Electrochemistry of Molybdenum Aquo Ions Citation Paffett, Mark Thomas (1983) Electrochemistry of Molybdenum Aquo Ions. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/hv5n-dz91. https://resolver.caltech.edu/CaltechTHESIS:11012019-171533510 Abstract The electrochemical behavior of selected molybdenum aquo ions in acidic media is examined in relation to solution structure. The electrochemistry of Mo(VI) in non-complexing aqueous electrolytes is usually severely complicated by the oligomerization and subsequent adsorption of the reactant. This problem can be circumvented by employing dilute (≤ 10 -4 M) solutions of Mo(VI) in 1 to 2 M trifluoromethanesulfonic acid. Under these conditions staircase voltammograms and pulse polarograms exhibit single, reversible waves that are consistent with the one-electron reduction of an unadsorbed, monomeric Mo(VI) species. The pH dependence of the reduction potentials suggests that two protons are consumed in the reduction of each Mo(VI). The monomeric Mo(V) reduction product undergoes spontaneous dimerization with a rate constant estimated as 10 3 M -1 s -1 . It also reduces perchlorate and nitrate anions at a significant rate. The Mo 2 (V)/Mo 2 (III) redox couple in acidic solution involves an overall four electron-six proton transfer connecting the two participants. This redox process is characterized by extreme electrochemical irreversibility. Reduction of the Mo 2 (V) aquo ion to the Mo 2 (III) aquo ion proceeds with αn a equal to 0.73 and a proton reaction order of 1.4. A chemical step with an inverse dependence on proton concentration precedes the reoxidation of aquo Mo 2 (III) to aquo Mo 2 (V). Plausible mechanisms are given for these observations. The trinuclear ions containing Mo(IV), Mo 3 O 4 (H 2 O) 4+ 9 (Mo 3 (IV)) and an oxalato derivative, Mo 3 O 4 (C 2 O 4 ) 3 (H 2 O) 2- 3 , can be reversibly reduced in acidic media to trinuclear Mo(III) species. The reductions involve two sequential electron transfer steps with formal potentials that are pH dependent: [chemical equations; see abstract in scanned thesis for details]. Two waves are evident in voltammograms and polarograms of Mo 3 O 4 (C 2 O 4 ) 3 (H 2 O) 2- 3 but with Mo 3 (IV) the two formal potentials are too close together to observe separate waves. However, logarithmic analysis of the shapes of normal pulse polarograms allowed the two formal potentials to be evaluated. The reductions of both complexes are believed to be accompanied by protonation of the bridging and capping oxo-ligands. The new, trinuclear Mo 3 (III) species resulting from the three-electron reduction of Mo 3 (IV) exhibits a characteristic EPR spectrum. The mixed-valent intermediate, Mo 3 (III, III, IV), is diamagnetic. Possible structural changes that accompany the addition of electrons and protons to Mo 3 IV) are discussed. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: Chemistry Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Gray, Harry B. Thesis Committee: Anson, Fred C. (chair) Grubbs, Robert H. Marcus, Rudolph A. Gray, Harry B. Defense Date: 12 April 1983 Other Numbering System: Other Numbering System Name Other Numbering System ID UMI 8315854 Record Number: CaltechTHESIS:11012019-171533510 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:11012019-171533510 DOI: 10.7907/hv5n-dz91 Related URLs: URL URL Type Description https://doi.org/10.1021/ja00342a025 DOI Article adapted for Chapter 1. https://doi.org/10.1021/ic50225a073 DOI Article adapted for Chapter 2. Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 11883 Collection: CaltechTHESIS Deposited By: Mel Ray Deposited On: 02 Nov 2019 00:50 Last Modified: 07 Aug 2025 17:42 Thesis Files PDF - Final Version See Usage Policy. 5MB Repository Staff Only: item control page

Electrochemistry of Molybdenum Aquo Ions T hesis by M ark Thomas Paffett In P a rtia l Fulfillm ent of the R equirem ents for the Degree of Doctor of Philosophy C alifornia Institute of Technology Pasadena, California 1983 (Submitted A pril 12,1983) R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Acknowledgments /V V V V V \A A ^ « V N (V V V \ I would like to thank the following p ro fesso rs: F red Anson, for his patience in dealing with my attem pts at scientific w riting and often fragm ented logic; H arry Gray, fo r his b rilliant sim ple explanations and for his help in proving that chem istry is most definitely not a sober science; John B ercaw , Bob G rubbs, T e rry Collins, and Sunney Chan for th e ir scientific input and social interactions. I am indebted to my fellow co-w orkers and p e ers for th e ir helpful c ritic ism , scientific discussions, general debauchery and many unmentionable a c ts. The following is a list of those people that have influenced me for any of the above reasons: Jay (Goober) Audett, Steve R ice, T erran ce P . Smith, Jeff (Leon) G elles, Pete (Reefer) W olczanski, Jim m y M ayer, Greg (Dr. Duck) Hillhouse, M ark (Babs) Thompson, Jay W inkler, Don Nocera, E ric (DM) M oore, John T u rn er, Steve C ram er, Bruce (the Dinosaur) C lem ens, Roger B aar, Dan Buttry, Rich Durand, C arl M urray, B rian W illett, M oses M ares, a ll other past and p resen t m em bers of Fred Anson’s re sea rc h effo rts, a ll of the a ss o rte d m em bers of the AASS, Lee, and H azel’s b a r. In addition, the expert typing of H enriette W ymar is greatly appreciated. Finally, I would like to thank my parents fo r th e ir g en eral support and my wife, L aurie, and son, Cole, for th e ir enduring patience and inspiration. R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . iii Abstract. The electrochem ical behavior of selected molybdenum aquo ions in acidic media is exam ined in relatio n to solution stru ctu re. The electro ch em istry of Mo(VI) in non-complexing aqueous electrolytes is usually severely com plicated by the oligomerization and subsequent adsorption of the reactan t. This problem can be circum vented by employing dilute (< 10“4 M) solutions of Mo(VI) in 1 to 2 M trifluorom ethanesulfonic acid. Under these conditions s ta ir­ case voltam m ogram s and pulse polarogram s exhibit single, rev ersib le waves that a re consistent with the one-electron reduction of an unad­ sorbed, monomeric Mo(VI) sp ecies. The pH dependence of the reduction potentials suggests that two protons a re consumed in the reduction of each Mo(VI). The monomeric Mo(V) reduction product undergoes spontaneous dim erization with a ra te constant estim ated as 103 M - 1 s ' 1 . It a lso reduces perch lo rate and n itrate anions a t a significant ra te . The Mo5>(V)/M0 3 (111 ) redox couple in acidic solution involves an overall four ele ctro n -six proton tra n s fe r connecting the two p articipants. This redox pro cess is ch aracterized by extrem e electrochem ical i r r e ­ versib ility . Reduction of the Mo^(V) aquo ion to the Mo2 (III) aquo ion proceeds with c?na equal to 0.73 and a proton reactio n order of 1 .4 . A chem ical step with an inverse dependence on proton concentration precedes the reoxidation of aquo Mo^III) to aquo Mo^V). Plausible m echanism s a re given for th ese observations. The trin u c le a r ions containing Mo(IV), Mq3 0 4 (H20 )g+(Mo3 (IV)) and an oxalato derivative, Mo3 0 4 (C2 0 4 )3 (H2 0 ) 3 , can be reversibly R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . reduced in acidic m edia to trin u cle a r Mo(ni) species. The reductions involve two sequential electron tra n s fe r steps with form al potentials that a re pH dependent: MOg(IV) + 2e" Ef Mo3 (m , m , IV) Ef Mo3(III, m , IV) + le " Mo3(m ). Two waves a re evident in voltam m ogram s and polarogram s of Mo3 0 4 (C2 0 4 )3 (H20 )3” but with Mo^IV) the two form al potentials a re too close together to observe sep arate waves. However, logarithmic analysis of the shapes of norm al pulse polarogram s allowed the two form al potentials to be evaluated. The reductions of both complexes a re believed to be accom panied by protonation of the bridging and capping oxo-ligands. The new, trin u cle a r Mo^III) species resulting from the th re e -e le ctro n reduction of Mo3 (IV) exhibits a ch aracteristic EPR spectrum . The m ixed-valent interm ediate, Mo3 (III, III, IV), is diam agnetic. Possible stru c tu ra l changes that accompany the addition of electron s and protons to Mo^IV) a re discussed. R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . v T a b le o f Content s Pag Chapter 1. The S tructure of Aqueous Molybdenum 1 Compounds Chapter 2. The Reduction of Mo(VI) in T rifluoro- 26 methanesulfonic Acid Chapter 3. E lectrochem ical O bservations on the 72 D im eric Mo(V)-Dimeric Mo(III) Redox Couple Chapter 4. The E lectro ch em istry of T rin u clear Aquo 106 Mo(IV) and an Oxalato Derivative in Acidic Media Appendices 168 R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 1 CHAPTERJ. The Structure of Aqueous Molybdenum Compounds 1 R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 2 Introdudym Molybdenum aquo ions exist in the oxidation states II through VI, and within each distinct oxidation state the coordination environment is quite varied . The stru c tu re s of these complexes in solution have been addressed by an asso rtm en t of physical techniques. The most inform a­ tion has been obtained via two techniques, X -ra y diffraction of d eriv a­ tive complexes and extended X -ra y absorption fine s tru c tu re (EXAFS) analysis of the aquo ions them selves. The re su lts of th ese studies will be briefly reviewed using representative compounds to aid in under­ standing the electro ch em istry and chem ical reactivity discussed in la te r chap ters. F o r com parative purposes, the selected c ry sta l s tru c ­ tu re s w ill be lim ited to those with ligands containing predominantly oxygen bound to the cen tral m etal atom(s). X^RjjjCrjsbajJStr^^ Mo(VI) The synthesis of Mo-containing compounds m ost often begins with Mo(VI), which in nature usually e x ists a s the te tra h e d ra l anion, M 0 O4 . Below pH 7.0 , octahedral coordination prevails as w ater in s e rts into the inner coordination sphere. Under certain conditions h ig h er-o rd er 2 oligom ers, term ed polymolybdates, form . The polymolybdates exist q in a multitude of s tru c tu ra l ty p es 0 that will not be discussed h e re . The p ertinent s tru c tu re s that Mo(VI) form s in aqueous environm ents include th re e distinct types: m onom eric, oxo-bridging dim eric, and noninter­ acting dim eric species. A short M o-0 m ultiple bond, designated as the te rm in a l oxo bond, R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . is present in all th ree stru c tu ra l types. It a ris e s from the strong ct and it donation of O to the empty d orbitals of Mo(VI). When two or th re e term in al oxo functionalities a re present, the typical cis a rra n g e ­ ment dictates optimal multiple bonding to the Mo core. This is seen in the s tru c tu re 4 of M o0 2 (CH3 COCHCOCH3 ) 2 shown in Figure 1.1A. The te rm in a l oxo bond, h e re afte r abbreviated as Mo-O^, has a bond length of 1 .7 1 A a s com pared to 1.76 A found in Mo0 4 . T ran s to each Mo-Ot bond a re the ligand oxygen atom s at the considerably longer distance of 2.24 A. The cis ligand oxygen atoms resid e at 1.99 A, again reflecting the tra n s influence of the strong Mo-Oj. bond. The bonding argum ents given for monomeric Mo(VI) a re also applicable to the two dim eric stru c tu re s shown in Figure 1. IB and C. The edta (edta = ethylene diamine tetracetate) complex 6 (Figure 1.1B) contains two noninteracting MoOa subunits which a re attached to oppo­ site ends of the chelating ligand. The oxo functionalities a re also cis to one another and have bond lengths comparable to the monomeric species (1.69 A). The Ba[Mo2 0 5 (C2 0 4 >2 (H2 0 )2l s tru c tu re 6 in Figure 1.1C exhibits a linear Mo-O-Mo bridge with two cis term in al oxo groups on each Mo. The bridge oxygen, O^, e x erts le ss of a tra n s influence than the te rm in a l oxo groups and p o ssesses an increased bond length of 1.88A. Mo(V) The exceptionally short term in al oxo bond that dominates the chem istry of Mo(VI) is also prevalent in Mo(V) stru c tu re s. In very (7 _ strong acid Mo(V) ex ists a s the species MoQX5 ( e .g . , X = Cl , B r , NCS"). Upon lowering the acidity, dim erization occurs with the R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow ner. Further reprodu ction prohibited without p erm ission . 4 Figure 1.1 . A) The stru c tu re 4 of M o0 2 (CH3 COCHCOCH3)2, B) The structure® of Mo2 0 5 (C20 4 )2 (H2 0 ) 2 in Ba[M 0 2O 5 (C2 O4 )2 (H2 O)2 l, C) The structure® of M o0 3 (edta)Mo0 3 . in Na4 [Mo0 3 (edta)M o03f • 8H2 0 . R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 5 R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 6 O initially form ed dim er postulated to contain a lin ear Mo-O-Mo bond. The exact geom etrical arrangem ent of the Mo-Ofc bonds is unknown, although an analysis of the bonding iso m ers by a simple m olecular O that the two Mo-Oj- functionalities m ust be orbital method determ ined perpendicular to each other to account fo r the observed solution p a ra ­ m agnetism . To date, no crystalline derivatives of aqueous Mo(V) com­ plexes possessing a linear oxygen bridge have been obtained with ligands bearing only coordinated oxygen. rj Lowering the acidity fu rth er re s u lts in a bonding change in the dim eric core with the u su al species obtained from such solutions containing a di-p,-oxo bridge, a s exem pli­ fied by the stru c tu re 9 of Ba [Mo2 0 4 (C20 4 )(H20 )2] (Figure 1.2 ). The significant bond distances a re : Mo-Mo 2.56 A, Mo-Oj. 1.70 a , and Mo-O^ 1.90 A. It is argued 9 that the observed diam agnetism and close proxim ity of the two Mo atom s is due to a m etal-m etal bond, and th ere is physical evidence 10 to support th is idea. The two Ot bonds a re cis to each other and, as expected, exert a significant tra n s influence. The central Mo atom s a re situated up out of the plane of the four apical oxygen ligands. In basic solution the cis di-^i-oxo core b reak s apart to form a stru ctu rally u n characterized insoluble polym eric molybdenum hydroxide complex. Mo(IV) The c ry stal stru c tu re s of ions isolated from aqueous solution containing molybdenum in oxidation state (IV) have been determ ined fo r. anionic complexes containing oxalate 11 and edta 12 as ligands. Both stru c tu re s a re based upon a trim e ric core of composition Mo30 4+ a s shown for Cs 2 [Mo30 4 (C20 4 )(H2 0 )3] (Figure 1.3). In addition, the R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 7 Figure 1.2. The structure® of Mo2 0 4 (C2 0 4 )2 (H2 0 ) 2 in Ba [Mo2 0 4 (C20 4 )2 (H2 0 )21 • 5H20 . R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Figure 1 .3 . The structure** of Mo3 0 4 (C20 4 )3 (H20 ) 3 in Cs 2 [Mo3 0 4 (C2 0 4 )3 (H2 0 )31 • 4H2 0 - i H 2 C2 0 4. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 11 stru c tu re of an isothiocyanato complex has been surm ised 13 to be trim e ric with the sam e cen tral core composition. The term in al oxo bond, so prevalent in the stru c tu re s of molybdenum compounds in higher oxidation states, is not present in the trim e ric Mo(IV) com­ plexes. Unique to these compounds is the presence of a triply bridging ’capping’ oxygen with a Mo-O bond distance of 2.019 A, longer than that observed for the other bridging oxygen atom s, 1.921 K. In addition, the Mo-Mo bond distance of 2.49 A is suggestive of a significant bonding interaction among the th re e molybdenum cen ters. Mo(III) Structural studies of aqueous Mo(III) complexes a re few, presum ably due to th e ir sensitivity to m olecular oxygen. The aqueous species of in te re st include m onomeric, dim eric, and trim e ric aquo 7 14 ions, of which only the dim eric ion has been characterized stru ctu rally ’ as a derivative complex. The edta complex of a Mo(m) dim er (Figure 1.4) has been synthesized by reduction of the parent Mo(V) dim er. Noteworthy a re the absence of term inally bound oxygen atom s and the presence of a bridging acetate ligand. In addition, the bridging oxygen atom s a re protonated and have a M o-0 bond length of 2.04 A, considerably longer than that found in the Mo(V) d im er. The dihedral angle between the two Mo(OH) 2 planes is 166°; the corresponding angle found for the MoOz unit in the Mo(V) dim er is 151 *. The Mo-Mo distance is 2.43 A in the Mo^UI) complex, significantly sh o rte r than in the corresponding Mo(V) d im er. Mo(II) To complete the sequence of Mo aquo ions, a discussion of dim eric R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 12 Figure 1.4. The s tru c tu re 1 4 of Mo2 (OH)2 (0 2 CCH3 )edta“ in K[Mo2 (OH)2 (0 2 CCH3 )e d ta ]. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 13 R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 14 Mo(n) complexes would be useful. The dim eric ions po ssess short m etal-m etal distances ch arac te ristic of a quadruple bond. F o r com 4+ parison to the following EXAFS studies on the MOg ion, the stru ctu re 15 of M o 2 (0 2 CCHs ) 4 is shown in Figure 1 .5 . An exceedingly short Mo-Mo distance of 2 .1 1 A is found in th is well-studied*® entity. The high sym m etry (D ^) is another ch arac te ristic feature of dim eric Mo(II) com plexes. EXAFS of Selected Mo Aquo Ions As a sim ple aquo ion, molybdenum in the oxidation states II through V is extrem ely difficult to isolate a s a crystalline solid. Although Mo(VI) species a re well ch aracterized by X -ra y diffraction as sim ple aquo ions, the other oxidation states a re stru ctu rally c h a ra c te r­ ized only from derivative com plexes. Despite th is lim itation, a certain knowledge of solution stru c tu re has been realized from the EXAFS analysis of selected molybdenum aquo ions.* A detailed description of the theory and analysis of EXAFS is beyond the scope of th is work; 17 how ever, for the in terested re a d er sev eral recent review s a re available. The ability to probe the stru c tu re of an ion in solution o r of a complex that does not cry stallize well is one of the principal strengths of EXAFS studies. The specific inform ation th at can be obtained from an EXAFS analysis includes: 1) the distance between the X -ray absorbing and scatterin g atom s, 2 ) the number of backscattering atom s of a p articu lar type, Nb (coordination num ber); and 3) the root mean square deviation of Rab , oab (better known as the Debye-W aller R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 15 Figure 1.5. The structure**5 of Mo2(02CCH3)4. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 16 R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 17 factor). This information is listed in Table 1.1 for selected molyb­ denum aquo ions and compounds. Conspiciously absent from Table 1.1 is angular information regarding each a b so rb e r-sc a tte re r type. This is a m ajor flaw of the EXAFS technique and lim its the analysis to suggesting sev eral possible s tru c tu re s. N evertheless, from the known c ry sta l stru c tu re s for each oxidation state and the observed solution chem istry, likely stru ctu ral candidates fo r each species can be inferred. The end resu lt of the EXAFS analysis for a v ariety of aquo ions is shown in Figure 1 .6 . The specific features of each ion w ill be dis ­ cussed in tu rn . Mo(V) The EXAFS sp ectra of the Mo(V) dim er in acidic solution were analyzed 1 with the following th ree scattering components: a Mo-Mo distance at 2.56 A and two separate M o-0 components at 1.68 and 1.93 a . The scattering amplitudes were compatible with the di-jn-oxo core stru c tu re , Mo20 4+. The bond lengths for the th re e components a re consistent with those observed in the stru ctu re of Ba [Mo20 4 (C20 4 )2 (H2 0 ) 2 l,. mentioned e a r lie r. Mo(IV) The EXAFS analysis was done on two Mo(IV) sp ecies, solid Kg [Mo3 0 4 (C20 4 )3 (H20 )3] . and the Mo(IV) aquo ion in 4M CH3 S0 3H. E ssentially identical EXAFS sp ectra w ere obtained for both species. The scatterin g amplitude analysis for the oxalate salt produced two Mo-Mo interactions at 2 .4 9 A, two Mo- 0 components at 1 . 8 8 A, and four Mo-O' components at 2 . 0 5 ± 0 . 0 9 A. This second sh ell of oxygen atom s for the oxalate salt is in reasonable accord with the mean R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Reproduced with permission of the copyright owner. Further reproduction prohibited without p erm ission . 2 2 1 K2 [Mo3 0 4 (C2 0 4 ) 3 (H20 )3] a M o(m ),b 3M CH3 SO3H (aq) 2 2 2 0.04 0.03 0.03 0.04 2.56 2.49 2.49 2.54 d. Solid isolated from electro ly sis solution (see Chapter 4). c. T rim e ric cation (see C hapter 4). b. D im eric cation (see C hapter 3). a. Solid sam ple. 2.14 2.03 4 4 0.04 1 0.05 2.48 2 M03(0 H)4(C20 4)’ d Mo(II), 1M CH3 SO3H (aq) 2 .1 2 - 2.49 2.06 2.06 1.91 1 .8 8 1.93 Rab (A) Mo-O Component 4 3 Nb Rab (A) aab (A) Mo-Mo 2 M o(m ),c 4M CF 3 SO3 H (aq) 1 Mo(IV), 4M CH3 SO3H (aq) Nb Mo(V), 3M HC1 (aq) Sample Table 1 .1 . EXAFS Analysis for Selected Molybdenum Ions 0 .1 0 0.05 - 0.04 0.04 0.03 0.04 aab (A) 2.05 4 2 .2 0 2.04 3 1 .6 8 1 Rab (A) 4 Nb Mo-O' 0.08 0.09 0.08 0.04 °ab (A) 19 Figure 1.6 . Aquo Mo core stru c tu re s 1 as determ ined by EXAFS: A) Mo2 (V), B) Mo3 (IV), C) Mo3 (m ), D) Mo 2 (m ), E) Mo2(n). R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 21 distance in the c ry s ta l stru c tu re of one capping oxygen (ji 3 - 0 ) at 2.019 A, two oxalate oxygens at 2.091 A, and one coordinated w ater molecule at 2.154 A. For the aquo ion the analysis produced two Mo-Mo interactions at 2.49 a , two M o-0 components at 1.88 A, and four Mo-O' components at 2.04 A. Presum ably these second shell oxygen interactions a re also a weighted average of capping (f i 3- 0 ) oxygen and coordinated w ater m olecules. Thus, in light of the known s tru c tu ra l p a ra m e ters fo r [Mo3 0 4 (C2 0 4 )3 (H2 0 ) 3 ] 2 , the aquo Mo(IV) EXAFS data can be logically in terp reted in te rm s of a trim e ric core (Figure 1 .6 ). In solutions le ss acidic than 0.01 M H+ the EXAFS sp ectra of aquo Mo(IV) display changes that have been attrib u ted 1 to an opening of the trim e ric co re. In addition, the presence of halide ions had no effect on the EXAFS sp ectra, suggesting no inner sphere coordination. However, outer sphere ion pairing could occur without any revealing effect on the sp ectra. Mo(III) Two distinct Mo(III) stru c tu ra l types have been examined by EXAFS: the postulated dim eric Mo(III) aquo ion and the Mo(III) ions resulting from reduction of th e ir trim e ric Mo(IV) counterparts (see C hapter 4). The dim eric Mo(III) data w ere analyzed in te rm s of one Mo-Mo constituent at 2.54 A and two different Mo - 0 interactions, each of coordination number th re e , at 2.06 and 2.20 A. The m etal-m etal distance is clearly longer than that found in the c ry stal stru c tu re of K[Mo 2 (OH)2 (0 2 CCH3 )edta] and suggests that the acetate ligand influences R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 22 the Mo-Mo bonding in the la tte r compound. The 2.06 k M o-0 compo­ nent can be reasonably assigned to bridging hydroxyl groups with the longer M o-0 distance due to coordinated w ater (it is noteworthy that among the various oxidation states only in the aquo Mo2 (III) species did Mo-OH2 interactions make a significant contribution to the EXAFS). The analysis clearly ru les out an oxo bridged stru ctu re for Mo2 (m ), although the distinction between a di-p-O H stru ctu re o r a tri-fi-O H stru ctu re (confacial bioctahedron) is not evident. The second a lte r­ native is likely considering the fact that other Mo(III) ions with halide ligands exist with confacial bioctahedral stru c tu re s 1 8 (e .g ., Mo2 C1^’ , Mo2 B r92-). The EXAFS analysis iq for the Mo(III) ions resulting from reduction of the Mo(IV) aquo ion and [Mo30 4 (C20 4 )3 (H20 )3f seem s con­ sistent with a trim e ric form ulation. F o r the aquo ion the Mo-Mo distance of 2.49 A is p reserv ed and the M o -0 interaction is best fit with average oxygen shell of amplitude = 4 at 2.06 A. In the oxalate ion the Mo-Mo interactions resid e at 2.48 A with the average (Nfe= 4) M o-0 component at 2.03 A. No fu rth er improvement in the EXAFS curve fitting analysis re su lts by addition of coordinated w ater to the p aram eter set. The increased M o-0 components a re due to the presence of Mo-OH bridges and a re consistent with the observed electrochem istry (Chapter 4). Mo(II) The EXAFS sp ectra of the dim eric Mo(II) ion w ere analyzed in te rm s of a single Mo-Mo elem ent at 2.12 A and four M o-0 interactions a t 2 . 14 A. The Mo- 0 distance is reasonable for coordinated w ater and R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 23 is relatively disordered, a s judged by the larg e Debye-W aller factor (0.1 A). The Mo-Mo bond distance is in excellent accord with that previously discussed for Mo2 (0 2 CCH3)4. Concluding R em arks The stru c tu ra l details of the molybdenum aquo ions should facilitate a b etter understanding of th e ir rich redox behavior and chem ical reactivity. In C hapter 2 the electrochem ical behavior of MO(VI) in strong acid and the reactiv ity of a tran sien t Mo(V) monomer toward perchlorate and n itrate reduction w ill be exam ined. Chapter 3 ad d resses the in terfacial e lectro n tra n s fe r p ro p erties of the Mo2 (V)Mo2 (III) couple with the aim of understanding why th is m ulti-electron redox reaction is so electroehem ically irre v e rs ib le . The e le ctro ­ chem ical response of trim e ric Mo(IV), with p a rtic u la r reg ard to the aspects of coupled pro to n -electro n tra n s fe r to m etal clu ster ions, is presented in Chapter 4. The goal of th ese studies is to achieve a better insight into how molybdenum functions in complex environm ents, such a s supported cataly sts, amorphous m ate ria ls, and m etalloenzym es. R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 24 1. Portions of th is chapter have appeared in print: C ram er, S. P . ; Eidem , P. K .;Paffett, M. T .; W inkler, J . R . ; Dori, Z . ; and G ray, H. P . . .T. Am. Chem. S o c.. 1983, 105, 799. 2. Evans, H. T ., J r . , P e rsp e ct. Struct. C h em .. 1971, 4, 1. 3. Cotton, F. A ., and W ilkinson, G ., ’’Advanced Inorganic C hem istry” , Wiley, New York, 1972. 4. K am enar, B. and Penavic, M ., C ry st. Struct. C om m un., 1973, 5. P a rk , J . J . ; Glick, M. D.; and Hoard, J . L . , J. Am. Chem. . Cotton, F . A .; M orehouse, S. M .; and Wood, J. S . . Inorg. C hem .. 7. Stiefel, E. I ., P ro g r. Inorg. C h em .. 1977, 22, 93. . Blake, A. B .; Cotton, F . H . ; and Wood, J . S . , J . Am. Chem. 9. Cotton, F . A .; M orehouse, S. M .. Inorg. C h em ., 196£, 4, 1377. 10. W inkler, J. R . ; Ph.D . T hesis, Caltech, 1984. 11. Bino, A .; Cotton, F . A .; and Dori, Z .. J . Am. Chem. S o c .. 12. Ib id ., 1979, 101, 3842. 13. Murmann, K. and Shelton, M .. J . Am. Chem. Soc., 1980, 102, 14. Kneale, G. K .; Geddes, A. J . ; Sasaki, Y .; Shibahara, T. and 15. Lawton, D. and M ason, R . . J . Am. Chem. S o c ., 1965, 87, 921. 2, 41. Soc. . 1968, 91, 301. 6 1964, 3, 1603. 8 S o c.. 1964, 8 6 , 3024. 1978, 100, 5252. 3984. Sykes, A. G .. J . Chem. Soc. Chem. C om m un.. 1975, 356. R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 25 16. T ro g ler, W. C. and G ray, H. B .; A ccts. Chem. R es. , 1978, 11^, 17. (a) Lee, P . A .; C itrin , P . H .; E isen b erg er, P. and Kincaid, 232. B. M .; Rev. Mod. P h y s ., 1981, 53, 769. (b) C ram er, S. P .; Hodgson, K. O .; Stiefel, E . I. and Newton, W. E . ; J. Am. Chem. Soc., 1978, 100, 2748. 18. Ref. 7, p. 138. 19. C ram er, S. P . ; private communication, January 13, 1982. R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reprodu ction prohibited without p erm ission . 26 CHAPTER J The Reduction of Mo(VI) in T rifluorom ethanesulfonic Acid* R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 27 Introduction^ The electrochem ical reduction of aquo molybdenum(VI) has been studied in a variety of supporting e le c tro ly te s.2"® An e arly polarographic study 2 in HC1 suggested the initial production of a chem ically unstable Mo(IV) species while la te r work by Souchay and co-w o rk ers 3 * 4 proposed that sev eral form s (monom eric, te tra m e ric , e tc .) of Mo(V) w ere produced and subsequently reduced to M o(ni). A re p o rt by Hull® indicated that Mo(VI) is reduced in sulphuric acid to produce a Mo(V) species that adsorbs on the electrode but no stru c tu re s of possible Mo(V) products w ere proposed. In all of the previous w ork the voltam m etric responses w ere highly sensitive to the concentration of Mo(VI) and the medium employed. Adsorption on the m ercury electrodes was often invoked to account for complex voltam m etric behavior, although oligom erization of the variety of molybdenum(VI) oxo-species present in homogeneous solutions has also been suggested. The objective of the p resen t work was to estab lish the nature of the initial reduction product of Mo(VI) in a strong noncomplexing e lectroly te, trifluorom ethanesulfonic acid. It w ill be shown that low concentrations of Mo(VI) a re n ecessary to su p p ress adsorption at m ercury electrodes and solution oligom erization. In addition, the catalytic reactions of a reduced Mo(VI) species at low concentrations (ca. 5 x 10“ 5 M) with p erch lo rate and n itrate ion w ere monitored in the hope that insight into atom tra n s fe r reactions might re s u lt. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 28 Exj^Brim^ntSl M aterials Trifluorom ethanesulfonic acid (Minnesota Mining and Manufac­ turing C o.) was purified by distillation under Argon. The purified acid was diluted with w ater and sto red in a re frig e ra to r. Reagent grade sodium molybdate was used as received. O rtho-nitroaniline (Aldrich Chem ical C o.) was re c ry stallize d twice before u se. Solutions w ere deoxygenated by bubbling with argon or nitrogen that had been passed successively through a solution of V(n) and over hot copper turnings. Solutions w ere p rep ared with trip ly distilled w ater or distilled w ater that was fu rth er purified by passage through a purification tra in (B arnstead Nanopure D2790). Solutions w ere checked fo r chloride im purities by pulse polarography. Impurity levels in 2M solutions of trifluorom ethanesulfonic acid w ere below 0.1 /j,M. Stock solutions of Mo(VI) w ere standardized g ravim etrically by precipitation of PbMo04. 7 Instrum entation and Techniques UV sp ectra w ere recorded on Cary 17, V arian 219, or HewlettPackard 8450 spectrophotom eters. E lectrochem ical experim ents w ere c a rrie d out in conventional com partm entalized cells. Experim ents at v ariable tem p eratu res w ere c a rrie d out in a cell with the working ele c ­ trode com partm ent jacketed for tem p eratu re control. The referen ce electrode rem ained at room tem p eratu re. Most electrochem ical m easurem ents w ere perform ed with appropriate combinations of com­ m ercially available instrum ents (Princeton Applied R esearch Models 173, 174, 175 and 179). The Model 174 Polarographic A nalyzer was O Cyclic stairc ase voltam m etry modified to provide v ariab le pulse width. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 29 and chronocoulometry w ere c a rrie d out with a com puter-based digital data acquisition and analysis system sim ila r to that previously described. Q S taircase voltam m etry IQ was perform ed with a fixed step height of 4.88 mV. V ariation of the effective sweep ra te ( i . e . , [step height] x T step width]-1) was obtained by appropriate changes in the step widths. The a re a of the hanging m ercury drop electro d es was 0.032 cm2. The dropping m ercury electrode had a m ercury flow ra te of 1 to 1.5 mg s -1. P otentials w ere m easured and a re quoted with resp ect to a saturated calom el reference electrode. The Hammett acidities of solutions of C F 3 S03H between 1 and 4M w ere determ ined from the spectrum of o-nitroaniline indicator in each solution. Digital sim ulations of sta irc a se voltam m ogram s employed the method of Nicholson and O lm stead . 1 1 (See Appendix 1 for a listing of the p ro g ram .) R gsults V oltam m ogram s fo r the reduction of Mo(VI) in 1.9M CF 3 S03H show sev eral distinctive featu res that depend upon the concentration of Mo(VI) and the length of tim e that the m ercury electrode is exposed to the solution. Figure 2.1 shows a set of cyclic stairc ase voltammo­ gram s for a 0.5 mM solution recorded a fte r various tim es of exposure. T hree reduction peaks a re discernible (labeled A, B, and C in Figure 2.1); the most prom inent peak appears near -0 .5 volt. Plots of peak cu rre n ts v s. the square root of the effective scan ra te ( i.e ., vs. [step tim e]" 2 ) a re shown for peaks A and C in Figure 2 .2 . (Peak B is not w ell enough resolved at th is concentration for a sim ila r a n a ly sis .) R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow ner. Further reprodu ction prohibited without p erm ission . 30 Figure 2 .1 . Cyclic sta irc a se voltam m ogram s of 0.5 mM Mo(VI) in 1.9 M CF3SO3H. B efore the potential scan the m ercury electrode was exposed to the solution for: 1) 0.5 , 2) 5 .0 , 3) 15.0, 4) 45 .0 sec . Effective scan ra te was 12.2 V s " 1, R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Current, mA .30 -3 0 0 600 E, mV vs SCE R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 32 i Figure 2 .2 . Dependence of peak cu rren t on (step tim e) 2 i . e . , i (effective scan ra te )2, for peaks A and C of Figure 2 .1 . R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 1.5 1.0 o 0.5 Or 0 I 2 3 - 1/2 - 1/2 (step tim e) , (m sec) R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 34 The increasing positive deviations of the peak c u rre n ts from the .1 expected linear dependence on (step tim e) 2 is indicative of strong adsorption of the reactant which a lso accounts for the otherw ise un­ expected dependence on electrode exposure tim e. At concentrations of Mo(VI) of 0.025 mM or le ss, peak B in Figure 2.1 is b etter resolved and exhibits a lin ear dependence of peak cu rren t on (step tim e) 2. Thus, peak B appears to correspond to the reduction of a diffusing reactant while peaks A and C a re dominated by an adsorbed re a ctan t. At concentrations of Mo(VI) g re a te r than ca. 0.5 mM the voltam m etric responses become increasingly complex with obvious evidence of extensive adsorption. A v ariety of adsorbed species appears to be involved under th ese conditions which we avoided in o rd e r to concen­ tra te on the sim pler behavior available with m ore dilute solutions. Chronocoulometric M easurem ent of the Adsorption of Mo(VI). The extent of adsorption of Mo(VT) was estim ated from the in te r- cepts of single step chronocoulom etric ch arge-(tim e ) 2 plots. 12 The double layer charging biank, estim ated from identical potential steps in the pure supporting electrolyte, was subtracted from each experim ental intercept to obtain the quantity of adsorbed Mo(VI). Adsorption equi­ librium was assum ed to p revail when continued exposure of the elec­ trode to the solution produced no fu rth er changes in the adsorption. T hirty seconds of exposure w ere usually sufficient for equilibrium to be reached. The re su lts of these m easurem ents a re shown in Figure 2 .3 for sev eral initial electrode potentials. The most noteworthy feature for p resen t purposes is the sharp decrease in adsorption at concentrations of Mo(VI) n ear 0 .2 -0 .3 mM. A dsorption of Mo(VI) at R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 35 Figure 2.3, A dsorption of Mo(VI) at 0 .3 V a s a function of the concen­ tra tio n of Mo(VI). The potential was stepped from +0.3 to -0 . 6 V. Supporting electrolyte: 2 M CF 3 S0 3H. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 0.30 0.25 FT, mC cm 0.20 0.15 0.10 0.05 Total Mo(vi) C oncentration, M R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 37 concentrations below ca. 0.1 mM ap p ears to be negligible. Chem ical Speciation of Aquo Mo(VI) in Strong Acid In strong acid solution (<pH 1) Mo(VI) at high dilution exists p re JO . (H2 0 ) 3 Mo0 2 (OH) . As the to tal dominantly a s the monomeric cation, Mo(VI) concentration is increased condensation leads to the formation of a s e rie s of dim eric cationic species. Equilibrium constants for the protonation and distribution of Mo(VI) among monomeric and dim eric form s in p erchloric acid solutions have been evaluated from spectral 14 m easurem ents by Cruywagen and co -w orkers. The significant equi­ libria a re shown by equations 2 .1 -2 .4 . Mo(OH)5OH+ (= HMoO^) (2 . 1 ) H2 Mo2 Og+ (2 . 2 ) HMo20 3 + H+ H2 Mo2Og+ (2.3) H2 Mo20 8+ + H+ H3 Mo2 0 36+ (2.4) Mo(OH) 6 + H+ 2HMoOj kd . We repeated th e ir m easurem ents in solutions of CF 8 S03H and observed very sim ila r sp ec tra . We th erefo re adopted th e ir approach to evaluate a conditional equilibrium constant for the m onom er-dim er equilibrium in 2M CF 3 S0 3 H: CM o2(VI) kd = — Mo(VI) <2- 5> w here C;mo (v i ) is the to tal concentration of monomeric Mo(VI) without re g a rd to its state of protonation and CMo ^y^ is the corresponding R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 38 concentration of dim eric fo rm s of Mo(VI). The value of at 25 *C was 392 M”1. (The value rep o rted by Cruywagen et a l. in 2M HC104 w as 150 M- 1 . ) Since we also found it d esirable to examine the electro ch em istry of Mo(VI) at 50°C in 2M CF 3 S03H , was estim ated from sp ec tra l m easurem ents at th is te m p e ra tu re . A value of 270 M " 1 was obtained. A calculated distribution diagram fo r the sum of monomeric and dim eric form s of Mo(VI) a t 25° and 50° C is given in Figure 2 .4 . Note that th e re is no sharp change in the concentrations of the monomeric and dim eric species a t bulk concentrations n ear 0.1 to 0 .2 mM where the sharp increase in adsorption of Mo(VI) occurs (Figure 2.3) The im plication is that the sp ecies responsible for the adsorption is not one of the predominant form s in solution but is produced on the electrode surface, possibly as a re su lt of condensation reactio n s among the p re ­ dominant solution species that a re p resen t at concentrations of Mo(VI) g re a te r than ca. 0.2 mM but exhibit only weak adsorption. Pulse Polarography N orm al and re v e rs e pulse polarography 1 5 , 1 6 w ere utilized to inspect the behavior of Mo(VI) at a dropping m ercu ry electrode (F igure 2 .5 ). At concentrations above 0 .2 mM, norm al pulse polarogram s exhibited d isto rted shapes with c u rren t peaks preceding depressed limiting c u rre n ts that signaled extensive adsorption of the reactan t. 17 R everse pulse polarogram s w ere free of such d istortions; however, the half-wave potential displayed a significant anodic shift. At concentrations below 0.1 mM norm al pulse polarogram s w ere also essentially undistorted (Figure 2 . 6 ). F o r a one-electron p ro cess the R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 39 Figure 2.4, D istribution of Mo(VI) between monomeric and dim eric form s as a function of the concentration of Mo(VI) at 25° (---- ) and 50eC ( - --) in 2 M CF 3 S0 3H. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 40 100 M onom er Per cent 80 60 40 20 Dimer Total Mo(vi) Concentration, M R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 41 Figure 2.5, N ormal and re v e rs e pulse polarogram s of 0.49 mM Mo(VI) in 2 M CF 3 S0 3 H. The drop tim e was 1 sec. The pulse widths w ere 1) 10.5, 2) 18.2 and 3) 36.3 m sec. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 42 Normal Reverse 0 -300 -600 -900 E, mV vs SCE R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 43 F igure 2 .6 . N orm al and re v e rs e pulse polarogram s of 0.05 mM Mo(VI) in 2 M CF 3 S0 3H. Droptime: 1 s e c . ; pulse width: 10.5 m sec. Inset: -E v s . log (iL - i/i) for the norm al pulse polarogram . R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 44 Reverse I8O1 140 E 100 Normal ^ 60 2 0 ' ‘ - 1.3 X T 200 100 X 0 -100 • 1 ‘ 0.5 - 0.5. -200 X T -300 -400 E, mV vs SCE R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 45 lim iting reduction cu rren t in Figure 2 .6 , i^ , corresponds to a diffusion coefficient of 1 .3 x 10" 5 cm 2 s ” 1 for Mo(VI) a t th is high dilution where it e xists predominantly a s a monomeric ion (Figure 2 .4 ). The plot of ir i ■ . -■) shown in the inset in Figure 2.6 is lin ear with a slope E v s . log( of -57 mV pointing to a one-electron, nernstian electrode reaction. R everse pulse polarogram s recorded from an in itial potential of 0.45 volt (where Mo(VI) is reduced to Mo(V) during the growth of each m ercury drop before the potential is pulsed to m ore positive values) produced anodic limiting c u rre n ts that w ere alm ost equal to the r e ­ duction cu rre n ts obtained in the norm al pulse polarogram s of Mo(VI) so long as electrode drop tim es were re s tric te d to 1 second or le ss. This is the behavior expected when a stable and re-oxidizable reduction product is produced at the electrode su rfa c e . 1 5 , 1 6 However, at longer drop tim es the ra tio of anodic to cathodic c u rre n ts d ecreased as ex­ pected when the product of the electrode p ro cess, Mo(V) in the present case, is unstable. A plot of the norm al pulse polarographic half-wave potentials for the reduction of Mo(VI) a s a function of Hammet acidity (recorded with drop tim es short enough to avoid significant decomposition of the r e ­ duction product) is shown in Figure 2 .7 . The slope of 102 mV is reasonably close to the 118 mV value expected if the one-electron r e ­ duction reaction consumed two protons. Cyclic S taircase V oltam m etry Conventional cyclic voltam m etry with reactant solutions as dilute a s those required to elim inate the com plications from oligom erization and adsorption of Mo(VI) yields cu rren t responses that a re dominated R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 46 Figure 2 .7 . Polarographic half-wave potential v s. Hammett acidity function, HQ, for reduction of monomeric Mo(VI) in CF3SO3H. The pKa of the o-nitroaniline indicator used to evaluate HQ was taken a s -0 .3 R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 47 , mV vs SCE 90 ^ 130 Ll I i R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 48 by the capacitive background c u rre n t. Cyclic stairc ase voltam m etry elim inates much of th is capacitive charging c u rre n t 1 0 and was th e re ­ fore the p re fe rred voltam m etric method for these studies. Figure 2 . 8 shows a set of cyclic sta irc a se voltam m ogram s for sev eral concen­ tra tio n s of Mo(VI). These voltam m ogram s w ere recorded at 50eC because at this tem p eratu re higher concentrations of Mo(VI) could be utilized without encountering the sev ere adsorption that occurs near room tem p eratu re. A rev ersib le couple is clearly evident n ear -0 .1 volt and, in contrast with the behavior at room tem p eratu re o r in m ore concentrated solutions, th e re is no dependence of the peak c u rre n ts or wave shapes on the length of tim e the electrode is exposed to the solution before the voltammogram is recorded. The cathodic and anodic peak c u rren ts a re equal and linearly dependent on the square root of the effective scan ra te between 2 and 100 v s _1. However, at scan ra te s below ca. 2 V s " 1 the anodic peak cu rren t falls below its cathodic counterparts as the decom position of Mo(V) begins to deplete its concentration at the electrode surface. The separation of peak potentials in the cyclic sta irc a se voltam ­ m ogram s is dependent on the effective scan ra te and even at the lowest scan ra te s employed (1 V s ”1) it rem ained somewhat g re a te r than the 80.6 mV value expected (at 50°C) when a 4.88 mV s ta irc a se step height is applied to a nernstian reaction (10 h). It is probable that both uncom­ pensated resistan ce and slow electron tra n s fe r contributed to this behavior but we did not examine th is feature in g re a te r detail. At concentrations of Mo(VI) g re a te r than ca. 0.1 mM significant quantities of the dim eric ion a re form ed (Figure 2.4) and a wave which R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 49 Figure 2 . 8 . Cyclic sta irc a s e voltam m ogram s for Mo(VI) in 2 M CF 3 SO3 H at 50eC. Initial potential: +0.25 V. S e p tim e: 0.976 m sec (effective scan ra te = 5 V s ”1). Mo(VI) concentrations w ere A) 0.098; B) 0.24; C) 0.49 mM. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 50 O.IV 20 0 O.IV ■20 40 O.IV •40 R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited without p erm ission . 51 we believe to be due to the reduction of the dim er ap p ears at m ore positive potentials in sta irc a s e voltam m ogram s (Figure 2 ,8 B ,C ). By recording the voltam m ogram s at sufficiently high effective sweep ra te s (>5 V s ’ 1) the monomer and dim er equilibrium w ere essentially "frozen" and the m agnitudes of the two waves were com pared with those calculated on the b asis of the conditional equilibrium constant for the dim erization at 50eC in 2M CF 3 S0 3H. Figure 2 .9 shows a com parison of experim ental stairc ase voltam m ogram s with those obtained from a digital sim ulation of the sta irc a se response for solu­ tions containing a m ixture of the monomeric and dim eric species. (The dim er was assum ed to be reduced in a single, tw o-electron step and to have a diffusion coefficient 0.65 tim es as large as that of the m onom er). The reasonable agreem ent between the observed and sim ulated voltam m ogram s supports the assignm ent of the firs t wave to the reduction of dim eric Mo(VI). At effective scan ra te s slow er than 5 V s ’ 1 the wave attributed to dim eric Mo(VI) in creases at the expense of the m onomeric Mo(VI) wave. The reported*® value of 2 .2 (=1. 71 x 105 M ’ 1 s ’ 1) for reaction m easured by the tem p eratu re jump method in p erchlorate media is consistent with this observation. E lectrochem ical m easurem ent of th is value was not possible due to the unknown diffusion coefficient of Mo2 (VI). The reduction of the fam iliar, dim eric form of molybdenum (V), Mo2 (V), is known to occur n e ar -0 . 8 volt. No wave corresponding to th is pro cess is evident in the stairc ase voltam m ogram s for Mo(VI) when they a re reco rd ed at scan ra te s large enough to p reserv e equality R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reprodu ction prohibited without p erm ission . 52 Figure 2 .9 . C om parison of experim ental (left hand column) and sim ulated (right hand column) stairc ase voltam m ogram s. The experim ental voltam m ogram s w ere taken from Figure 2 .8 for potentials between +0.15 and -0.45 V. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . O.IV 20 O.IV -20 40 O.IV ■40 R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 54 of the anodic and cathodic peak cu rre n ts. However, at lower scan ra te s , where s m aller anodic to cathodic peak cu rren t ratio s resu lt, a new wave begins to appear at the potential w here Mo^(V) is reduced to Mo2 (III) (Figure 2. 8 B, C). 20 The c le ar implication is that the initial Mo(VI) reduction product undergoes a subsequent reaction leading to the form ation of the stable molybdenum(V) dim er, Mo2 (V). Controlled Potential E lectro ly sis Reduction of a 0.1 mM solution of Mo(VI) at a s tirre d m ercury pool at -0 .25 volt consumed one faraday per mole of Mo(VI). V oltam­ m ogram s recorded during various stages of the e lectro ly sis showed that a wave corresponding to the reduction of Mo2 (V) to Mo^(m) developed as the original Mo(VI) reduction wave diminished. Thus, on the tim e scale of controlled potential electro ly ses (20-40 minutes) the reduction of monomeric Mo(VIl produces Mo2 (V). Kinetics of the D isappearance of Mo(Vl Chronocoulometry provides a convenient procedure for evaluating the ra te s of chem ical reactions entered into by the products of an e lectrode reaction. 21 The procedure involves the m easurem ent of the ra tio of faradaic charge consumed in the electrochem ical production of an unstable species to the charge required for its subsequent e le ctro ­ chem ical reconversion to starting m aterial. This technique was applied to the Mo(VT)-Mo(V) system at a concentration of 0.1 mM and te m p e ra ­ tu re s between 35° and 55 *C to minim ize adsorption. The data w ere analyzed by means of a working curve derived from a published digital sim ulation of the case that the chem ical reaction is a second-order dim erization reaction 22 (see Appendix 2). The resulting dim erization R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 55 ra te constant could be estim ated only roughly because of complications from resid u al adsorption of Mo(VI), increasing concentration of dim eric Mo(VI), and the sm all signal-to-noise ra tio . The values obtained at sev e ra l tem p eratu res and th e ir estim ated precisio n a re shown in the A rrhenius plot in Figure 2 .10. Extrapolation of the plot to 298°K leads to a ra te constant of ca. 10 3 M - 1 s “\ The estim ated activation enthalpy and entropy a re 9 k cal/m o le and -12 e .u . , resp ectiv ely . Catalyzed Reduction of P e rc h lo ra te and N itrate If m oderate amounts of p erchloric or n itric acid a re added to dilute solutions of Mo(VI) in 2M C F 3 S03H the resulting cyclic voltammo­ gram s (Figure 2.11) exhibit the featu res expected for a catalyzed 23 regeneration of a reactan t from its reduction product (equation 2 . 6 , 2.7). Ox + ne — Red (2 . 6 ) Red + Z - ! ^ O x + Y (2.7) The current-voltage curve becom es flat ra th e r than peaked, the anodic wave re tra c e s the forw ard scan cu rren t, and the voltam m ogram s a re scan ra te invariant under the conditions listed. Since Mo2 (V) does not re a c t with e ith e r anion the catalytically active species seem s likely to be the monom eric form of Mo(V). A quantitative determ ination of the stoichiom etry of the catalytic reaction was not attem pted with e ith e r anion due to the competing dim erization of monomeric Mo(V). However, chloride ion was observed to appear in long te rm reductions of Mo(VI) in the presence of perch lo rate. R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 56 Figure 2 .10. A rrhenius plot of chronocoulom etrically determ ined ra te constants governing the dim erization of Mo(V) monomer generated from 0.097 mM Mo(VI) in 2 M CF3SO3H. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 57 ln [k d(M’,s')] 10.0 9.0 8 . 5. 3.3 io 3/ t R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 58 Figure 2.11. Effect of p erch lo rate and n itrate on the cyclic stairc ase voltam m ogram s of 0.050 mM Mo(VI). Supporting e le ctro ly tes: 1) 1.9 M CF 3 S03H + 0.1 M HN03, 2) 1 .9 M CF 3 S03H + 0.1M H C lO 4, 3) 2M CF 3 S0 3H. 50 mv s ’ 1 scan ra te . R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 59 T T ♦200 *100 0 -100 -200 -300 -400 E, mV vs. SCE R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 60 An extensive analysis of the theory of catalytic following reactions 24 In general, the (Er CJ) has been rep o rted by Saveant and V ianello. experim ental data and an aly sis assum e that Cz » C ^ . Under these conditions Cz rem ains v irtu ally constant and pseudo firs t-o rd e r condi­ tions govern reaction 2 .7 . By defining the kinetic param eter k 'C z prri A = k' C t (= ----- z y nF }), w here y = scan ra te , two limiting cases can be distinguished depending on the value of a . In the region of sm all a (< 0.04) voltam m ogram s of substance Ox display norm al diffusional behavior. When a becom es g re a te r than 1 the cu rren t attains a limiting value independent of scan ra te which is given by equation 2 . 8 . ( 2 .8 ) Evaluation of k' can be accom plished using equation 2 .8 or from the following equation which accounts for the stoichiom etric factor (ct) in m ore complex catalytic schem es. 24 <u* <V d i _ . y i | . y ° k'.cl 0.447 0.447 {2 9) nF H ere (ip)d is the cu rren t due to Ox in the absence of catalytic su b strate Z at scan ra te y . A somewhat consistent value of ( i i s obtained at several concentrations of C ° for both anions (Table 2.1). Assuming that the initial reaction of su b strate with catalyst is ra te determ ining, the apparent ra te constants a re 8 .2 (± 1.2) x 101 M _ 1 s ” 1 fo r perchlorate and 1 .2 (± 0 .1) x 103 M ” 1 s _ 1 for n itrate. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 61 Table 2.1 50 HCIO, = Z Cz , M Mo(VI) = 0.36 ijlB. 1 = 2 .0 adjusted with HTFMS 50 m v /s (Uc/C? (Uc^Vd a k' (M " 1 s " 1) ( l i A / M) 0.05 5.6 3.5 96. 0 .1 0 4 .7 4 .1 65. 0 .2 0 5 .0 6 .2 75. 0.5 5.5 1 0 .8 91. avg. = 82 ± 12 M " 1 s " 1 HNO, = Z * (^c^Vd to (liA /M ) ba (Uc/C? jx M 0.05 4 .6 13 1 0 .1 0 6.4 18 1 .2 .3 x 1 0 3 0 .2 0 9.2 26 1 .3 x 1 0 3 0.50 13.8 38 1 .1 x 103 x 103 avg. = 1 . 2 ± 0 . 1 x 1 0 3 M" 1 s ” 1 R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 62 SisssssiSBv The im portant monomeric form s of Mo(VI) p resent in strongly acidic solutions w ere term ed molybdic acid and protonated molybdic acid by Cruywagen et a l. who w rote the form ulae Mo(OH) 6 and Mo(OH)5OH^, resp ectiv ely . We p re fe r to depict these two species in equation 2 . 1 a s trio x o and cis-dioxo derivatives as shown below: O H + (HzO)3 M o=0 + H - o (H2 0 ) 3 M =0 (!) (2. 10) OH for which Cruywagen et al. ^ re p o rt an equilibrium constant of 11.4 M”1. Thus, in 2M CF 3 S0 3H, over 95% of the monomeric Mo(VI) is present as As shown in Figure 2.4, dim er form ation does not (H2 0 ) 3 M =0 OH exceed sev e ra l p ercent with concentrations of Mo(VI) of 0.1 mM or le ss so that under these conditions the observed ele ctro ­ O (H2 0 ) 3 J!f=0 OH chem istry should be that of the dioxo cation The p a tte rn of electrochem ical resp o n ses exhibited by dilute solutions of Mo(VI) is consistent with the following p a ir of reactions governing the course of the reduction: O O (H2 0 ) 3 JJlo=0 • 2H+ + e “ - (H2 0 ) 4 !Mo-OH 1 2+ (2.11) <!>h R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 63 2+ o 2+ kd . (H2 0 ) 4 Mo-OH ° O ° (H2 0 ) 3 M o ^ ^M o(O H 2), Cr + 2H+ + 2H,0 (2. 12) Reaction 2.11 takes account of the pH dependence of the half-wave potential for the reduction of Mo(VI) (Figure 2.7) and reaction 2.12 is based on a plausible stru ctu re that has been proposed for the stable dim er of Mo(V). ^ D irect evidence fo r the re v e rs e of reaction 2.12 is sp arse : Murman has m easured the kinetics of the exchange with the solvent of labeled bridging o k o groups in the Mo(V) dimer^® but the mechanism of th is p ro cess need not include the re v e rse of reaction 2 . 1 2 . E pr signals for sev eral monomeric complexes of Mo(V) have been reported, 27 but such experim ents have always involved the presence of added ligands that form very stable complexes with Mo(V). The kinetics of dim erization of a m onomeric Mo(V) catechol com28 and a mechanism proposed that sh ares plex w ere reported recently s ev eral of the features of reactions 2.11 and 2.12. However, large differences in pH and solution compositions prevent a m ore detailed com parison. Since the Mo(V) monom er, but not the d im er, 20 exhibits an anodic wave at -0 .2 volt (Figure 2.8) we sought to detect any monomer in equilibrium with the dim er by m eans of anodic norm al pulse polarography with a 10 mM solution of MOj(V) p rep ared by exhaustive ele ctro ­ lytic reduction of Mo(VI) in 2M CF 3 S0 3H. No anodic response above background levels was detected in th is experim ent. We estim ate the maximum concentration of monomer that could have gone undetected a s 6 x 10“ 6 M which places a lower lim it of ca. l ( f M (25® C) on the R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 64 equilibrium constant fo r reaction 2 . 1 2 (assuming that the proton depen­ dence is c o rre c t as shown). The value estim ated for the ra te constant governing the d im eri­ zation of Mo(V), ~ 103 M _ 1 s " 1 (25* C), is qualitatively consistent with the behavior observed in the norm al and re v e rse pulse polarographic experim ents with 5 x 10“5M solutions of Mo(VI) (Figures 2.5). F or exam ple, the ra tio of anodic to cathodic limiting c u rren t decreased from unity to 0.71 as the drop tim e was increased from 1 to 5 seconds com pared with a calculated value of 0.79 assum ing sim ple, secondorder irre v e rsib le lo ss of the Mo(V) throughout the 5 second drop life. Although reoxidation of the m onomeric form of Mo(V) to Mo(VI) appears to proceed readily at the m ercury electrode, no fu rth er reduction of the monomer was observed before decomposition of the solvent commences at ca. -1 .0 volt. This re sista n c e of monomeric Mo(V) tow ards electro -red u ctio n to Mo(IV) m atches the behavior of the 3+ monomeric Mo(m) ion, Mo(OH2 ) 6 , which is not oxidized to Mo(IV) at m ercury electro d es. 2 0 The apparent b a rrie r to the generation of a monom eric form of aquo Mo(IV) is probably associated with the strong preference of this oxidation state to form m ulti-nuclear ions: The 29 30 stable form of aquo Mo(IV) has been argued to contain one, two IQ 01 and th re e ’ molybdenum c en ters but the co rre c t stru c tu re appears 4+ to be the trim e ric ion, Mo30 4 . ^1 » W The s tru c tu ra l differences separating the monomeric Mo(in) ion, Mo(OH2 )g+, and the stru ctu re proposed for monomeric Mo(V) in equation 2.11 do not appear to be large but the difficulty in passing through the evidently unstable mono­ m eric Mo(IV) state to reach Mo(OH2 )g+ is presum ably responsible for R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 65 the absence of a tw o-electron reduction of the Mo(V) monomer,, In an e a rlie r re p o rt 2 0 on the pulse polarography of monomeric Mo(OH2 )g+ (with the initial electrode potential at +0.15 volt) a prominent reduction wave was observed near - 0 . 1 volt that was tentatively ascribed to the reduction of monomeric Mo(V) generated at the electrode surface by oxidation of Mo(OH2 )g+. The present re su lts indicate that monomeric Mo(V) is not reducible in the accessible potential range but that the reduction of monomeric Mo(VI) proceeds n ear -0 .1 volt. F o r this reason assigning the wave at - 0 . 1 volt in the pulse polarography of Mo(OH2 )g+ to the reduction of Mo(VI) monomer generated by the (very slow ) 2 0 oxidation of Mo(OH2 )g+ at +0.15 volt seem s plausible. The general asp ects of atom tra n s fe r reactions with re g a rd to the reduction of p erchlorate and nitrate ions by tran sitio n m etal ions 33 have been addressed by Taube. P resen tly , th ere is no well defined c orrelatio n between AG and reactivity o r a good understanding of why le " reductants a re as reactive o r m ore so than 2e” reductants. The reactivity of monomeric Mo(V) tow ards perch lo rate and n itrate ions is thought to be related to its ability to stabilize Q2 and form an "yl" product, namely the Mo(VI) cation, O (H20)3Mo=0 OH Monomeric Mo(V) is an extrem ely reactive l e ” reductant possessing a ra te constant ca. 1 0 6 la rg e r than the m ore well ch aracterized le " reductant, Ti(m ).34 The reduction of perchlorate and n itrate is not lim ited to the m onomeric Mo(V) ion shown in equation 2.11. D eaerated solutions of R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 66 trim e ric Mo(IV) a re only stable for periods of ca. one day in solutions 29 3+ containing p erch lo rate. In addition, the Bowen-Taube ion, Mo(H20 )e , reduces nitrate with a ra te constant of 2.9 x 10“ 2 l.M " 1 s ” 1 according QC to the following stoichiom etry. 2Mo(HzO)g+ + 2N03" - M0 feO4 (HaO)J+ + 2N02" + 4H+ + 4H20 (2.13) It is interesting to note that the Mo(V) monomer produced by acidifi­ cation (> 6 N HC1) of Mo2 0 4 (H2 0 )2+ is not reactive tow ards perchlorate.®® O Apparently the [(H2 O)4 ]&0 -OH"|2+ unit is required for significant reactivity . A dsorption of Mo(VI) The sudden onset of extensive adsorption of Mo(VI) at bulk con­ centrations g re a te r than ca. 0 .2 mM (Figure 2.3) is not typical of 37 sim ple ionic adsorption at m ercury. It is m ore rem iniscent of adsorption that appears to re su lt in the form ation of new phases con- OO taining m ultilayers of the adsorbate on the surface. The behavior of OQ Mo(VI) differs from most previous exam ples in that no complexform ing ligands a re required to induce the adsorption. The well-known tendency for Mo(VI) to condense spontaneously into oligom eric ions a s 40 its concentration is increased seem s likely to underlie the adsorption. Specifically adsorbed McXj(VI) may be an in itiator for th is surface con­ densation p ro cess. At concentrations above 1 mM o r so the electrode surface ap p ears to become covered with a film of condensed polymolybdate of unknown composition that in te rferes with the reduction of Mo(VI) from the bulk of the solution leading to the distorted and R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 67 depressed polarogram s and voltam m ogram s that a re so fam iliar in the e lectrochem istry of Mo(VT).^"® Conclusions^ Highly dilute acidic solutions of Mo(VI) in which monomeric ions predom inate exhibit much sim p ler electro ch em istry than re s u lts with less dilute solutions. A re v e rsib le redox couple consisting of mono­ m eric Mo(VI) and Mo(V) ions can be observed in such solutions. The aquo Mo(V) ion undergoes spontaneous dim erization to form the stable Mo2 (V) ion which is not oxidizable at m ercury electro d es. The mono­ m eric form of Mo(V) is not fu rth er reduced in the accessible range of potentials probably because of the in trin sic instability of the monomeric Mo(IV). This m onom eric Mo(V) species is catalytically active tow ards reduction of perch lo rate and n itrate . R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 68 References^ n d Not e s 1. A slightly different v ersio n of th is chapter has appeared in print: 2. Haight, G ., Inorg. Nucl. C hem .. 1962, 24, 673. 3. Lam ache, M. and Souchay, P . , J . Chim. P h v s .. 1973, 2, 384. Paffett, M. T . and Anson, F . C ., Inorg. C h em .. 1981, 20, 3967. 4. Lamache, M .; Cadiot, J . and Souchay, P .. J . Chim. P h v s .. 1968, 65, 1921. 5. 6 Hull, M ., J r . , E lectroanal. Chem . . 1974, 51, 57. . W ittick, J . and Rechnitz, G ., Anal. C h em .. 1965, 37, 816. 7. B elcher, R. and Nutten, A. J . , "Quantitative Inorganic A nalysis", . Abel, R . ; C h ristie, J . ; Jackson, L . ; Osteryoung, J . and 2 n d e d ., B utterw orths, London, 1960, p. 133. 8 O steryoung, R ., Chem. Instrum . 1976, 123. 9. Lauer, G .;A b e l, R. and Anson, F . , Anal. C h em ., 1967, 39, 765. 10. (a) B ark er, G. C ., Adv. Polarography, I960, 1, 144; (b) C h ristie, J. H. and Lingane, P . J . , J . E lectro an al. Chem. 1965, 10, 176;(c ) Mann, C. K .t Anal. Chem ., 1961, 33, 1484; (d) Mann, C. K. , Anal. C hem . , 1965, 37, 326; (e) Zipper, J . J . and Perone, S. P . , Anal. C h em .. J[973, 45, 452; (f) F e rr ie r , D. R. and Schroeder, R. R . t J . E lectroanal. C hem ., 1973, 45, 353; (g) Ryan, M. D ., J . E lectroanal. Chem. , 1977> 7 9 , 105; (h) Miaw, H .-L . and P e r one, S. P . . Anal. C hem . 1978, 50, 1989. 11. Nicholson, R. and O lm stead, M ., in "E lectro ch em istry : Calculations, Simulation and Instrum entation ", M attson, J . ; M ark,H . and M acDonald,H. E d s ., M arcel D ekker, New York, 1972, p. 119. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 69 (12) B ard, A. J . and Faulkner, L . R ., ’’E lectrochem ical Methods” , (13) Chojnacka, J . , Roczniki C hem . , 1965, 89, 161. John Wiley and Sons, New York, N .Y ., 1980, p. 199. (14) Cruywagen, J . , Heyns, J , and Rohwer, E ., J . Inorg. Nucl. C hem ., 1978, £0, 53. (15) Oldham, K. and P a rry , E . , Anal. Chem . , 1970, 42> 229. (16) Osteryoung, J . and K irow a-E isner, E . . Anal. C hem . . 1980, 52, 62. (17) Flanagan, J . B ., Takahashi, K. and Anson, F . C ., J . E lec tro ­ anal. C h em .. 1977, 85, 257. (18) Ojo, J . F . ; Taylor, R. S. and Sykes, A. G ., J . Chem. Soc. Dalton. 1975, 500. (19) Cotton, F. A. and Wilkinson, G ., ’’Advanced Inorganic C hem istry”, John Wiley and Sons, New York, N .Y ., 4th e d ., p. 8 6 8 . (20) Chalilpoyil, P . and Anson, F . C ., Inorg. C hem . , 1978, 17, (21) C h ristie, J . H ., J . E lectroanal. Chem. f ljJ67, ljJ, 79; 2418. Ridgeway, T . H ., Reilley, C. W. andV anD uyne, R. P . , J . E lectroanal. Chem ., 19J76, 67, 1. (22) Childs, W .;M alo y , J . ; K eszthelyi, C. and B ard, A. J . , J . E lectrochem . S o c.. 1971, 118, 872. (23) (24) Ref. 12, p. 455. Saveant, J . M. and V ianello, E . , Electrochim . Acta, 1965, 10, 905. (25) Ardon, M. and P ernick, A ., J . L ess Common M e t., 1977, 54, 233. R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 70 26. 27. M urman, K ., Inorg. C h em .. 1980, 19, 1765. Sacconi, L. and Cini, R ., J . Am. Chem. S o c.. 1954, 76, 4239; Spence, J . T . and Hey da n e k , M ., Inorg. Chem. 1967, 6 , 1489; Huang, T . J . and Haight, J r . , G. P . . J . Am. Chem. S o c.. 1970, 92, 2336; ibid... 1971, 93, 611; Im am ura, T .; Haight, J r . , G. P . , and Belford, R. L ., Inorg. C h em .. 1976, 15, 1047; Haight, G. P .; W oltermann, G .; Im am ura, T. and Hummel, P ., J . L ess Common M e t.. 1977, 54, 121. 28. Charney, L . M. and Schultz, F , A ., Inorg. C h em .. 1980, 19. 29. Ojo, J . F . ; Sasaki, Y .; T aylor, R. and Sykes, A. G ., Inorg. 30. Ardon, M .; Bino, A. and Yahav, G ., J . Am. Chem. Soc. 1976, 1527. C hem . . 1976, 15, 1006. 98. 2338; C ra m e r, S. P .; G ray, H. G .; D ori, Z. and Bino, A ., J . Am. Chem. Soc.. 1979, 101, 2770. 31. C ra m e r, S. P .;E id e m , P . K .;P a ffe tt, M. T .; W inkler, J . R .; Dori, Z. and G ray, H. B ., J . Am. Chem. Soc.. j^8 3 , 105. 799. 32. M urmann, R. K. and Shelton, M. E ., J . Am. Chem. Soc.. 33. Taube, H ., in "M echanistic A spects of Inorganic R eactions", 1980, 102, 3984. R orabacher and Endicctt E d s ., A m erican Chem. .Soc., 1982, Ch. 7. 34. Cope, V. W .; M iller, R. G. and F r a s e r, R . T . M ., J . Chem. Soc. A, 1967, 301. 35. Ketchum, P . A .; Taylor, R. C. and Young, D. C ., N ature. 36. Haight, G. P . , J . Inorg. Nucl. C hem . . 1962, 24, 663. 1976, 259, 202. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 71 37. Delahay, P . , ” Double Layer and Electrode Kinetics ", Wiley Interscience, New York, N .Y ., 1965, Ch. 4. 38. E lliott, C. M. and M urray, R. W ., J . Am. Chem. Soc. , 1974, 96, 3321; Parkinson, B. A. and Anson, F . C ., Anal. Chem ., 1978, 50, 1886. 39. Anson, F . C ., A ccts. Chem. R es. 1975, 8 , 400. 40. Reference 18, p. 852 ff. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 72 CHAPTERjJ O bservations on the E lectrochem istry of the D imeric Mo(V) - Dim eric Mo(III) Redox Couple R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 73 IntroducUon^ The efficient reduction of sm all molecules such a s 0 2, N2, and C jjHj, re q u ire s chem ical m oieties capable of multiple electron tra n s fe rs . In attem pts to mimic the catalytic reactions of m etalloenzym es dim eric m olecules capable of multiple electron tra n s fe r have i An example of th is is the use of the a ttra c ted considerable attention. Mo2(V)/Mo2(m) redox couple in the presence of complexing ligands 2-4 Although these system s a s a catalyst for acetylene reduction. p o sse ss no reactivity tow ard nitrogen it is noteworthy that biological nitrogen-fixing system s also reduce acetylene. With re g a rd to sm all molecule reductions the electrochem ical behavior of the Mo2(V)/Mo2(m) redox couple is of in te re st. Reduction of the dim eric Mo(V) aquo ion leads d irectly to a dim eric Mo(III) product, without passing through a stable Mo(IV) state. ® T his m u lti-electron, m ulti-proton redox reaction is noted for its highly irre v e rsib le c h arac te r. Specific factors which contribute to the sluggish electrode kinetics w ill be addressed by an electrochem ical study of the aquo ion and oxalate derivative. E xperim ental M aterials Solvent and electrolyte preparation a re mentioned in Chapter 2. Reagent grade sodium molybdate was used a s received. Solutions of 2+ M o20 4 w ere prepared by electrochem ical reduction (Chapter 2) o r by reduction with hydrazine sulfate followed by ion exchange purification with Bio-Rad AG 50W-X2 cation exchange re sin . Solutions w ere R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 74 deoxygenated by sparging with argon gas passed through solutions of either chromium(II) o r vanadium(II). Buffered oxalate solutions were prepared from oxalic acid and potassium oxalate. The extinction coefficient of M o ^ * was determ ined to be 3210± 100 M‘ 1cm “1 at 296 nm in 2M trifluorom ethanesulfonic acid by oxidation with standard­ ized eerie ion solution. This value com pared well with the value (3370 M"1 cm ”1) rep o rted 6 in 1 M p erch lo ric acid. Concentrations w ere evaluated spectrally using e = 3210 M"1 cm ”1. NH4 [M o20 4(C20 4)2(H20 )2] was prep ared by lite ra tu re m ethods7 or was generously supplied by Jay W inkler. Instrum entation E lectrochem ical and absorption spectroscopy instrum ents a re described in Chapter 2. R esu lts M o9(V) aquo ion The general featu res of the chem ically re v e rsib le Mo2(V)/M o 2(III) aquo ion redox couple w ere recently described by Chalilpoyil and A nson.6 Among the observations rep o rted w ere an o verall four electron reduction to M o^m ), v ery irre v e rs ib le electro n tra n sfe r pro p e rties, an apparent proton dependence in the reduction potential, and a slow chem ical step preceding the four electro n reoxidation of 2 MOjjCIII) to Mo (V). These experim ental observations w ill be examined in detail using sev eral electrochem ical techniques. Cyclic voltam m ogram s of the Mo2(V) aquo ion at two different acidities a re shown in Figure 3.1. The wave shapes a re very R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 75 Figure 3 .1 . Cyclic voltam m ogram s of A) 1.1 mM Mo^V) in 0.2 M HTFMS + 1.8 M LiTFMS and B) 0.56 mM Mo^V) in 2 .0 M HTFMS at scan ra te s of 1) 200, 2) 100, 3) 50, 4) 20 and 5) 10 mV s " 1. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 76 3 - 20- I— ♦300 '— '— I— 0 •— '— >— I— I— -500 •— I— »— <— I -1000 R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 77 asym m etric with a large potential separation between the cathodic and anodic peaks and an anodic /cathodic peak cu rren t ra tio of much less than unity. At scan ra te s between 0.02 and 0.2 V s " 1 the reduction p ro cess is diffusion controlled as determ ined from plots of i v ersu s i (scan ra te } 2 (inset Figure 3.1). At lowered acidity the reduction peak shifts to m ore negative potentials and the anodic/cathodic peak current ra tio in c re a se s. Also at low er acidity the slow scan voltam m ogram s (ca. 0.01-0. 02 V s ”*} of Figure 3 .1A display an unusual negative shift of the cathodic peak potential and a cathodic cu rren t in crease above that expected for a diffusion controlled reaction. P resen tly , th ere is no explanation for th is observation. V oltam m ogram s at fa s te r scan ra te s were recorded using the cyclic stairc ase technique. The inherent advantages of th is technique w ere discussed in C hapter 2. Most of the qualitative featu res observed in the cyclic voltam m ogram s a re seen in the s tairc ase voltam m ogram s (Figure 3.2}. These features include very asym m etric wave shapes, a negative shift in peak potentials with effective scan ra te , diffusion controlled reduction peaks a s judged by lin ear ipC v e rsu s (step tim e } ” 2 behavior (inset Figure 3.2), and anodic/cathodic peak cu rren t ratio s that a re le ss than unity. The decrease in anodic cu rren t is m ore pronounced at the fa ster scan ra te s . In Figure 3.2B the anodic cu rren t is scan ra te invariant for effective scan ra te s above 0.5 V s ' 1 In less acidic solution (Figure 3.2A) the voltam m ogram s show a slight in­ c re ase in anodic cu rren t with increasing effective scan ra te ; however, at sufficiently fast effective scan ra te s ( > 5 .0 V s"1) the anodic cu rren t is independent of scan ra te . Reoxidation of Mo2 (III) to MOj(V) R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reprodu ction prohibited without p erm ission . 78 F igure 3 .2 . Cyclic stairc ase voltam m ogram s of A) 1 .0 mM Mo2 (V) in 0.2 M HTFMS + 1 . 8 M LiTFMS and B) 1.1 mM Mo2 (V) in 2 M HTFMS at effective scan ra te s of 1) 5 .0 , 2) 2.0, 3) 1.0, and 4) 0.5 V s " 1. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 79 A < 0.2 0.11 0.025mA i ■ 300 i 100 - ■ I___i -100 JL I_____, -300 I----------------1--1--------.--------1 -500 -700 -900 -800 -1000 E (m V ) < 0.2 0.025mA (m s 200 -200 -400 ) -600 E(mV) R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reprodu ction prohibited without p erm ission . 80 is preceded by a chem ical step displaying an inverse proton depen­ dence. The norm al and re v e rse pulse polarogram s clearly dem onstrate the highly irre v e rsib le nature of the Mo2 (V)/Mo 2 (in) redox couple (Figure 3.3). A gen eral description of the following term inology and theory of pulse polarographic cu rren t-p o ten tial curves is given in Appendix 3. The re v e rs e pulse polarogram s a re split into two well separated components, as expected fo r an electrode reactio n with v ery O In addition, the tc ta l re v e rse pulse slow electron tra n s fe r p ro p e rties. limiting cu rren t ( ip p j + *Rp2 ) 2 M HTFMS is substantially less than the norm al pulse lim iting c u rren t (iNp) fo r a ll pulse widths. In less acidic solutions (0.2 M HTMS: Figure 3.3B) the ra tio of to tal re v e rse pulse lim iting cu rren t ( ip p j + to norm al pulse limiting c u rren t (i^ p ) is approxim ately unity at long pulse widths. Table 3.1 lis ts the values of i ^ p i / i ^ p *o r different acidities and pulse widths. Reasonable agreem ent is found with theory for irre v e rsib le electron tra n s fe rs at all pulse width v a riatio n s. In Table 3.2 the ra tio s ( ip p j + ip p 2 ^ //*NP a re given for the sam e acidity range and pulse width v ariatio n . As seen from the data d ecreasing the tim e p aram eter (pulse width) re s u lts in a p ro g re s ­ sively decreasing value of (ij^pj + * rp 2 ^ N P ' ^ his *s consis^en* a chem ical step preceding the reoxidation of Mo2 (m) to Mo^V). Again, the preceding chem ical reaction displays an inverse proton dependence such that at the lowest acid ities (0.048M HTFMS) the re v e rs e and norm al pulse lim iting cu rre n ts w ere essentially equal at a ll pulse w idths. It was not possible to work in solutions le ss acidic than pH ca. 1.5 because the reduction wave shifts into the background R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Figure 3 .3 . N orm al (N) and re v e rse (R) pulse polarogram s of 1.1 mM Mo^V) in A) 2 .0 M HTFMS and in B) 0 .2 M HTFMS + 1 . 8 M LiTFMS a t a pulse width of 18.2 ms and a 1 s drop tim e . R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 82 L X 300 X X 100 0 -100 J -300 -500 -700 900 E (mV) B L 300 X X 100 0 -100 _L -300 X X -500 X JL -700 J -900 E (mV) R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.156 0.109 10.5 5.05 0.13 0.18 0.23 b. Ionic strength adjusted to 2 .0 with LiTFMS. a. R eference 9. 0.206 18.2 0.39 0.52 0.13 0.18 0.23 0.39 0.13 0.19 0.24 0.42 0.55 0.358 54.9 0.50 0.472 95.5 0.13 0.16 0 .2 2 0.29 0.24 0.18 0.42 0.55 0.048 0.41 0.53 0 .2 ^RPl-^NP 0.5 Tm (ms) 1 .0 valuea i* nl T O l'T C P [H+] b = 2 .0 Experim ental Values T heoretical Pulse width Table 3.1. Ratio of R everse Pulse C urrent 1 to N orm al Pulse C urrent Table 3.2. Ratio of Total Reverse Pulse Current to Normal Pulse C urrent 84 R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 85 discharge current due to hydrogen production. The norm al pulse cu rren t-p o ten tial curves w ere analyzed in the fashion p rescrib ed by Oldham and Parry® by plotting log [ ^(*» ^ .,+ x .). -j v e rsu s -E , where x is i/i^ . The slope of the resu ltin g line is equal to (1-x) (mV-1), where a is the tra n s fe r coefficient, and na is the number of electrons involved in the ra te determ ining step. Figure 3.4 displays such norm al pulse polarographic log plots for the Mo2 (V) aquo ion. The product a tn & is determ ined to be ca. 0.73 over the acidity range 2 .0 to 0.048 M HTFMS in the absence of a double layer c o rre c tio n .1® The shift in half wave potential with H 0 is 106 mV p e r H0 unit. The reaction o rd er with resp ect to protons can be d e te r­ mined from a plot of logx v ersu s H0, under conditions of e le ctro ­ chem ical irrev e rsib ility (x < 0.12). The slope of the line in such a plot is 1.4 (Figure 3.5). The significance of th is value is explained in the discussion section. The norm al pulse lim iting c u rren ts a re equivalent to an overall four electron reduction with a diffusion coefficient of 3.2 x 10 “ 6 cm 2 s " 1 in 2M HTFMS. The value of kg could not be determ ined since the standard potential for the M o^vVM o^III) redox couple is not presently known. The chem ical reaction preceding reoxidation of the Mo2 (III) aquo ion was also qualitatively examined using double potential step chronocoulom etry. As described in Appendix 2 a key experim ental o b ser­ vable relevant to the homogeneous solution chem istry is the ra tio of charge at the end of the re v e rse step to that at the end of the forward step (Qg/QF; assum ing appropriate co rrectio n for double layer charging). For the Mq2 (V)/Mo 2 (III) redox couple the initial potential R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 86 Figure 3 .4 . Normal pulse polarographic log plots fo r Mo^V) reduction in (• ) 2 .0 M, (+) 1 .0 M, (□) 0.5 M, (A) 0 .2 M and (O) 0.048 M HTFMS. The pulse width was 54.9 ms and the drop tim e was 1 s. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 87 2.0 1.0 (1.75+x ) (l-x) 0.0 an0«I.O ano“0.5 800 900 1.0 ■2.0 ■3.0 •4.0 500 600 700 - E (mV) R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 88 F igure 3.5 . Proton reaction o rd er log plot for the Mo2 (V) aquo ion reduction. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 89 2.5 1 2.0 0.51 -0.3 0.0 0.3 0.5 0.8 -log [H*] R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 90 was stepped to a value sufficiently negative to insure diffusion con­ tro lled reduction of M o^V). The re v e rse potential step was ca. 200 mV positive of the apparent oxidation peak of Mo^(ni). So that, in the absence of the homogeneous preceding chem ical reaction, the reoxi­ dation should have proceeded at the diffusion controlled ra te . However, the observed ra tio of Q g /Q F is substantially less than that predicted from theory for diffusion controlled reduction and reoxidation (0.5858). Table 3.3 lists the experim ental values of Q g /Q F for the Moj,(V)/Mo^(in) couple at various switching tim es (r) and acid ities. Noteworthy are the increasing values of Q g /Q F at all acidities a s r in c re a se s. The in­ v e rse proton dependence in the chem ical reaction preceding reoxidation is also m anifest from the Q g /Q F v alues. The charge ra tio s displayed no dependence on to ta l concentration of Mo2 (V). C ontrolled potential ele ctro ly sis of the M o^y) aquo ion has been K reported to consume four electrons per equivalent of dim er in p ro ­ ducing the Mo2 (III) aquo. ion. Fully reduced solutions p o ssess an ab­ sorption spectrum identical to that of the Mo2 (III) aquo ion. ^ Reoxi­ dation of the M o^m ) aquo ion has been rep o rted to be sluggish, evidently due to an intervening chem ical step. Attem pts to duplicate ihe coulom etric reduction of Mo2 (V) produced v ariab le re s u lts. Although the reduced solutions produced the c o rre c t absorption spectrum for Mo2 (III) the number of equivalents req u ired to reach background cu rren t levels exceeded four by severalfold. In spite of this difficulty, it was possible to reduce the Mo2 (V) aquo ion quantitatively to Mo^(ni) and subsequently to reoxidize the Mo^III) aquo ion back to Mo2 (V). R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.471 b. Ionic strength adjusted to 2 .0 with LiTFMS. 0.479 0.385 0.482 0.471 0.422 a. Potential steps explained in text. 0.048 0 .2 0.5 0.490 0.295 0.464 0.160 0.321 0.348 0.320 0.195 0 .2 2 1 1 .0 0 .1 0 t (s ) 2 .0 0.15 0 .2 0 0.25 [H+l b 0.5 Mo2 (V)/Mo 2 (ni). 0.489 0.445 0.272 0.075 0.471 0.428 0.347 0.252 0.130 0.05 0.484 0.394 0.296 0.224 0 .1 0 0.025 Table 3 .3 . E xperim ental values of Q ^ /Q p for Double P o te n tia l Step Chronocoulometry of 0.453 0.280 0.08 0 .0 1 92 MoaQ,,(CA),(H,0)r The reduction of th is Mo^(V) derivative was studied in the pH range 2.5 to 5 .0 in buffered oxalate solutions. The electrochem ical responses exhibited by the oxalate derivative will be com pared with those rep o rted by Schultz et al. 12 1 ? ’ for the cysteine and edta deriv a­ tiv e s. In addition, the information gained in th is le ss acidic region complem ents the electro ch em istry of the uncomplexed Mo^V) aquo ion described in the previous section. Cyclic voltam m ogram s of Mo20 4 (C2 0 4 )2 (H2 0 ) 2 in oxalate media a re characterized by a highly irre v e rsib le reduction (Figure 3.6). The reduction peak is diffusion controlled a s judged from the linear 1. dependence of peak c u rren t on (scan ra te ) 2 (see inset in Figure 3 .6 A ,B ). The reduction peak potential shifts to m ore positive potentials with in­ creasing acidity suggesting coupled p roton-electron tra n s fe r in the reduction p ro c e ss. The anodic cu rren t is very dependent on scan ra te and pH of the m ed iu m .. At sufficiently fast scan ra te s (ca. 1 V s" 1) one anodic wave is seen ca. 600 mV positive of the reduction peak. A s the scan ra te d e crea ses the relativ e height of the anodic wave d e crea ses and other waves at m ore positive potentials ap p ear. The behavior is m ore complex in the le ss acidic solution (pH = 4.69), with a s many a s th ree waves appearing. In the m ore acidic solution (pH « 3.1) two anodic waves a re obtained at 0.02 V s" 1, with the predominant one centered at ca. -400 mV. Throughout the pH range studied the anodic cu rre n ts never attained the magnitude of the original cathodic c u rre n t. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 93 Figure 3 . 6 . Cyclic voltam m ogram s of 0 .9 mM Mo^0 4 (C20 4 )2 (H20 ) 2 in A) pH 4.69 and B) pH 3.07 oxalate media at scan ra te s 1) 200, 2) 100, 3) 50, 4) 20, and 5) 10 mV s " \ Ionic strength adjusted to 0.5 with KC1. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 94 R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Controlled potential electro ly sis of the Mo2 0 4 (C2 0 4 )2 (H2 0 )2~ ion in oxalate solutions at potentials negative of the reduction wave gave irreproducible re s u lts. The number of equivalents passed equaled four a fte r ca. four hours and a substantial cathodic current was still p resent even though sam pled cyclic voltam m ogram s indicated that the well defined Mo2 (V) reduction peak had disappeared. E lectro ly ses, that w ere continued until the current attained background levels, consumed v ariab le equivalents (6 - 1 0 faradays) and produced a fine brown precipitate. The final pH of such solutions was m easured at ca. 7, indicating considerable proton consumption. Coulometric red u c­ tions w ere generally c a rrie d out in pH 4.69 solutions to achieve suffi­ cient potential separation from background reduction of protons to hydrogen. Reoxidation of the fully reduced solutions was also irre p ro ducible and failed to reg en erate the starting complex. Reduction of the Mo2 0 4 (C2 0 4 )2 (H20 ) 2 species is evidently both chem ically and e le ctro - chem ically irrev e rsib le producing an u n characterized brown precipitate. The irre v e rsib le electron tra n s fe r p ro p erties of the Mo2 0 4 (C2 0 4 )2 (H20 ) 2 ion a re also evident in the pulse polarogram s. The re v e rs e pulse polarogram s a re split into two distinct portions, sim ila r to those of the Mo2 (V) aquo ion, and the ratio s a re consistent with theory (see Appendix 2) for a totally irre v e rsib le electron tra n s fe r. The norm al pulse lim iting current corresponds to an overall fourelectro n reduction step with a diffusion coefficient of 5 .2 (± 0.7) x 10 " 6 cm 2 s " 1 in 0.5 ionic strength oxalate buffer. Log plots for the norm al pulse polarogram s of Mo2 0 4 (C2 0 4 )2 (H2 0 ) 2 at varied pH a re shown in Figure 3 .7 . The Tafel slope is essentially the sam e at all R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 96 Figure 3.7 . Normal pulse polarographic log plots for the reduction of Mo2 0 4 (C20 4 )2 (H2 0 )2 - in (®) pH 3.07, (■) pH 3.88 and (A) pH 4.69 oxalate media adjusted to ionic strength 0.5 w ith KC1. The pulse width was 48.5 ms and the drop tim e was 1 s. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 97 3 .0 1 2.0 (l-x) 0.0 -4.0 900 1000 1100 1200 -E (m V ) R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . th re e acid ities and a n a is determ ined to be 0.70. The half wave poten­ tia l shifts 15 mV p e r pH unit, considerably le ss than that exhibited by the Mo2 (V) aquo ion. The proton reaction o rd er dependence (Alogx/Alog[H+]) is 0.25, also considerably less than that shown by the aquo ion. Since the standard potential is unknown for th is complex and appears to be unobtainable due to the chem ical instability of the reduced products, kg could not be evaluated. The chem ical instability of the reduced products also prevented an independent determ ination of 14 oi in the usu al m anner. D iscussion The solution stru c tu re s of the in itial and final states of the Mokj(V)/Mo2 (III) redox couple w ere discussed in C hapter 1. The Mo2 (V) aquo ion has a d i-p -o x o core stru c tu re (Figure 1.6 A) with a term in al oxo on each molybdenum atom . 1R Elution studies of the Mo2 (III) aquo ion from cation exchange colum ns have dem onstrated a net charge in solution of +4. The two following dim eric s tru c tu re s of the Mo2 (m ) aquo ion a re consistent with th is observation: i) a di-hydroxy bridged species, Mo2 (OH)2 (H20 )^4, or ii) a linear oxo bridge ion, MOgCKHgO)^4. Since the EXAFS analysis cle arly ru le s out1** the lin ear oxo bridge species, the most likely s tru c ­ tu re is the di-hydroxy species shown in Figure 1.6D . Thus, possible redox pathways to account for the electrochem ical re su lts will be assum ed to involve species with the stru c tu re s shown in Figure 1.6A and D. It is c le ar that proton tra n s fe r and possible other chem ical re arran g em en ts must accompany the addition of electrons to Mo2 (V) to R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 99 produce Mo2 (m ). In dissecting the possible ra te determ ining steps of th is complex electrode reactio n the following analysis u tilizes a general schem e of squares 20 in which each electro n and proton tra n s fe r is assigned an independent pathway a s shown in Figure 3 . 8 . F o r sim ­ plicity, chem ical steps other than proton tra n s fe r a re neglected, but in principle, they could be easily included in th is schem e. From inspection of Figure 3 .8 a multitude of possible pathways link the initial and final sta te s of a g en eral redox sequence involving m electrons and n protons. Proton tra n s fe rs to oxygen and nitrogen bases in aqueous solution in c ase s w here the free energy is favorable (AG have been m easured a t close to diffusion controlled ra te s . 21 0) Under such conditions coupled electro n -p ro to n tra n s fe rs a re generally 20 (e .g ., quinone). observed, a s in the reduction of organic m olecules M athem atical descriptions of complex electrode p ro c e sse s such as those for the case m = n = 2 have appeared . 2 0 F o r the Mo2 (V)/Mo 2 (III) redox couple the electrode reactio n is sufficiently complex that an exact m athem atical explication of a ll of the possible redox pathways has not been attem pted. However, the electrochem ical data and chem ical intuition allow a delineation of the likely pathways involved in proceeding from Mo2 (V) to Mo2 (III) and vice v e rs a . F or the Mo2 (V) aquo ion two possible ra te determ ining steps appear a s likely candidates in the overall reduction to Mo^III). Equations (3.6) and (3.7) re p re sen t two a ltern ativ es that a re consistent with the observed value of a n a = 0.73 and the proton reaction o rd er dependence of 1.4. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 100 Figure 3.8 . The scheme of squares fo r an o verall m electro n n proton electrode reaction (see text). R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 101 0,1 „ t ± A IN ' 2+ 0 0 II .C K A 0,0 nn = Mo . . I' Mo s 0 " . 4 + \ s = M of^M o to re R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 102 M 0 fcO4 (HaO ) 8 •+ r . d . s . +e +H LM o203(OH)(H20 ) b M o^O H ^ L (3.6) +J^ [ Mo r 0 (H 0); Mo20 4 (H2 0)*+ + 2e + 2H+ 2 3 2 (3.7) The electrochem ical evidence strongly suggests that the reoxi­ dation of Mo2 (m) to Mofe(V) is preceded by a ra te determ ining proton dependent step. Deprotonation of coordinated w ater m olecules to form term in al oxo or hydroxyl groups is a plausible in terp retatio n (equation 3.8). X I Mo X '' H Mo 1 X X I ^ x 1 H X ^ x +4 Y H Y | 1 JK Mo Mo x '' 1 ^ 0 ^ 1 ^ x X H X +(n-4) X. r . d . s. -nH+ (3.8) -4e -( 6 -n)HH 2+ O X^JI / O . yS Mo ■L | X ' r x (X = H20 ; Y = OH" o r O ") However, th e re is no evidence to rule out alternative chem ical re a rra n g e ­ ments of the McGill) species involving the bridging oxygen atom s which R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 103 impede the reoxidation to Mo2 (V). The observed reduction and oxidation pathways of the Mo2 (V)/MOj(III) redox couple a re clearly quite different and a re not n ecessarily the m icroscopic re v e rs e of one another because of the different possible pathways connecting the two states (Figure 3.8). Oxidation of the monom eric Mo(III) aquo ion to monomeric Mo(V) aquo ion (which d im erizes to form Mo^(V)) is a lso kinetically limited® perhaps because of a deprotonation step to form a te rm in a l oxo or hydroxyl group p rio r to electro n rem oval. E ssentially identical T afel slopes a re observed for the reduction of Mo2 0 4 (C2 0 4 )2 (H2 0 ) 2 and the M o^y) aquo ion. The equality of a n & for the two oppositely charged species suggests a common electron tra n s fe r route for reduction. The proton reaction o rd er for the reduction of the oxalate ion is 0.25, considerably sm aller than that for the aquo ion. Sim ilar proton reaction o rd ers have been observed1® in the reduction of MOjjOJcys) 2 (cys = cysteine) which also shows a dependence on the to tal buffer concentration. This point was not ad d ressed in the case of the oxalate ion. Chem ical irre v e rsib ility is a lso clearly evident in the reduction 215 of Mo20 4 (C2 0 4 )2 (H2 0 ) 2 , a feature that has been previously observed in the fou r-electro n reduction of Mo20 4 (cys ) 2 . In com parison, the four-electro n reduction 3 7 of M o ^ e d t a ) 2- is chem ically re v e rsib le . In accounting for the chem ical stability of the two species the authors 15 could not a sc e rta in w hether sulfur bonding by the cysteine ligand labilized the Mo^O2* core or ligand encapsulation by edta stabilized the Mo2 0 4+ co re. It seem s c le ar from the reduction of Mo20 4 (C2 0 4 )2 (H2 0 ) 2 that stabilizing the MOgO2* core re q u ire s a ligand, such as edta, that effectively p ro tects the bridging oxygens and prevents core breakup. R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 104 1. Koval, C ., P h .D .T h esis, California Institute of Technology, 1979. 2. Ichikawa, M. and M eshitsuka, S ., J . Am. Chem. Soc. . 1973, 95, 3411. 3. Zueva, A. F . ; P etrova, G. N .; Efimov, O. N. and Strelets, V. V ., R uss. J . Phvs. C h em .. 1979, 53, 210. 4. Efimov, O. N .; Zueva, A. F . ; Petrova, G. -N^-and Shilov, A. E ., Koord. K him .. 1976, 2, 62. 5. Chalilpoyil, P . and Anson, F . C ., Inorg. C h em .. 1978, 1_7, 2418. 6 . A rm strong, F . A. and Sykes, A. G ., Polyhedron. 1982, 1 , 109. 7. 8 Spittle, H. M. and W ardlaw, W .f J . Chem. S o c.. 1928, 2742. . Matsuda, H ., Bull. Chem. Soc. Japan, 1980, 53, 3439. 9. Oldham, K. B. and P a rry , E. P . , Anal. Chem. t 1968, 40, 65. 10. Delahay, P . , ’’Double L ayer and Electrode K inetics” , In te r­ 11. Richens, D. T . arid Sykes, A. G ., Comm. Inorg. C h em .. 19ftt, 12. Ott, V. R. and Schultz, F . A ., J . E lectroanal. Chem . , 1975, 13. Ibid ., 1975, 59, 47. 14. B ard, A. J . and Faulkner, L. R ., ’’E lectrochem ical M ethods", 15. Ardon, M ., and P ern ick , A ., Inorg. Chem. 1974, 13., 2275. 16. a) Chapter 1; b) Lee, P . A ., Phys. Rev. , 1976, B13, 5261. 17. A lbery, W. J . and H itchman, M. L ., ”Ring-D isc E lectrodes” , science, New York, N, Y ., 1965, Ch. 3. 1, 141. 61, 81. John Wiley and Sons, New York, N. Y. ,1980, p. 108. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 105 Oxford University P r e s s , London, 1971, Ch. 7. 18. Eigen, M ., Angew. C h em .r 1963, 75, 489. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 106 CHAPTER 4 The E lectrochem istry of T rin u clear Aquo Mo(IV) and an Oxalato D erivative in Acidic M edia 1 R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 107 IntroducMon Notable discrepancies regarding solution stru ctu re have appeared in the published re se a rc h on aquo Mo(IV). Souchay and co-w orkers, 2 in the initial synthesis of aquo Mo(IV), postulated a monomeric s tru c ­ tu re . A kinetic study of the equilibration of NCS" with aquo Mo(IV) led Sykes et a l. O 2+ to favor a monomeric form ulation, MoO (or possibly Mo(OH)2 +). In a la te r rep o rt Ardon and cow orkers^ disproved this assignm ent when they dem onstrated that sev eral species a re present when aquo Mo(IV) is equilibrated with NCS". From th e ir acid c ry o 4 5 scopy m easurem ents and the ion exchange behavior, they concluded that aquo Mo(IV) exists as a dim eric ion with the probable stru ctu re shown in Figure 4 . 1A. F u rther support for the dim eric ion came from the initial EXAFS study of C ram er and Gray, ® although the resu lts w ere somewhat inconclusive as to whether aquo Mo(IV) is dim eric or trim e ric in s tru c tu re . Finally, the dim eric stru c tu re was also favored by Chalilpoyil and Anson^ in an electrochem ical study of the aquo Mo(IV) ion. As described in Chapter 1, m ore recent s tru c tu ra l studies show 8 9 conclusively that aquo Mo(IV) is trim e ric ’ with the composition MO3 O4 4" (Figure 4. IB ). A re-exam ination of the electro ch em istry of th is ion was undertaken to see if it is consistent with the presence of th re e reducible cen ters in the ion. While th is study was in p ro g ress Richens and Sykes rep o rted the re su lts of experim ents on aquo Mo(TV) that included some electrochem ical m easurem ents. 11 W here they overlap, the experim ental observations coincide with those described by Richens and Sykes 1 1 although a different interpretation of some of R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 108 Figure 4 .1 . A) Postulated stru ctu re of aquo Mo(IV); B) Actual 9 12 core stru ctu re ' of trim e ric Mo3 (IV) complexes. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 110 the electrochem ical response exhibited by the aquo Mo(IV) ion w ill be given. Experim ental M aterials. Cs 2 Mo3 0 4 (C2 0 4 )3 (H2 0 ) 3 was synthesized according to a published procedure. 12 Mo3 (IV) aquo ion was p repared as previously described and fu rth er purified by ion exchange on a (Bio-Rad) AG50W-2X cation exchange column (14 x 2 cm). The concentration of Mo3 (IV) was determ ined by titratio n with a standard solution of Ce(IV). The m olar absorbance of MOg(IV) at 508 nm in 2M trifluorom ethanesulfonic acid was m easured as € 5 0 3 = 192 M " 1 cm " 1 which agreed with a previously rep o rted value 13 in p-toluenesulfonic acid. Solutions of what is alm ost certainly Mo3 (III) w ere p rep ared by controlled potential reduction of Mo3 (IV) at a m ercury pool electrode. Trifluorom ethanesulfonic acid, (Minnesota Mining and Manufac­ turing Co.) was purified by distillation a s described in C hapter 2. The concentrated, purified acid was diluted with distilled w ater that had been fu rth er purified by passage through a purification tra in (B arnstead Nanopure D2790). Stock solutions of lithium triflu o ro methanesulfonate w ere p rep ared by neutralization of reagent grade L^COg. O ther reagent grade m aterials w ere used as received. O-Nitroaniline (Aldrich C hem ical C o.) was re c ry stallize d tw ice. Solutions w ere deoxygenated by bubbling with p re-p u rified argon. Instrum entation and Techniques. Spectra w ere recorded on C ary 17 or H ew lett-Packard 8450A spectrophotom eters. EPR sp ectra were recorded on a V arian E -L ine Century Series sp ectro m eter. E lectro ­ R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . I ll chem ical instrum entation is described in Chapter 2. To perm it sp ectra of a ir-se n sitiv e ele ctro ly sis solutions to be recorded without rem oval from the e lectro ly sis cell an H -cell with a spectroscopic cuvette attached by an L -shaped arm was constructed. During e le ctro ­ lysis the solution level was below the inlet to the cuvette. To reco rd spectra the cell was tipped to fill the cuvette and the p ro cess was re v e rsed when additional e lectro ly sis was d esired . Digital sim ulation of the m ultiple electron tra n s fe r case employed the finite difference equation method of Feldberg*^ (see Appendix 1 for a program listing). Results^ The tris-o x a la to complex of Mo(IV). The complete form ula of the t r i s 2“ oxalato complex is Mo30 4 (C2 0 4 )3 (H20 ) 3 . 12 H ereafter we w ill omit the w ater m olecules in w riting the form ula of th is complex. An e a rlie r polarographic study* ^ of the Mo3 0 4 (C2 0 4)2” ion reported the presence of two reduction waves but possible stru c tu ra l changes accompanying its reduction were not considered. Cyclic voltam m ogram s of Mo30 4 (C20 4 )3 exhibit two w ell-sep arated reduction steps (Figure 4 .2 ). The separation of the two steps sim plifies the interpretation of the behavior of th is complex. For th is reason we will consider it firs t because the behavioral p attern it exhibits will prove useful in u nder­ standing that of the Mo3 (IV) aquo ion to be described subsequently. The magnitudes of the cathodic peak c u rre n ts in Figure 4 .2 a re consistent with a tw o-electron step followed by a one-electron step. The first reduction peak is diffusion controlled a s determ ined from the plot of its peak cu rren t v e rsu s (scan rate)z (inset in Figure 4.2 ). The R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 112 Figure 4 .2 . Cyclic voltam m ogram s of 0 . 8 mM Mo30 4 (C20 4)3 in 0.1 F (H2 C2 0 4 + K2 C2 0 4) at pH 1.53. The ionic strength was adjusted to 0.5 M with KC1. Initial potential: -300 mV. Scan ra te s: 10, 20, 50, 100 and 200 mV s"1. Negative potentials a re plotted to the right and reduction cu rren ts a re plotted upward. i_ Inset: Peak curren t v s. (scan ra te ) 2 for the firs t cathodic peak. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 113 V,1 ' /2(volt *V'2 R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 114 separation between the cathodic and anodic peak potentials of the first wave in creases as the scan ra te in creases a s expected if the electrode reaction w ere only q u asi-n ern stian . At a scan ra te of 10 mV s " 1 the peaks a re separated by 55 mV compared with the 30 mV separation expected fo r a tw o-electron nernstian reaction (or the 60 mV expected if the reduction involved only one electron). The second reduction pro c e ss is also diffusion controlled with an invariant peak splitting of 60 mV. E lectrolyte composition had no effect on the peak splitting of the second wave; however, adsorption of the reactant was evident in solutions free of chloride ion. The chloride was added to the supporting electrolyte employed to reco rd Figure 4 .2 both to adjust the ionic strength and to suppress th is adsorption. Controlled potential reduction of Mo30 4 (C20 4 )3 in 0.5 M oxalic acid consumes two faradays p er mole of complex when the electrode is held at a potential slightly negative of the first wave (-600 mV). At m ore negative potentials ( e .g . , -900 mV) th ree faradays per mole of complex a re consumed. The fully reduced species is stable in the absence of a ir for at least a week. Its spectrum is shown in Figure 4 .3 (curve A) along with that of the original complex (curve C). A spectrum of the tw o-electron reduction product is also shown in Figure 4 .3 (curve B) but the solution a lso contains a sm all amount (~5%) of the fully reduced complex whose form ation is difficult to avoid at the potential where the tw o-electron product is generated at a convenient ra te . The fully reduced ion exhibited the EPR spectrum shown in Figure 4.4A in a frozen solution at 77"K. Solutions of the tw o-electron reduction product showed essentially no EPR response under the same conditions. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 115 Figure 4 .3 . Spectra of: A ) Mo3 (OH)4 (C20 4)3” ; B) Mo3 (OH)4 (C2 0 4)3; C) Mo3 0 4 (C2 0 4)3" in 0.5 M H2 C20 4. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . WAVELENGTH (nm) R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 117 Figure 4 .4 . ESR sp ectra of: A) Mo3 (OH)4 (C20 4 )3 ; B) Aquo M o^m ) ion. Microwave frequencies and modulation am plitudes w ere A) 9.225 GHz, 1G; B) 9.168 GHz, 2G. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 118 — ,— 3IOo" 3200 3300 34 0 0 3500 3600 3700 H (Gauss) R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 119 P ulse Polarography. N orm al and re v e rse pulse polarograms*® for solutions of Mo^0 4 (C20 4 )3 ~ also contain two reduction steps (Figure 4.5). The separation between the two steps is la rg e r in the re v e rse pulse polarogram s (Figure 4.5B) because of the differing electron tra n s fe r kinetics exhibited by the two reduction steps: the half-wave potential of the tw o-electron, q u asi-n ern stian step is shifted to a m ore positive value in the re v e rs e pulse polarogram while that of the one-electron n ernstian step rem ain s fixed. The two w ell-developed lim iting c u rren ts in the re v e rse polarogram have the expected ra tio of 2 to 1. The shapes of the norm al and re v e rse pulse polarographic waves w ere ij-i 17 1 r analyzed by plotting log (-■- -- ) a s a function of the electrode potential: > The re su lts a re shown in curves C and D of Figure 4 .5 . The slope of the logarithm ic plot corresponding to the foot of the fir s t reduction wave is close to 30 mV p er decade, a s expected for a tw o-electron reaction. The slope in creases as the wave is ascended and the quasinernstian ch arac te r of the wave is expressed. The corresponding plot for the fir s t oxidation wave in the re v e rse pulse polarogram has a slope near 60 mV over most of the wave a s expected for a nernstian oneelectron reaction. The two reduction steps evident in Figure 4.5A a re m ore clearly separated when th e ir derivatives a re recorded as in differential pulse 19 polarography. Figure 4 . 6 shows a set of differential pulse polaro­ g ram s for a s e rie s of Mo30 4 (C20 4 )3 " solutions with varying pH. The peak corresponding to the firs t tw o-electron reduction shifts to more negative values as the pH in c re a se s until it m erges with the second, one-electron peak whose position is insensitive to pH before the m erg er. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 120 Figure 4 .5 . Normal (A) and re v e rse (B) polarogram s of 0 .8 mM Mo30 4 (C20 4 )3 . Supporting electrolyte as in Figure 4 .2 . id - i C and D a re the corresponding plots of log ( ---------) i vs. E (see text). R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 121 400 ' 500 ± 600 JL X 700 L 400 JL 500 -L 600 - E vs. SCE(mV) 700 * ' ^ -I.2 l R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 122 Figure 4 .6 . D ifferential pulse polarogram s of Mo304(C204)g as a function of pH. All solutions contained 0.1 F to tal oxalate and the ionic strength was maintained at 0.5 M with KC1. The pH values w ere: (A) 1.25; (B) 1.57; (C) 1.95; (D) 2.49; (E) 3.05; (F) 3.85; (G) 4.69. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 123 0.1/xa 300 I 500 700 900 - E vs. SCE (mV) R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 124 The single peak rem aining a fte r the reduction steps have coalesced continues to shift to m o re negative potentials with fu rth er increases in pH. (The sm all wave appearing at the foot of the main waves in F igure 4 .6 aro se from slight a ir oxidation of the Mo3 0 4 (C2 0 4) 3 stock solution. The wave is not p resen t in freshly p rep ared solutions). The peak potentials of the firs t (or m erged) wave in Figure 4 .6 a re plotted v s. pH in Figure 4 .7 . At pH values of 2 and below the firs t wave shifts by 120 mV p er pH unit while the peak potential of the coalesced wave shifts by 52 mV p e r pH unit. These electrochem ical re su lts can be accommodated by the s e rie s of electrode reactio n s depicted in Scheme I: SCHEME I pH < 2 F irs t step: 2_ +2e, +4H+ Mo3 0 4 (C20 4) 3 ^ - 2 e~ -4H Mo3 (OH)4 (C20 4) 3 q u asi-n ern stian Second step: Mo3 (OH)4 (C20 4) 3 ^ +- ---- > Mo3 (OH)4 (C2 0 4)3" -e nernstian pH > 2 2_ +3e, +3H+ Two steps m erged: Mo^04 (C 2 0 4 ) 3 <v -3e , -3H 2Mo3 0 (OH)3 (C20 4 ) 3 Scheme I im plies that one of the oxo-groups in the Mo30 ^ core is less basic than the other th re e and re s is ts protonation in the fully reduced R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 125 Figure 4.7. D ifferential pulse polarographic peak potentials v s . pH for the reduction of Mo30 4 (C20 4 )3 . Conditions as in Figure 4 .6 . R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 126 800 (mV) 700 a 600 LlI I 500 400 3.0 O.K 2.0 4.0 5.0 pH R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 127 ion at pH values above 2. The form al potential of the resulting th ree electron, th ree-proton reduction step would be expected to shift by 59 mV p er pH unit which is reasonably close to the slope of the line in F igure 4 .7 at pH values above 2. The Aquo Mo,(IV) Cation. The number of w ater m olecules coordinated to the Mo3o J+ core in aquo Mo(IV) has net been determ ined. On the b asis of the known stru c tu re s of the oxalato and edta complexes 12 20 ’ nine coordinated w ater m olecules seem likely but we will abbreviate 4+ 4+ the aquo ion as Mo3 0 4 , Cyclic voltam m ogram s of Mo^04 in a supporting electrolyte composed of 1 .0 M trifluorom ethanesulfonic acid (HTFMS) and 1 .0 M HC1 consist of a single reduction and oxidation wave (Figure 4 .8 ). The cathodic peak cu rren t in creases linearly with (scan ra te ) 2 (inset in Figure 4.8) and the separation between the peak potentials does not depend on the scan ra te . In the absence of chloride less ideal behavior is observed witn unequal anodic and cathodic peak 7 In the presence of chloride, but without explicit electronic c u rre n ts . compensation to overcome uncompensated resistan ce in the cell, a separation of 33 mV between the peak potentials was previously in te rpreted as a sign of a nernstian tw o-electron reduction. 7 However, a th re e -e le c tro n nernstian reduction in the presence of some uncompen­ sated cell resistan ce could also have produced a peak splitting in excess of the theoretical value of 20 mV. One purpose of the present e x p eri­ ments was to check th is point. Controlled potential electro ly sis of solutions of Mo3 0 4+ at a m ercury pool a t -500 mV consum es one electron p e r Mo atom . 7 The R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 128 Figure 4 .8 . Cyclic voltam m ogram s of 0.31 mM Mo3 0 4 . Supporting electrolyte: 1 M HTFMS + 1 M HC1. Initial potential: -100 mV. Scan ra te s: 10, 20, 50 and 100 mV s ”1. i Inset: Cathodic peak c u rre n ts v s. (scan ra te )2. Negative potentials a re plotted to the left and reduction cu rren ts a re plotted upward. Inset: Cathodic peak cu rren t vs. (scan ra te )2. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 130 resulting complex is readily re-oxidized to Mo3 0 4 at the electrode or by careful exposure to dioxygen. 1 0 > 1 1 Prolonged exposure of Mo3 0 4+ to dioxygen re su lts in its eventual oxidation to Mo(VT). Polarography N orm al and re v e rs e (as well a s differential) pulse polarogram s 4*4" of solutions of Mo3 0 4 exhibit only one apparent reduction wave in t r i fluorom ethanesulfonic acid solutions at acid concentrations between 0.5 and 4 M. Figure 4 .9 contains rep resen tativ e norm al and re v e rse pulse polarogram s. L ogarithm ic analysis of these two polarogram s produced non-linear plots (Figure 4 .9 , curves C and D). The slopes of the logarithm ic plots did not depend upon the duration of the pulses (in the presence of chloride) showing that slow electron tra n s fe r was not an im portant fa c to r. 21 The slopes of the logarithm ic plots a re consistent with the p resen ce of two successive reduction steps just as was tru e with the Mo3 0 4 (C2 0 4 ) 3 complex. However, the two form al potentials fo r the reduction of the Mo3 0 4+ ap p ear to lie much c lo ser to each other. A th eo retical an aly sis of the shapes of polarographic waves for overlapping, m u lti-step , nern stian electrode p ro c e sse s has been p re sented by R uzic. 22 4+ T his treatm en t was applied to the case of Mo30 4 by assum ing that a tw o-step reduction involved was analogous to that observed with Mo3 0 4 (C20 4)3’ (Reaction 4.1): Ef Mo3 (IV) + 2e Mo3(m , III, IV) + e Mo^III, HI, IV) E* M03(111) (4.1a) (4. 1b) R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 131 Figure 4 .9 . N orm al (A) and re v e rs e (B) pulse polarogram s of 0.31 mM Mo3 o J+. Supporting electrolyte as in Figure 4 .8 . P a rts C and D a re the corresponding iH • v s. E (see text). plots of log R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 132 _L j. j. 400 300 - E vs. SCE(mV) 200 200 500 400 300 - E vs. SCE(mV) 600 -l.4L R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 133 It is convenient to define a comproportionation equilibrium constant relating the th ree species depicted in equation (4.1). 3Mo3( m , m , iv) 2Mo3(m ) + M o3(IV) K„ = [Mo3(m , m , iv)]3 (4.2) (4.3) [Mo3(m)]2[Mo3(IV)l Kc can also be expressed in te rm s of the form al potentials of the two redox steps: K (4.4) «*<>] = exp w here nAand n-j a re the number of electrons involved in the two su ccesid - i sive steps. The ra tio ( — — ) used in the logarithm ic analysis of the polarographic wave shapes for this case can be expressed a s in equation (4.5). ^ ( K cp V ‘+^ +1 (4.5) 1 Hi— ( j ) ni + "2 + 1 = e x p { - ^ [ ( n 1 - n 2 ) E - n 1 E f - n 2 E^]} (4.6) and E is the potential on the polarographic wave corresponding to each value of i in equation (4.5). Plots of log (- -) v e rsu s E w ere R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 134 calculated from equation (4.5) fo r sev e ra l values of (e | - e J) with nx = 2 and = 1 (reaction 4 .1 ). The re s u lts a re shown in Figure 4 .10 along with the experim ental points resu ltin g from the corresponding 4+ plot for a norm al pulse polarogram of the reduction of Mo3 0 4 . Equation (4.5) produces calculated curves with the sam e general morphology as the experim ental data fall close to the curve calculated for (E 2 - Ex) = -40 mV. It is noteworthy that the calculated curves in Figure 4.10 show that clearly non-linear logarithm ic plots a re to be f f f f expected for values of E£ - Ej a s positive a s +20 mV. If (E 2 - Ex) is even m ore positive, lin ear plots re su lt with slopes corresponding to the sum of nx and r^. Another useful (but not independent) method for estim ating (E2 - e[) is to observe the difference in potential between the points w here id " i log (-=:— ) equals 1 .0 and -1 .0 . An analogous procedure fo r the 1 23 analysis of cyclic voltam m ogram s was described by M eyer and Shain. These potential differences (calculated from equation (4.5) a re plotted in Figure 4.11 a s a function of (E 2 - e [). When th is curve was used to analyze the experim ental data shown in Figure 4.10 a value of (E 2 - E^) of -(35 ±2) mV resu lted . Cyclic V oltam m etry. The cyclic v oltam m etric response to be expected from a tw o-step nernstian electrode reaction that proceeds according to reaction (4.1) can be calculated by m eans of a digital sim ulation 24 procedure described recently by Sokol et a l . . Application of th is procedure to the p resen t case (1 M HTFMS + 1 M HC1) gave the best agreem ent between the experim ental and calculated voltam m ogram s with E 2 - e J set equal to -36 mV (and nx = 2 and = 1). A com parison R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 135 Figure 4.10. Plots of log[(id - i)/i] v s. E calculated from equation 5 for different values of E \ - E*. The experim ental points f f (i) w ere taken from Figure 4.9C . V alues of E 2 - E x w ere: (A) +90; (B) +20; (C) 0; (D) -20; (E) -40; (F) -90 mV. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 0.8 0.4 0.4 - 0.1 -u« 40 -40 ■80 ■120 E(mV) R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 137 F igure 4.1 1 . ij - i Separation in the potentials where log (— -— ) equals +1.0 and -1 .0 as a function of E* - e [. Evaluated from the curves in Figure 4.10. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 138 160 A E (m V ) 120 80 40 120 80 -40 -80 R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reprodu ction prohibited w ithout p erm ission . 139 is shown in Figure 4.12A. The agreement is excellent for the cathodic portion of the wave but deviations appear in the anodic portion. The 24 sam e behavior was a lso observed by Sokol et a l. who attributed them to difficulties in making adequate correctio n s for the background cu rren t during the second half of the cyclic voltam m ogram . The good agreem ent we observed for the cathodic portion of the wave adds fu rth er support to our supposition that equation 4.1 re p re sen ts a re a listic picture of the pathways involved in the electro -red u ctio n of M o3o J + . Estim ating the closely spaced form al potentials of the multiple e lectron redox reaction 4.1 from peak separations in the cyclic voltam ­ m ogram s is a ra th e r dubious procedure. Simulated cyclic voltammo­ gram s fo r various values of (E^-E*) (Figure 4.13) show no apparent co rrelatio n between cathodic to anodic peak separation and form al potential differences. In fact, the second electron tra n s fe r is not readily apparent until the form al potential separation reach es -60 mV. Acid Dependence of the Half-W ave P otential for MoflOll+ Reduction. The dependence of E_i fo r the composite norm al pulse polarographic 2 44- wave for the reduction of Mo3 0 4 in solutions containing increasing concentrations of protons is shown in Figure 4 .1 4 . The Hammet acidities of each solution, H0 , w ere evaluated from sp ec tra l m easurements with o-nitroaniline. OK The non-linearity of the plot is to be expected if the two step s identified in reaction 1 have different acid dependences. At the low er acid ities (H0 < 0.1) a lim iting slope of ca. 60 mV p e r H0 unit re s u lts while at higher a cid ities the slope increases to ca. 90 mV p e r H0 unit. T hese data show that protons a re consumed R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 140 F igure 4.12. Experim ental (solid line) and sim ulated (points) cyclic voltam m ogram s fo r MOgO**. Supporting electrolyte: (A) 1 M HTFMS + 1 M HC1, Scan rate: 200 mV s ’ 1. (B) 2 M HPTS, Scan ra te : 50 mV s " 1. Initial potential: -100 mV. R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 141 A B R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 142 Figure 4.13. Simulated cyclic voltam m ogram s (dim ensionless cu rren t units) plotted for different values of E* - E* (the cathodic to anodic peak separation is given in p arentheses): A) 0 (25) mV; B) -20 (26) mV; C) -40 (31) mV; D) -60 (31) mV; E) -80 (31) mV; F) -100 (31) mV. R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 143 +2.0i + 1.0 +0.5 0.0 -0 .5 +100 +50 -5 0 ■100 -150 -200 E (mV) R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 144 Figure 4.14. Polarographie half-wave potential v s. Hammett acidity function, H0, for reduction of MOgO^. Supporting electrolyte: 0.1 M HC1 + HTFMS + LiTFMS adjusted to m aintain an ionic strength of 2 .0 M. R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 145 410 390 > E CNJ LxJ 370 I 350 - 0.2 0.2 -0.4 Hr R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 146 in the reduction reaction throughout the range of acidities te sted . To dissect the acid dependence into its component p a rts Figure 4.11 was used to obtain values of Eg - Ef from the logarithm ic analysis of polarogram s recorded in solutions of varying acidity. Figure 4.15 displays the log plots obtained a t various a cid ities. (The lim its on the range of acidities tested w ere set on the high side by the d esire to maintain constant ionic strength and on the low side by changes in the stru ctu re 4+ of the Mo3 0 4 core at acid ities below ca. 0.1 M .) Q A plot of the resulting values of ( e J - e J ) v e rsu s H0 is shown in Figure 4 .16. The data fall on a straight line of slope 43 ± 5 mV p er H0 unit. A number of possible acid dependences of the two reduction steps in reaction 4.1 w ere considered to account for the slope of the line in Figure 4.16. The closest correspondence re su lts if the fir s t, tw o-electron step con­ sum es th re e protons and the second, one-electron step consum es one additional proton a s depicted in Scheme n . SCHEME II E: 44 4 . +2e, +3H+ 51 ^ — ,..-2: Mo3 0(OH ) 3 -2e, -3H F ir s t step: Mo30 Second step: 5+ +e, +H+ Mo3 0(OH ) 3 —— Mo 3 (OH) 4 -e , -H 5+ The slope of a plot of eJE-eJ v s . H0 would be predicted to be 30 mV p er H0 unit on the b asis of Scheme II. The observed slope (43 ± 5 mV) R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 147 Figure 4.15. Plots of log[(id - i)/i] v ersu s E for different acidities (the ionic strength was maintained at 2 . 0 by addition of LiTFMS): A) 2.00; B) 1.52; C) 1.12; D) 0.64. R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 148 149 Figure 4,1 6 . Values of E g-E* evaluated from F igure 4.11 plotted v s . H0 . R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 150 100 TT .20 ,20 .30 H, R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 151 does not seem unreasonable considering the possible sources of e rro r in the many m easurem ents that w ere req u ired for the preparation of Figure 4. lb . A bsorption S pectra. U v-visible absorption sp ectra of solutions con­ taining only Mo3 (IV) o r only Mo^HI) in 0.5 to 4 M HTFMS agreed with those rep o rted previously . 1 0 ’ 1 1 However, s im ila r solutions containing m ixtures of these two ions and, th erefo re, Mo3 (III, HI, IV) ion a s well, produced somewhat different sp ec tra . To see if th is difference was a property of the acidic electrolyte u tilized in the previous work (p-toluenesulfonic acid, HPTS), we also recorded sp ectra of 2:1 m ix­ tu re s of Mo3 (m ) and Mo3 (IV) in th is acid. The resulting sp ectra were identical to those rep o rted previously . 1 0 , 1 1 p-Toluenesulfonic Acid Media. The dependence of the absorption sp ectra on the nature of the acid led us to examine the electrochem ical behavior of Mo3 (IV) in H F rs. A cyclic voltam m ogram for Mo3 (IV) in 2M HPTS is shown a s the solid line in Figure 4 . 12B. The presence of two reduction steps is evident indicating that the separation between the form al potentials of the two steps is la rg e r in HPTS than in HTFMS supporting ele ctro ly te s. N orm al pulse polarogram s w ere recorded in 2M HPTS and th e ir shapes w ere analyzed by menas of the curve in Figure 4.11 to estim ate a 6 8 mV separation between the form al poten­ tia ls of the two reduction step s. In 4M HPTS the apparent difference in the two form al potentials in c re a se s to ca. 106 mV so that the two stages of the reduction a re even m ore clearly distinguishable. Thus, in HPTS the reduction of Mo<j(rV) appears m ore s im ila r to that of Mo3 0 4 (C2 0 4 ) 3 than it does in HTFMS supporting e lectro ly tes. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 152 E stim ation of F o rm al Potentials and Comproportionation Constant. The form al potentials of the half-reactions in Scheme n and the equi­ librium constant for reaction 4 .2 w ere estim ated at sev eral concen­ tra tio n s of HTFMS from an analysis of the shapes of norm al pulse polarogram s by means of the curve in Figure 4.11. The resulting values of E 3 - e [ w ere substituted in equation (4.4) to obtain the values f f of Kc listed in Table 4 .1 . The variation of (E £ -E x) and, therefo re, of Kc with acidity is much sm aller than that reported by Richens and Sykes in HPTS electro ly tes. ** A s a re su lt, and in co n trast with HPTS,** reaction 4 .2 cannot be forced to proceed completely to the right and the two reduction waves of Mo3 (IV) cannot be completely separated by in­ creasing the concentration of HTFMS. The values of E^ and E* in Table 4.1 a re sim ila r in magnitude to some of the "reduction potentials” reported by Richens and Sykes but they re fe r to distinctly different half-reactio n for reasons to be discussed. The aquo Mo,(III) cation. Cyclic voltam m ogram s for a solution of 4+ MOg(ni) produced by controlled potential reduction of Mo3 0 4 a re shown in Figure 4.17. Two anodic peaks a re clearly evident. This contrasts with the anodic response shown in Figure 4 .8 during the second half of 4+ cyclic voltam m ogram s recorded with solutions of Mo3 0 4 where only a single anodic peak ap p ears. The im plication is that a portion of the Mo3 (m) formed initially from the reduction of Mo3 (IV) undergoes some stru c tu ra l rearran g em en t on the tim e scale of controlled potential e le ctro ly sis (up to sev e ra l hours) to produce a form that is re-oxidized at a m ore positive potential than the un rearran g ed Mo3 (ni). The R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 153 Table 4 .1 . Evaluation of Form al Potentials and the Comproportionation Equilibrium Constant. [H+]a fb -Ef -* r -(E*-E*) M mV mV mV 4.10 305 351 46.0 36e 2.00 345.5 389 43.5 30 Kcd 1.52 353.5 395 41.5 25 1.12 364 398 34.0 14 0.64 382.5 409.5 27.0 8 a Except for [H+] = 4 ,1 M a ll solutions w ere p rep ared from triflu o ro methanesulfonic acid s, 0.1 M HC1 and sufficient lithium triflu o ro methanefulfonate to m aintain an ionic strength of 2.0 M. ^F orm al potential of step 1 in Scheme n . c F orm al potential of step 2 in Scheme n. ^Equilibrium constant for reactio n 4.2. e Solution contained only 4.1 M HTFMS. R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 154 Figure 4 . 1 7 . Cyclic voltam m ogram s of M O g ( i n ) produced by controlled potential reduction of Mo3 (IV). Supporting electrolyte: 2 M HTFMS. Initial potential: -500 m illi­ volts. Scan ra te s: 10, 20, 50, 100 and 200 mV s ”1. Negative potentials a re plotted to the left and reduction c u rre n ts a re plotted upward. R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 155 lOOmV R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 156 rearrangem ent would have to proceed too slowly to be detected by cyclic voltam m etry a t scan ra te s as low a s 10 mV s ” 1 (Figure 4 . 8 ) o r re v e rse pulse polarography with a drop tim e of 1 sec. (Figure 4 .9). To te s t th is supposition solutions of MOg(III) w ere p rep ared a s rapidly a s possible by pouring solutions of Mo3 (IV) through a column of zinc 2 -f m etal. (The Zn ion introduced into the solution was reduced at potentials outside the range of in terest and th e re fo re did not in terfere). The resulting solutions w ere examined periodically by the sensitive method of differential pulse polarography to detect if one o r two waves w ere presen t in the resp o n ses. The re s u lts, shown in F igure 4.18, dem onstrate that the second wave begins to appear a fter ca. 2 hours and reach es its final magnitude a fter ca. 30 hours under the ex p eri­ m ental conditions employed. This tim e dependence of the relativ e magnitudes of the two waves in solutions containing only Mo3 (III) shows clearly that the species initially form ed re a c ts to produce a m ore difficultly oxidized form of the same net oxidation state. Since cyclic voltam m ogram s of the solutions showed only a single reduction wave under all conditions, the two form s of Mo3 (III) a re apparently oxidized to the single, stable form of Mo3 (IV). T his in terp retatio n does not correspond to that proposed by Richens and Sykes who a lso reported two oxidation waves for Mo3 (in) under some conditions. ** The reaso n s for this interpretation a re given in the D iscussion section. EPR Spectrum of M o,(m ). Solutions of Mo3 (m ) produced EPR sp ectra such a s that shown in Figure 4.4B . The sim ilarity between the R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 157 Figure 4.1 8 . D ifferential pulse polarogram s of a solution of M 0 3 (111 ) at various tim es afte r its preparation by rapid reduction with zinc m etal. The age of the solution was (A) 20 minutes; (B) 8 hours; (C) 12 hours; (D) 22 hours; (E) 36 hours. Initial potential: -550 mV. Between recordings the solution was s tirre d with argon over a m ercury pool m aintained at -550 mV. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 158 0.05/j.q J 50 mV R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 159 spectrum for the aquo and oxalato complexes suggests sim ilar s tru c ­ tu re s for the two ions. Both sp ectra w ere elim inated by e le ctro ­ chem ical re-oxidation of the reduced ions. When a solution of Mo3 0 4+ in 2M trifluorom ethanesulfonic acid was electrolytically reduced by one-third electro n p e r molybdenum atom an EPR spectrum identical to that in Figure 4.4B was obtained but its intensity was only about 10% of that resulting when the e le ctro ly sis was c a rrie d to completion. The failure of the sp ectru m ’s intensity to follow linearly the extent of reduction points to a rapid equilibrium among the various species present with appreciable equilibrium concentrations of a ll th ree of the species depicted in Scheme II. D iscussion C om parison of Moa0 4 (C9 0 4)^ and Mo,Oa+. electroreduction of Mo3 0 4 (C2 0 4 ) 3 The mechanism of the is reasonably tran sp aren t at acidities w here the two reduction steps a re well separated. The overall reduc­ tion proceeds a s indicated in Scheme I. The difference in the pH depen­ dences of the firs t and second step accounts for the merging of the two waves at pH values above 2. In solutions of p-toluenesulfonic acid (HPTS) the electrochem ical behavior of the aquo Mo3 (IV) cation, M o,04+, p a ra lle ls that of the oxalato complex. Adjustment of the form al potentials of the two red u c­ tion step s by control of the acid concentration allows large equilibrium concentrations of the partially reduced ion, M o ^m , HI, IV), to be generated. By co n trast, in trifluorom ethanesulfonic acid (HTFMS) solutions the sm aller separation of the form al potentials for the two R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 160 reduction steps of Mo3 0 4 and th e ir le s s e r pH dependence leads to much g re a te r disproportionation of the partially reduced ion under all experim entally accessib le conditions. This prevented us from using sp e c tra l data to evaluate the equilibrium com positions of solutions of Mo(III, III, IV) in HTFMS at any of the concentrations w here Richens and Sykes w ere able to do so in HPTS . 1 1 The acid ities of equally con­ centrated solutions of HPTS and HTFMS do not differ g reatly (as judged from the ra tio of protonated to unprotonated o-nitroaniline in the two solutions) so that the difference in the electrochem ical responses of Mo3 0 4+ in the two acids probably a ris e s from differences in specific ionic interactions between the molybdenum cations and the PTS" or TFMS" anions. Mo, (III) Aquo Ion. The p a ir of anodic peaks in the voltam m ogram for an aged solution of Mo3 (III) (Figure 4.17) and the single oxidation peak obtained during the oxidizing half of cyclic voltam m ogram s for solutions of Mo3 (IV) (Figure 4.8) clearly point to the occurrence of a chem ical reaction subsequent to the electro -red u ctio n of Mo^(IV). Sim ilar behavior w as rep o rted by Richens and Sykes** who attrib u ted the double peaks to the existence of two, slowly in ter-co n v ertin g fo rm s of M o^m , HI, IV) only one of which could be fu rth er reduced to Mo3 (m ). The im plication was that Mo3 (IV) was reduced only to the irred u cib le form of Mo3 (m , ni, IV) on the tim e scale of cyclic voltam m etry so that only a single reoxidation wave appeared. The longer tim e s involved in con­ tro lled potential electro ly ses w ere presum ed adequate fo r som e r e a r ­ rangem ent of the initially form ed Mo3 (III, III, IV) species followed by its further reduction to Mo^ni). The two waves observed in voltam m o- R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 161 gram s fo r the oxidation of Mo3 (III) w ere then presum ably ascrib ed (reference 1 1 is not explicit on th is point) to the form ation of the second form of Mq3 (in, HI, IV) followed by its fu rth er oxidation to Mos(IV) without a slow s tru c tu ra l rearran g em en t being required. This in terp retatio n su ffers from the fact that it p redicts a voltam m e tric peak cu rren t for the reduction of Mo3 (IV) that corresponds to two ra th e r than th re e e lectro n s. This is not observed. A fu rth er p re ­ dicted consequence would be a norm al pulse polarographic lim iting c u rre n t fo r the reduction of Mo3 (IV) that is tw o-thirds as larg e as that for the oxidation of an equilibrated solution of Mo3 (III). In fact, the lim iting c u rre n ts for th ese two solutions a re virtually identical. Thus, the two form s of M o(ni, HI, IV) proposed by Richens and ISykes1 1 a re not compatible with the observed electrochem ical resp o n ses. The most compelling evidence that the chem ical tran sfo rm atio n involved occurs at the level of Mo3 (m ) is contained in Figure 4.18: The second peak in the d ifferential pulse polarogram of solutions of Mo3 (IV) that have been rapidly reduced to McGill) develops as the fully reduced solution stands. Thus, it ap p ears that two electrochem ically distinguishable form s of Mo3 (III) a re generated in these solutions. The UV-Vis spectrum of fresh ly reduced solutions of Mo3 (m ) that exhibit just one anodic peak d iffers only slightly from that of an aged solution that exhibits two peaks (Figure 4.19) and both form s of Mo^III) a re readily oxidized to the sam e Mo^IV) sp ecies. In addition, very slight changes in the EPR signals a re observable a s the M 0 3 (1 11 ) solution ages. The stru c tu ra l differences between the two form s of Mo3 (III) (including the possibility that one form may contain m ore than th ree Mo atoms) R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 162 Figure 4.19. Spectra of Mo3 (m ): (A) immediately afte r preparation; (B) 48 hours la te r. R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 163 1000 BOO 600 E o 5 400 200 400 600 700 500 WAVELENGTH (nm) 800 R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 164 rem ain to be elucidated. However, the existence of two electrochem ically distinct form s of Mo3(III) means that th ere a re two form al poten­ tia ls connecting the M o^in) and Mo3 (m , HI, IV) oxidation states to be considered. The values given in Table 4.1 w ere obtained under con­ ditions where only freshly form ed Mo3(III) was p resent so that they re p re sen t the form al potential relating M o(m, III, IV) and that initial form of Mo3(ni). Both the magnitudes and the assignm ents of the form al potentials given in referen ce 11 re q u ire some rev isio n in the light of these re su lts. Conclusion The trin u cle a r Mo3(IV) ion is reduced in a tw o-electron step followed by a one-electron step at potentials that a re v ery close together. The reaso n s for th is reductive p attern a re presum ably related to stru c tu ra l changes that accompany the reductions. A re le vant m olecular orbital calculation of Cotton 2fi and m ore recen t calcu­ lations27 suggest that the addition of electrons to the Mo3C>4 + core re su lts in increased electro n density on the bridging and capping oxo groups. This is consistent with the coupled electron-proton reduction steps outlined in Schemes I and n in which the form ation of hydroxo groups is indicated in the reduced products. It is interesting to note that molybdenum in oxidation state (III) is now known to form at least th re e sim ple aquo ions: Monomeric 28 Mo(OH2)e+, dim eric9 Mcfe(OH)£+ and the trim e ric ion whose core com­ position is believed to be Mo3(OH)4 +. In addition, the re su lts presented here indicate that th ere a re two electrochem ically distinct form s of the R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 165 trim e ric ion. Only the trim e ric ion is electro-oxidizable to the t r i m eric molybdenum(IV) ion, MOgO**. Mo(OH2)g+ is electro-oxidized with difficulty7 and yields the molybdenum(V) d im er, MOgO**. 4+ M o2(OH)2 is electro-oxidized m ore readily to the sam e product. 7 Mo(OH2)g+ apparently undergoes slow spontaneous condensation2®possibly to Mo2(OH)2+ but the relativ e therm odynam ic stab ilities of the dim eric and trim e ric form s of aquo Mo(m) rem ain to be established. R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 166 R eferences 1. This chapter was adapted from a paper in p re s s: Paffett, M. T. and Anson, F . C ., Inorg. C hem .. 1983. 2. (a) Souchay, P .; Cadiot, M. and Duhameaux, M ., C. R. Acad. Sci. ^L966, 262. 1524; (b) Souchay, P . ; Cadiot, M. an d V io ssat, B ., Bull. Soc. Chim. F r . . 1970, 3, 892. 3 . Ojo, J . ; Sasaki, Y .; T aylor, R . and Sykes, A ., Inorg. C h em .. 1976, 15, 1006. 4 . Ardon, M .; Bino, A. and Yahav, G ., J . Am. Chem. Soc., 1976, 98, 2338. 5. 6. Ardon, M. and P ern ick , A .. J . Am. Chem. S o c.. 1973, 95, 6871. C ra m e r, S. P . ; Gray, H. B .;D o r i, Z. and Bino, A ., J . Am. Chem. Soc. 1979, 101, 2770. 7. Chalilpoyil, P . and Anson, F . , Inorg. Chem. 1978, _17, 2418. 8. M urmann, R. and Shelton, M ., J . Am. Chem. Soc., 1980, 102. 3984. 9. C ram er, S .; Eidem, P .; Paffett, M .; W inkler, J . ; Dori, Z. and Gray, H ., J . Am. Chem. Soc. . 1983, 105, 799. 10. Richens, D. and Sykes, A ., Inorg. Chim. Acta. 1981^, 54, L3-L4. 11. Richens, D. and Sykes, A ., Inorg. C hem . . 1982, 21, 418. 12. Bino, A .; Cotton, F . and Dori, Z .. J . Am. Chem. Soc. . 1^978, 100. 5252. 13. Richens, D. T . and Sykes, A. G ., Comments Inorg. C hem .. 1981, 1, 141. 14. Feldberg, S. i n ’’C om puters in C hem istry and Instrum entation” , Vol. 2 ’’E lectro ch em istry ", M attson, J . S .; M ark, H. B . , J r . R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reprodu ction prohibited w ithout p erm ission . 167 and MacDonald, H. C ., J r . , E d s ., M arcel Dekker, New York, 1972, Chap. 7. 15. Wendling, E . and R ohm er, R ., Bull. Soc. Chim. F r . . 1964, 360. 16. B ard, A. J . and Faulkner, L . , ’’E lectrochem ical Methods” , John Wiley and Sons, In c ., New York, N. Y ., 1980, p. 186. 17. Oldham, K. and P a rry , E . , Anal. C h em .. 1968, 40, 65. 18. Matsuda, H ., B ull. Chem. Soc. Japan. 1980, 53. 3439. 19. Reference 16, p. 190. 20. Bino, A .; Cotton, F . and D ori, Z ., J . Am. Chem. Soc.. 1979, 101. 21. 3842. Fonds, A ., Brinkm an, A. and Los, J . , J . E lectroanal. C h em ., 1967, 14> 43 • 22. Ruzic, I . , J . E lectronanal. C hem ., 1970, 25, 144. 23. M yers, R. and Shain, I., Anal. Chem. , 1969, 41_, 980. 24 . Sokol, W .; Evans,. D .; Niki, K .; Yagi, T . , J . E lectro an al. Chem .. 1980, 108, 107. 25. Paul, M. and Long, F . , Chem. R evs.. 195j7, 57, 1. 26. Cotton, F . , Inorg. Chem . . 1964, 3, 1217. 27. B ursten, B . ; Cotton, F .; H all, M. and N ajjar, R ., Inorg. C h em .. 1982, 21, 302. 28. Bowen, R. and Taube, H .. J . Am. Chem. Soc. 1971, 93,3287. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 168 Appendix 1 Com puter P ro g ram s The following program s a re listed in o rd er of th e ir appearance in this th e sis. With the exception of the sim ulated cyclic sta case voltam m ogram s of C hapter 2, the p ro g ram s a re self-explanatory and fully referenced in the opening comment statem ents. The cyclic s ta ir ­ case voltam m ogram s sim ulated in Chapter 2 w ere constructed from a sim ple addition of the cu rrent-voltage profiles of the two components computed separately from pro g ram SCVNRS. FTN. All program s a re w ritten in FORTRAN. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 169 C C PROGRRM SCVNPS I 5TRIRCRSE VOLTRMKETRV - REVERSIBLE CRSE C FROM PROGRRM BV J. H. CH R IS TI E C C J TURNER C B RUG 7B C C MRINLINE PROGRAM Z- COMMON / B L K l / COMMON / B L K 2 / *DTE<3> C C INPUT C FC3BDB).5<3BBB> MFS<1B>,NTDC1 B>.D EC 1B >.N ELE C< 10> .NP PS< 1B >, OF PRRRMETERS CRLL SC VNRK JR> C C CRLCULRTIOM OF CURRENT FUNCTION C RND SRVING OF DRTR C CRLL SCVNF:2CJR> END F I L E 7 CRLL E X IT END R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 170 SUBROUTINE S C V N R K J R ) COMMON / BL K1 /F <3 BB B> , 5< 2B 0B ) COMMON / B L K 2 / N F S C 1 0 ) , N T D < 1 0 > , D E < 1 0 > . E l ( I B ) . NELECC1B), NPPS<1B), * D T E (3 > C C PROGRAM SCVNR5 - SAVES DATA C SUBROUTINE SCVNR1 - PARAMETER INPUT C STAIRCASE VOLTAMMETRV - REVERSIBLE REACTION C FROM PROGRAM BV J. H. C HR IS TI E C DATED 2 - 1 8 - 7 5 C C J TURNER C 38 NOV 77 - MODIFIED 8 RUG 78 C WRITEC6, I B B ) CALL DATECDTE) URI TE( 6, 1B5> C D T E U ) , 1=1, 3 ) C C PARAMETER INPUT SECTION C CALL V AR IN I < J R , ' I N P U T NO. OF RUNS ' , 1 8 , 1 , 1 0 ) DO I B J I = 1 , J R NRITE <6, 1 1B ) J I 2 CALL V A R I N K N F S C J I ) , ' N O . OF FORWARD STEP5 ' , 2 2 , 0 , 4 0 0 ) CALL V A R I N K N R S , ' N O . OF REVERSE STEPS ' , 2 2 , 1, 4B 0) CALL V R R I N K N P P S C J I ) , ' NO. OF POINTS PER STEP ',2 4 ,1 ,5 0 ) N FS <JI)=N F5<JI)+1 NTD< J I ) = N F 5 < J I ) + N R 5 M = N P P 5 C J I)*N T 0 <J I> *1 * I F ( M. LE. 2BBB) GO TO 5 WRITE<6, 1 1 5 ) GO TO 2 5 CALL VA RI NC D EC J I), ' INPUT STEP HEIGHT - <MV) ', 2 6 ,0 .1 ,5 0 .) CALL V R R I N < E I < J I ) , ' INPUT I N I T I A L POTENTIAL <WV V5 E l / 2 ) ' , 3B, *<-1. BE2, 1 0 E 2 ) CALL V A R I N I ( N E L E C C J I ) , ' INPUT NO OF ELECTRONS ',2 3 ,1 ,1 0 ) 10 CONTINUE • RETURN 10B FORMAT < / , ' STAIRCASE VOLTAMMETRV - REVERSIBLE R E A C T I O N ' , / / ) 1 05 FORMAT ( ' * DATE OF CALCULATION ' , 3 R 4 ) 11B FORMAT < / , ' FOR PARAMETER SET NO. ' I 4 > 1 15 FORMAT < / / , ' TOO MANV POINTS ! • ' , / > END R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 171 » : ! 1 SUBROUTINE 5CVNR2<JR> COMMON / B L K l r T < 2 0 0 0 > , 5 < 2 00 0> COMMON /BL K2 7N FS <1 0> , NTDC10>, DE<10>, E I< 1 B > , NELEC<10>, NPPS<10>, *DTE<3> DIMENSION CURRC5B0) I C : : ! C PROGRAM SCVNRS - SAVES DRTA C SUBROUTINE SCVNR2 - CALCULATION ROUTINE C STAIRCASE VOLTAMMETRV - REVERSIBLE REACTION C FROM PROGRAM BV J. H. C H R IS TI E C DATED 2 - 1 B - 7 5 C C J TURNER C 20 NOV 77 - MODIFIED B AUG ?B C DEFINE F I L E 7 d 0 , 1 0 2 3 . U. NKT> NXT = 1 C C: D E F I N I T I O N OF CONSTANTS C NAME=2HNR 12 PI=3. 141593 DO 50 J I = 1 , JR W R IT E < 6, 1 20 > J I ANST = 2. B 9 2 2 2 E - 2 * N E L E C < J I > C0 = 2. /5RRT<F LO AT<N P P 5 C J I >) > L P 1 = N P PS < JI >- H M= NPPSCJn*NTD<: J I> * -1 C C SOLVES THE IHTERGRRL USING THE STEP FUNCTION METHOD C AS EXPLAINED BV NICHOLSON AND OLMSTEAD C IN ELECTROCHEMISTRY' MATTSON, MARK ft MACDONALD ED C CHAPTER 5 PG 127 C C: CALCULATION OF S ARRAV C TEMP=0. ~ • DO 15 1=1, M 5Q= 5QR T<FLDRT(I>> S < I > =5Q-TEMP TEMP=SQ 15 CONTINUE C C SOLUTION SECTION C ' Fd>=0. N=NTDCJI> DO 20 1=1, N t IM 1 = I-1 i R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 172 LR M B = - IM l I F< I . GT. NFSC J I > > LRMB=I « -l -2 * N FS < J I > PO«EI CJI >+ LRM B*D Ec. JI> E P 5 P l = i . + EKPC RN5T*PD> DO 20 K«=l» LP1 M= N F P S C J I > * I H H - K - 1 SM=0. 25 26 20 50 12 0 DO 25 J = l . M SM = 5M + F <J >* i5CH -J + 2> TEMP = (P I/ <. C G * E P S P 1 >> -S M F < M * l > =TEHP I F <K. EQ. LP1>CURRC I >*=TEMP CONTINUE CONTINUE NRITEC 7 ' NXT> N R M E , N F S C J I > . N T D C J I > . D E < J I > . E I C J I > , N E LE C C J I). NP PSC JI) ♦DTE#CURR CONTINUE RETURN FORMAT COMPUTING PRRRMETER SET NO. ' I 4 > END . R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 173 C PROGRAM TOME C C0MPUTE5 I 7 I D RND L O G ! I D - 1 7 1 1 PL 0T5 FOR C 5E0 UENTIRL ELECTRON TRRN5FERS C EE CR5E C 5EE I . R U Z I C , J. ELECTRORNRL. CHEM. . 25. 144 , < 1 9 7 0 ) . C PROGRAMMED BV MRRK PRFFETT 47B2 C DIMENSION ER P<6B1>.CURR<601>,TOMEC601> C C INPUT PRRRMETER5 C CRLL VRRINCA, ' INPUT NO. ELECTRONS 1ST STEP ' , 2 0 , 1 . , IB . > CRLL VRRINCB, ' INPUT NO. ELECTRONS 2ND STEP ' , 2 0 . 1 , IB . > 5 WRITECS,1B0> EP01=B. 0 CRLL VRRIN<EPD2, ' INPUT POTENTIRL CMV) 2ND STEP ' , 2 B , - 1 0 0 . 0 , IBB. t RNST = 2 . B 9 2 5 6 E - 2 L I M I T =6 01 RB=R+B CK=EXP<< R*B *<E PD 1-E PD 2>> *RN 5T > BRP = *-150. 5 WR ITEC6,1B5> DO 95 1=1, L I M I T BRP=BRP-0. 5 E R P C I > =BRP C C COMPUTE L O G ! I D - 1 7 1 1 PROFILE C TRI P = EXP<RB*:fiN5T*:<BRP-<c;R7RB>*:E P D l ) - < ( B 7 R B > * tE P0 2 >) > T R IK = l.B 7 T R IP TR E =C K* <T RI K* *R > SRE = TRE ** C1 . 7RB) T0P = (<B7RB>*i5RE>+-l. 0 bre = ck7< trik> * b > rre =bre * * c: i . 7 rb > BDT = <<:R7RB>*RRE)+1. 0 T0 PE =T RI P* CT 0P 7B 0T > C C COMPUTE 1 7 1 D PROFILE C T R U = < C K * < T R I P * * B > > * * ( 1 . 07RB) TRV=CCR7RB>*TRU>«-1. 0 BRV = TR IP + TRU*-1. 0 VR0=TRV7BRV CURRCI>=VRO TOMECI>=RLDG10(TDPE> 95 CONTINUE NRITECB, 110>CK NRITE< 6 . 112> MRI TEC 6, 115> C (. ERPC I >, CURR<I>, T D M E C I) ) , 1 * 1 , L I M I T ) 100 FORMRTC1X,' 1 S T POTENTIRL SET TO 0 . 0 MV ' , 7 7 ) 105 FORMRT<I X , ' E APPLIED 5TRRT5 <-150 MV FROM EPOl ' , 7 7 ) 110 FORMRT<1K« ' CK « ' , E12. 6, 7 7 ) 112 FORMRT(5X» ' E RPPLIED ' , 15X, ' I 7 I D ' , 15X, ' LOG! I D - I 71 3 ' , 7 7 ) 115 FORMRT( 2X» E16. B, 6X, E16. B, 6X, E16. B> END R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 174 PRDGRRM CVRR CVCLIC VDLTRMMETRV - MULTI STEP ELECTRODE RERCTION PROGRRM 5UPPLIED BV D. H. EVRNS SEE J. ELECTRDRNRL. CHEM. , IBB, 1 B P - 1 1 5 <1BBB> MRRK PRFFETT 4^B2 DIMENSION UB<5BB>, U K 5 B B > , U2«!5BB>. U3<5BB> DIMENSION CHI SVC 5BB>» PDTSVC5BB> INPUT OF PRRRMETERS CRLL VRRI NC TEMP, ' TEMP <C. > = ' , 14, B. B, IBB. B> RTF = 25. e 9 * C 2 7 3 . 15«-TEMP>/29B. 15 CRLL VRRI NC El MV, ' I N I T POT NRT EOl = ' . 2 t . - l E 3 . i E 3 > CRLL VRRI NC SMMV. ' SWITCH POT WRT TO ED1CMV> «= ' . 29. - 1 . E3, CRLL VRRINCEBD, ' E02 WRTE01CMV> = ' , 26, - 1 . E3. t . E 3 > CRLL VRRI NC ECO, ' E02 WRTE01(MV> * ' . 2B, - 1 . E3, 1. E3> CRLL VRRI NC SCRNP. ' SC-RWP= F V /R T •= R = ' . 2 2 , - 1 . E l , 1. E l > PNR=EIMV/RTF PNB=CEIMV-EBO>/RTF PNC=CEIMV-ECO>/RTF PMDVE = B. B THRIK=EXPC-PNR> THB IN =EKP<-PHB) THCIN=EXPC-PNC> MTREV=C SWMV-EI HV> /(. RTF*SCRNP> MRXTT =2*MTREV TTMRX=MRKTT D= B. 45 NVEMK*6. B*S0RT(D*TTMRK>*-2. B CHI RT-B. B POTMV=B. B SCRMF=S0RTCfiBSC5CRNP*D>> NPT 5= 280 NSRVE=MRKTT// NPTS«-1 MM=B CLERR RRRRVS iB DO 2BB 1 = 1 . NVEMK UBC I >*B. B U l < I > “ B. B U2C I > =0. 0 U3 ( I > = 1. B R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 175 C SOLUTION S E C T IO N - F I N I T E DIFFERENCE EOURTIDN5 C FELDBERG'5 METHOD C DO BOO NTU=1, MRXTT TT=MTU IF<NTLI-MTREV> 22B, 2LB, 22B 21B 5CRNP=-5CRNP 22B CONTINUE UUBl = UB(:i> UU11=U1C1> UU21=U2C1 ) UU3 i=U 3<1 > UUB2=UBC2> UU12=U1< 2> UU22=U2C2> UU22=U2C2> PMOVE=PMDVE+SCRNP S HIF T=EXPOPMDV,E> THETR = THR IN*-5HIFT THETB = THBIN»:SH IF T THETC = THCIN»:SHIF T GRMfl = l . B*-THETR*-THETR*:THETB^THETR»:THETB^THETC UU3B = <! UU31+-UU21+-ULH1+-UUB1> /GRMR UU2 B= UU3 B * T HE T fi UU1B = LIU2B»=THETB UUBB = UU1B*:THETC DD = 2. B*D ZB=DD*<UUBL-UUBB> Z l = D D * = a i U l l -U U lB > Z2 = DD*<:UU21-UU2B> Z2=DD*< UU31-UU3B> NVE*6. B*SRRT<D*:TT>+1. B UBC1>=UUB1«-DKUUB2-UUB1>-ZB U ld > = U U L H -D *a iU 1 2 -U U ll> -Z l U2d>=UU2H-D*<UU22-UU2L>-Z2 U 3d>= UU2H-D»<UU22-U U21>-Z3 DO 4BB 1=2, NVE UUB2 = UB< I *-l> UU13 = U l d d > UU23 = U 2 d « - l > U U 33=U 3d *1> R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 176 4BB 6 00 BOO B50 90O 1OO0 1O05 1 01 0 UB<I>=UUB2«-D*CUUB3-2. B*UUB2+UU01> Ul< I> = U U 1 2 + -D *< U U 1 3 -2 . B*UU12+UU11> U 2 (I > = U U 2 2 * D fc ( U U 2 3 - 2 . B*UU224-UU21> U3< I >=UU3 2*D *< UU 33 -2 . 0*UU32+UU31> UUB1=UUB2 UU11=UU12 UU2L=UU22 UU31=UU32 UU02=UU03 UU12=UU13 UU22=UU23 UU32=UU33 UU32=UU33 ZFRR=Zl*-2. B*Z2*-3. B*Z 3 CHIRT = ZFRRr'5CRNF I F <M TU/ N5R VE* :N5RVE-NTU> BOB. 60 0 . BBB MM= MM+-1 CHI 5V(MM>=CHIRT PDTSVCMM^EIMVt-PMDVEfrRTF CONTINUE MRITEC6, B5B> FORMRT( I K , ' CVCLIC VOLTRMMETRV EEE CRSE ' , / / > WRITEC6, 1BBB> MM WRITEC6, 1BB5> DO ODD 1=1, MM WRITEC6, 1 B 1 0 ) P D T 5 V C I > , C H I 5 V < I > FORMRT< I X , I 4, r V ) FORMRT<14K, ' P O T E N T IR L ' , 1 5 K , ' C H I ' , /Y > FDRMRTCIBX, E1G. B, 5K, E16. B> END R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited without p erm ission . 177 AppendbC-2 M easuring Homogeneous C hem ical R eactions Following Electrode Reactions by Double P otential Step Chronocoulometry (DPSCC) In general, DPSCC experim ents a re perform ed as follows: F or the simple redox scheme (equation A2.1) Ox + ne 5 E0 ='.."--■■> Red (A2.1) the initial electrode potential is posed at a value (E0) w here no faradaic cu rren t flows and is stepped to a potential (EA) sufficient to produce Red at a diffusion controlled ra te . A fter tim e t the potential is stepped back to a potential (E2) n ecessary to regenerate Ox at a diffusion controlled ra te . The charge is monitored as a function of tim e during both potential step s and the ch arg e-tim e behavior is described by equations A 2.2 and A2.3 which w ere derived by C hristie'1 fo r the sim ple electrode, reaction (A2.1). Q p(t s t ) = 2nFAC0 QB(t > r) = 2nFAC0 + Aqw • [ / t - Vt - t ] + (A 2.2) + Aq12 . (A 2.3) The electrochem ical v ariab les have th e ir usual meaning and Aq^ and Aq12 a re the values of the charge consumed by the double layer capaci­ tance upon changing potentials from the resp ectiv e v alu es. It is m ore convenient to monitor the re v e rs e charge according to equation A 2.4. R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . i Equations A2.2 and A2.4 predict that plots of QF ( t r ) v ersu s t 2 and and Q g(t > r) v ersu s [v T - v T - Vt - r J should be linear. The in te r­ cepts, Aq01 and Aq12, should be equal to the double layer capacitance values determ ined in the absence of any electroactive m aterial. A key Q '( 2 t ) experim ental observable is the value of the ra tio , — £.------- which in the Q p fr' ’ % (2 r) _ |Q ^ ( 2 r ) |- U q lz Q ji (t ) I = 2 - V2 = 0.5858 (A2.5) - Aq^ absence of adsorption or homogeneous reactions should be 0.5858. In electrode reactio n s where following chem ical reactions occur, m athem atical solutions to the boundary value problem , w here they ex ist, become quite complex. F o r the simple EC electrode reaction (A2.6) Ox + ne <-—°-> Red - -> C . (A 2.6) C h ristie 1 has derive a complex analytical exp ressio n for the ra tio Q ^ 2 t) Q f (t) = 2nFACo J ~ K = 1 - / 2 + x f,(2 T,kT) (A 2.7) V w here the value of i|/(t, kt) for t = 2r is given by R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 179 ,^ ,F .(n + 4, n + 1, kr) / w \ n' ^ ( 2 r , k r ) = -exp(-2kT) { £ ----------. [-^ ~ n=l (2n - 1): I + D (kr)11-1"1 - U ---------- :-------— K ]} i=l (A2.8) (2 n -2 i-l)i: 2 + £ l . e rfV k 7 # exp(-kr). £ (n + 2 V k7 n=0 n + 1, k r) # (2n, 1)J: 2n! The function 1F1(a ,b ,z ) is K um m er's confluent hypergeom etric function.* F or m echanism s w here no analytical solution exists digital 2 sim ulation allows one to compute solutions for the mechanism at hand. 3 4 Several groups ’ have solved the EC mechanism using digital sim u­ lation and good agreem ent ex ists between the sim ulation resu lt and the Q r (2t ) — —------ . analytical expression (A2.8) for values of the ra tio Qf (t) Figure A2.1 displays the analytical and sim ulation re su lts in the form of a working curve. Values of k a re determ ined from Figure A 2 .1 by measuring the experim ental values of Q g (2 r)/Q F (T) at various switching tim es r . The charge ra tio s determ ined by digital sim ulation in referen ce 3 w ere converted to the present form at by the following function, where Rq is the norm alized QL(2 t ) —— Qf (t) =(1 - Rn) • 0.5858 (A2.9) ^ charge ra tio of referen ce 3 (its significance is poorly defined in reference 3). R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 180 Figure A 2.1. DPSCC working curve fo r the sim ple EC case of equation A 2 . 6 , (— ) analytical solution, (■) sim ulation re su lt of referen ce 3, (o! sim ulation re su lt of referen ce 4. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 181 0.6 0.5 0.4 0.3 0.2 0.0 *— - 2.0 - 1.0 0.0 log ( k r ) R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 182 A sim ila r working curve (Figure A2.2) is derived from the data in referen ce 3 for reaction A 2.10. E0 Ox + ne ^==5: Red k 2Red -5 = ^ Redj, (A2.10) The dim erization of monomeric Mo(V) was analyzed from DPSCC data and the working curve of Figure A 2 .2. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 183 F igure A 2 .2 . DPSCC working curve fo r the EC ra d ic a l-ra d ic al dim er ization mechanism of equation A 2 .10 (see text). R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 184 0.61 0.5 u. |o 0.4 0.3 0.2 0.0 * - 3 .0 - 2.0 - 1.0 0.0 2.0 log ( k dC r ) R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 185 R eferences 1. C hristie, J . H ., J . E lectroanal. Chem. . 1967, 13, 79. 2. B ritz, D ., ’’Digital Simulation in E lectro ch em istry ” , SpringerV erlag, B erlin, 1981. 3. Childs, W. V .; Maloy, J . T . ; K esthelyi, C. P . and B ard, A. J . , 4. Ridgway, T . H .; Van Duyne, R. P . and R eilly, C. N ., J . E lectrochem . S o c., 1971, 118, 872. J . Electroanal. C h em ., 1972, 34, 267. R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 186 Appendix 3 /v V k w v v v v N N orm al and R everse Pulse Polarographic C u rren t-P o ten tial Curves Pulse polarography u tiliz e s potential pulses applied to a working electrode (DME in th is work) and sampling the c u rre n t just p rio r to drop dislodgement. Between pulse applications the electrode potential is returned to the in itial potential (Ex). The applied potential pulse is linearly increased a s a function of tim e. In norm al pulse polarography the initial potential is poised such that no faradaic cu rren t flows. F o r re v e rse pulse polarography the in itial potential is set a t a value on the diffusion lim ited plateau of an electrode reaction and progressively pulsed to a potential w here no faradaic c u rre n t flows in the norm al pulse case. A key advantage of pulse polarography is the ability to reduce capacitive charging c u rre n ts, which decay exponentially, and _i selectively enhance farad aic cu rre n ts, which decay according to E 2. A general theory fo r pulse polarographic cu rren t potential curves has been elegantly derived by M atsuda.* The following discussion is a synopsis of the norm al and re v e rs e pulse polarographic c ase s. The current-po ten tial curve for norm al pulse polarography is described by equations A 3.1-A 3 .5 . The following equations w ere derived for an initial reduction p ro cess a s indicated by the su p ersc rip t c. 1 + exp(£2) * (x V ^ ) (A3.1) (A3.2) R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reprodu ction prohibited without p erm ission . 187 <&(e) = VtT - e • F0(e) = 'J tt • £ • exp(e2) erfc(e) (A3.3) kr k. X = -5 - + - r D2 D2 o R (A3.4) S 2 = ^ r (E2 - E s ) ( A3. 5) The variab le r m is the sampling tim e, E2 is the potential scanned to, q(tx + r m) is the surface a re a at the DMA evaluated between tim e t* and Tm anc* ^ e r variab les have th e ir usual meaning. Figure A3, la displays norm alized c u rren t potential curves fo r different values of ] . In the case of rev ersib le electro n tra n s fe r (k_ » 0.01 cm . se c ”1) the polarographic waves a re well defined and ip-i and traditional log treatm en ts ( e .g . , log[ —— ] v e rsu s E) give linear i plots. As the electro n tra n s fe r becom es le ss rev ersib le the p olaro­ graphic wave shape changes and the half-wave potential shifts to values negative of the standard potential. Under conditions where quasire v e rsib le and irre v e rsib le polarogram s a re obtained the appropriate log plot analysis is given by equations A 3.6 and A3.7 E = E * -------------• In {xf M S + » » { 1 t .??P(Ql)2 ] 2 } ana F i - x (l +exp(ft)) E* = E_ + ln [~ k 7 — ] s a r^ F V 3 s D (A3.6) (A3.7) The log plots in C hapter 3 u tilize a reduced form of equation A3.6 since under irre v e rs ib le conditions exp (ft) « 1. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 188 Figure A 3.1. C urrent-potential curves of a) norm al and b) re v e rse pulse polarography for values of log[ks m , 1) > 0 .5 (reversible), 2) 0.0, 3) -0 .5 , 4) -1 .0 , 5) -1 .5 , 6) -2 .0 , 7) -2 .5 , 8) -3 .0 . (Figure taken from reference 1.) R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 189 'n-pulse ' ''d'Cott 1.0 '-puls®^ ''d'Cott 3.0 - 1.0 0.2 - 0.1 - 0.2 E 2- E s (V) R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 190 The current-potential curve for re v e rs e pulse polarography is d escribed by equations A 3.8 and A 3.9. ‘kp = i +(exp(-m ' ‘ ‘« pl ‘ (A3. 8) *RP1 = nFl ( ‘)c o • (AS- 9) As seen in Figure A3, lb the re v e rs e pulse polarogram s for rev ersib le e lectron tra n s fe r have essentially the sam e shape a s the norm al pulse p olarogram s. As the electron tra n s fe r becom es le ss re v e rsib le the wave shape changes such that two different limiting cu rre n ts a re observed, iR p l and ip P 2 * Under irre v e rs ib le conditions the lim iting c u rre n t iR p l is given by the Ilkovic equation for instantaneous current o (equation A 3.9). Although not obvious,the half-wave potential for iR p j lies a few m illivolts negative of the half-wave potential fo r iN p. The ra tio of i ^ p l to i ^ p is given b y ,2 I i£ *RPl £ • i*NP (A3.10) w here t is the age of the m ercury drop. In addition, the ra tio of ^ R P l + *RP2^ *° *NP shou^ unity in the absence of homogeneous chem ical reactions o r adsorption p ro c e sse s. The potential of zero faradaic cu rren t is obtained in the re v e rs e pulse polarogram s on the lim iting cu rren t plateau i ^ p j . Experim entally, the polarogram s in R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reprodu ction prohibited without p erm ission . 191 C hapters 2-4 w ere displayed in the m anner of Figure 3.1b to em phasize the homogeneous ch em istry of the p articip an ts in the redox reactio n s. R e p r o d u ce d with p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 192 R eferences 1. M atsuda, H ., Bull. Chem. Soc. J p n .t H)80, 53, 3439. 2. Oldham, K. B. and P a rry , E . P . , Anal. C h em .. 1970, 42, 229. R e p r o d u ce d with p erm issio n of th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm ission .