerable uncertain ty in their in-terpretation. W e describe process D as a simple bimolecularreaction between IO,- and HSO,- according to rate law followedby rapid oxygen atom transferse2s4-d [ O,-]

Rb =- - k 6 [ I 0 3 - ] [ H S 0 3 - ]d tBuffer System. The reactant and product oxysulfur species

- - - -8R, 3R, 3R,[I-Id t= 3R, R, R, k[I,-]d t

- -W + l - -6R, 2Rp R,1d t

d [S03z- ]d t = R,, ko [SO3-]Wednesday, October 17, 2012


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d tBuffer System. The reactant and product oxysulfur speciesconstitute a buffer system that is continually titrated by theoxidation-reduction reactions. In turn th e solution p H establishedby the buffer system d ram atica lly affects the redox chemistry.The proton equilibria tha t a re significant over the experimental

pH range ar e given by reactions E.39 Th e major S IV ) speciesH2SO3 = H+ H S 0 3 -H S 0 3 - = H+ SO3,-HS04-= H+ S042

E l )E21E3)

are H2 S0 ,, HSO), and SO?- ll in rapid equilibrium. Th e S V1)species H S0 4- and S042 re also important in the buffer systembecause sulfite is partially acidified in the reactant stream withsulfuric acid and the primary oxidation product of the reactionis S V 1). W e neglect the protonation of ferrocyanide because itsconcentration in the reaction mixture is insufficient to significantlyaffect the buffer system. Empirical rate laws for reactions El- E3ar e obtained directly from t he elementary steps.

Empirical Rate Law ModelWe now develop an empirical rate law model based on the

d t = R,, ko [SO3-]0

d[S04,-]d t = R13 ko[S042-]

input of H2SO4 is accounted fand H S 0 4 - in the reactant s trincluded to account for the im pnum ber of species in model N iiron atom s in ra te law y allowvariable. Conservation of iodisimilar modifications of th e corthe model to be reduced to 8Rate Constant Assignments.is robust and readily reproduciand equilibrium constants werepossible. See Ta ble I1 for rascribed below.)Values of k,, and k in rateof the temperature dependencefor tun at^.^^ Appa rent activatiwere used with values measurefor 40.0 C.Value s for k,, an d k in rinvestigation by Biinau and Eigeof this very fast reaction has noit is expected to be sm all, we us22.0 OC. Th e formation constain rate laws /3 and 7 was obtainWednesday, October 17, 2012


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4872 J . A m . Chem. SOC.Vol 109 No. 16 1987Table 11. Rate and Eauilibrium Constants for Model N

k = 9.2 X IO M-) s I ka2 = 8.1 X IO8 M4 s Ik n = 2.2 X O M-I SK k = 2.3 x 109 M-1 s-1rk: = 1 .3 x 103 M-1 s-I) k = 6.1 X lo- M-2 s-I 1kYb= 8.5 X IO M-I s-Ikb = 0.25 M- s lkel = 3.4 x 106 s-Ike2= 8.1 x 103 s - ~k,, = 2.5 x 109 s ~K = 539 M-ke 2.0 X I O M- s Ik_ 2 = 5.0 X 1 O l o M-I s-IkE 1.0 X 10 M-l s-I

Values used in Figure 4. bValue used in Figures 3 and 5Rate measurements of process D ar e difficult because th ealternate autocataly tic pathway A ) 3 B) is usually dom inant.Th us , while process D is usually included in descriptions of theLandolt reaction, the form of the rate law and corresponding rateconstan t@) have not been experimentally determined . An earlystudy by Sk rab al and Za horka3 * reported a high-order two-termrate law; however, there is considerable uncertainty in their in-terpretation. W e describe process D as a simple bimolecularreaction between IO,- and HSO,- according to rate law followedby rapid oxygen atom transferse2s4

-d [ O,-]Rb=- - k6 [ I 03 - ] [ H S03- ]d t

Buffer System. The reactant and product oxysulfur species

- - - -8R,[I-Id t= 3R,[I,-]d t

- -W + l - -6R,d t

d[S03z- ]d t = R,,

Wednesday, October 17, 2012

cinetica landolt

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