THE REACTIONS OF CHROMIUM(II) AND THE ISOMERIC DIFLUOROC€€ROMIUM(rII) IONS BY YUAN-TSAN CHIA AND EDWARD L. KING Dept. of Chemistry, University of Wisconsin, Madison, Wisconsin Received 26th January, 1960 The transition state for the electron-transfer reaction of cis-difluorotetra-aquochromium (111) ion with chromium(1I) ion which involves two fluoride ions acting as bridging groups is not detected. Reaction by this pathway is very much slower than by the pathway involving a single fluoride ion acting as the bridging group. The values of AH* and AS* for the reactions of chromium(II) ion with cis-difluorotetra-aquochromium(II1) ion and with monofluoropenta-aquochromium(II1) ion are very similar. Bridged transition-states have been demonstrated to provide the predominant reaction pathway for many oxidation-reduction reactions involving metal ions.1 What of the possibility of a transition-state in which two anions act as a bridge between the reacting metal ions ? Although transition-states containing two anions are known for such reactions, e.g.the transition-states (Fe2C12+)* 2 and (Fe2F;+)+ 3 for the iron(I1)-iron(II1) exchange, it cannot be assumed, as has been suggested,4 that these reactions proceed by transition-states in which both anions act as bridging groups. The present study was designed to investigate this question for the reaction of chromium(1I) ion and cis difluorotetra-aquochromium(II1) ion ; because of the inertness of chromium(II1) species, this system is one which can be expected to provide unequivocal information.That a fluoride-bridged transition- state does provide the easiest pathway for the " electron-transfer " between chrom- ium(I1) and monofluoropenta-aquochromium(I1I) has been shown by the occurrence of chromium exchange between these two species unaccompanied by a q ~ a t i o n . ~ Chromium(I1) can be expected to catalyze the aquation of each isomer of difluoro- tetra-aquochromium(II1) ion by a path which involves a transition-state analogous to that for the exchange of chromium(I1) and monofluoropenta-aquochromium(II1) ion with a single fluoride ion acting as the bridging group, / \ + FCr(OH& '. \ / F(H20),CrF++Cr2+-+ Only the cis-isomer of difluorotetra-aquochromium(II1) ion can possibly form a transition-state with chromium(I1) ion in which two fluoride ions bridge between the two chromium atoms, and this transition-state for the exchange reaction can be studied only if it has a stability greater than or comparable to that of the monofluoro-bridged transition- state which accomplishes the net aquation of cis-difluorotetra-aquochromiurn(II1)- ion.109110 CHROMI UM(II) + DIELUOROCHROMIUM(III) REACTIONS EXP E RI MENTAL The isomeric difluorotetra-aquochromium(II1) ions, shown by analysis to have a ff uoridel chromium ratio of 2-02&0+09, have been prepared and separated from one another by an ion-exchange procedure 6 patterned after that which has proved successful for the preparation of the isomeric dithiocyanatotetra-aquochromium(II1) ions 7 and the isomeric dichlorotetra-aquochromium(II1) ions.8 As in these previously studied systems, the more easily eluted isomer is assumed to be the trans isomer, an assignment of configura- tion which is supported by the spectra of the two species." A solution of chromium(I1) perchlorate in perchloric acid was prepared electrolytically in the same manner employed previously.5 Chromium-51 was obtained from the Oak Ridge National Laboratory in the form of a very dilute solution of chromium(II1) chloride in hydrochloric acid.In the preparation of solutions containing tagged chromium(II), the radioactive chromium(II1) was either added to a perchloric acid solution containing a very large excess of chromium(II1) per- chlorate and heated prior to the electrolysis or added to the chromium(II), present in very large excess, and allowed to exchange ; 9 the chloride ion concentration of the resulting chromium(I1) solutions was less than 10-2 M.In the preparation of solutions contain- ing tagged difluorotetra-aquochromium(III) ion, the radioactive chromium(II1) was added to a large excess of chromium(II1) perchlorate prior to equilibration with fluoride ion; a comparison of the radioactivity and the difluorotetra-aquochromium(II1) ion content of the appropriate eluent portions demonstrated that the radioactivity of the eluent portions was due to chromium in the form of difluorotetra-aquochromium(II1) ion. The reaction mixture containing one of the isomeric difluorotetra-aquochromium(II1) ions and perchloric acid contained in a Pyrex glass vessel was rid of oxygen by bubbling carbon dioxide through the solution prior to the addition of chromium(I1).At various times, measured portions of reaction mixture were forced by the pressure of carbon dioxide into hydrogen peroxide solution which predominantly converts chromium(l1) into hexa- aquochromium(II1) ion.10 The difluorotetra-aquochromium(1LI) ion of charge + 1 was separated from the species of higher charge, monofluoropenta-aquochromium(II1) ion, hexa-aquochromium(II1) ion, and any polymeric chromium(II1) species by an ion exchange procedure. The separated difluorotetra-aquochromium(II1) ion was analyzed for radio- activity by use of a well-type gamma ray scintillation detector (Atomic Instrument Co., model 810) and for chromium content by a measurement of the absorbance at 372 mp, after conversion to chromate ion with alkaline hydrogen peroxide.11 In one run, the total chromium content of the difiuorotetra-aquochromium(II1) ion fractions was determined both by the chromate procedure and by a procedure using 1,5-diphenylcarbohydrazide ; 12 the results were in good agreement. In most experiments the chromium(II) Concentration of the reaction mixture was checked several times during the course of an experiment by using tri-iodide ion as the quenching agent; the excess tri-iodide ion was determined by titration with thiosulphate ion, The chromium0I) concentration decreased by no more than 2 % in the experiments in which it was followed.For experiments involving the cis isomer plots of In [CrFZ] against time were linear up to 65 %-SO % aquation and then started to level off; presumably this was due to the approach to equilibrium in the aquation reaction.The approach to bquilibrium was not studied carefully; since the reaction was carried out in glass vessels, the exact concentration of fluoride ion was not known. For the trans isomer, curvature in the plots of In [CrFtl against time occurred much earlier, and only experimental points during the first 20 %-25 % reaction were used in the evalu- ation of the rate constant. The cause of this behaviour of the trans isomer is not known. It cannot be due simply to the establishment of the aquation equilibrium; the trans isomer is the less stable isomer 6 and will, therefore, aquate more completely. The curvature is consistent with the aquation reaction being higher than first order in trans- difluorotetra-aquochromium(II1) ion, but too few experiments have been performed to confirm this possibility.(In none of the experiments at a particular temperature was the initial concentration of the trans isomer varied appreciably.) t The observed values of the second-order rate constant k2 = [Cr2+]-1 d In [CrF,+]/dt, are given in table 1. The aquation is shown by these data to be first order in the catalyst, chroniium(I1) ion. * A tabulation of the absorbance indices of the two isomeric difluorotetra-aquo- chromium(III) ions as well as monofluoropenta-aquochromium(II1) ion over the wavelength range 210 mp to 400 mp will be furnished upon request. Further experiments on the reaction of chromiuin(I1) ion and traat3-diflbiorotetra- aquochromium(ZT1) ion are in progress and will Ire reported at a later date.Y .CHIA AND E. L. KING 111 In certain experiments, chromium(i1) was tagged and the radioactivity of the separated difluorotetra-aquochromium(II1) ion was determined. The radioactivity of the samples taken at the shortest reaction times showed an apparent extent of exchange of -1 %; samples taken at a later time when 6 % to 15 % aquation had occurred showed no more exchange than those taken when 1 % to 2 % aquation had occurred. Whatever the cause of this small apparent amount of exchange, it is not due to the direct second-order exchange reaction. Considering the various experimental uncertainties, it can be stated that the second-order rate constant for the direct exchange reaction of cis-difluorotetra- aquochromium(II1) ion and chromium(I1) ion is definitely not greater than 1 % of the second-order rate constant for the chromium(I1)-catalyzed aquation of cis-difluorotetra- aquochromium(1II) ion.25" 34.6" TABLE 1.-vALUES OF THE RATE CONSTANTS FOR THE AQUATION REACTIONS cis- or ~ ~ ~ ~ s - ( H ~ O ) ~ C ~ F ~ + H ~ O + ~ ~ ( € - I ~ O ~ ) C ~ F ~ + + H F in 1 M perchloric acid k2 = [Cr2+]-1 d In [CrF$]/dt cis isomer trans isomer [Cr2+]~ 102 k 2 ( ~ 103 mole L-1 sec) [CrZ+]x 102 kz( x 103 mole 1.4 sec) temp. - 0" 2.83 1.18 1.68 020 4.1 3 1.1 1 3.29 017 calc.0 1.2 1.87 10.1 1.73 1.5 ca1c.a 10 0.95 17.4 1.53 8.9 1-85 22-5 1 *88 6 9 204 21.5 2.26 19.4 2.54 17.6 ca1c.a 19 45.5" ' 0.859 20 1-83 19 (a) calc. using the parameters given in table 2. A more accurate limit of the value of the rate constant for exchange should be derivable from experiments in which the aquation proceeds to a greater extent.In such experi- nients, of course, there will be interference from the reversibility of the aquation reaction, which provides a pathway for exchange. The reverse reaction HF+(H20),CrF2+%3++(H20)4CrF~ +H20 can be suppressed by thorium(IV) ion which forms a very stable fluoride complex13 but it was found that thorium(1V) ion also accelerates the aquation of difluorotetra-aquo- chromium(II1) ion, presumably by the direct reaction H, 0 + (M, O),CrF; + Th4+ +(H,0),CrF2 + +ThF3 +. Two experiments involving chromium(I1) and thorium(IV) ion at a concentration equal to that of the tagged difluorotetra-aquochromium(II1) ion did not reveal appreciable chromium exchange.The amount of exchange observed in experiments with trans-difluorotetra-aquo- chromium(II1) ion was also negligible. With this isomer, of course, direct exchange is not possible ; had direct exchange been observed, it would have indicated that the assign- ment of configuration to the isomers was incorrect. DISCUS SION Although the exchange of chromium atoms between chromium(I1) ion and cis-difluorotetra-aquochromium(UI) ion via the symmetrical difluoro-bridged112 c H R o M I u M (I I) + D I F L u o R o c H R o MI u M (I I I) RE A c TI o N s transition state seemed a reasonable possibility in view of the occurrence of such a four-atom-ring configuration in known compounds (e.g. the aluminium halides14~ 19, the reaction path was not detected in the present study.The transition state involving two bridging groups has also been shown to be unimportant relative to that with a single bridging group in the reactions of chromium(I1) ion with cis- diaquotetranaminecobalt(II1) ion or cis-diaquobisethylenediaminecobalt(II1) ion.16 In the absence of any direct experimental proof of the operation of transition states for metal ion oxidation-reduction reactions involving two bridging groups, and for most systems such proof seems inaccessible, it is reasonable to assume that the transition state involves, at most, one bridging group. TABLE 2.-vALUES OF THE PARAMETERS ASSOCIATED WIl'H THE RATE LAW rate = ~ [ k T / k ] exp (AS*/R) exp (- AH*/RT)[Cr2"][CrF~3-~)+l k2 at 34.6' a AS+ AH+ ( x mole 1.-1 sec) (X cal-1 mole deg.) (X kcal-1 mole) cr"* species (H20)sCrF2+ 4.9 x 10-2 -20 5 13.7 5 cis-(H20)&rF f 1.9 x 10-2 - 24 13 (a) kz = rate/[Crz+][CrFi3-')+] ; values presented are calculated using values of AS+ (b) calc.assuming K = 1.00. and AH+. A summary of the values of AH+ and AS+ for the reactions of chromium(I1) and various fluorcsaquochromium(II1) species via fluoridebridged transition-states is given in table 2. Before values such as these are compared with one another, a correction for the symmetry number factor should be made.17 The values are uncertain enough, however, that these small corrections will not be made. The similarity of the values of AH+ and AS* for the reactions of chromiun(I1) ion with cis-difluorotetra-aquochromium(II1) ion and monofluoropenta-aquochrom- ium(II1) ion is of interest for in each of these chromium(II1) species a water mole- cule is located trans to the fluoride ion which is bonded to chromium(I1) in the transition state.It is the trans group which is believed to exert the dominant influence upon the rate at which reactions of this type occur.18 We wish to thank the United States Atomic Energy Commission for financial support (Contract AT(l1-1)-64, Project No. 3) and Sister M. J. M. Woods., O.P., for help in performing the experiments. 1 Taube, Advances in Inorganic Chemistry and Radiochemistry led. Emeleus and Sharp) (Academic Press, New York), vol. 1, 1959, chap. I. 2 Silverman and Dodson, J. Physic. Chem., 1952,56, 846. 3 Hudis and Wahl, J. Amer. Chem. SOC., 1953, 75, 4153. 4 Zwolinski, Marcus and Eyring, Chem. Rev., 1955,55, 157. 5 Ball and King, J. Amer. Chem. SOC., 1958, 80, 1091. 6 Chia and King, to be published. 7 Hougen, Schug and King, J. Amer. Chem. SOC., 1957,79,519. 8 King, Woods and Gates, J. Amer. Chem. SOC., 1958, 80, 5015. 9 Anderson and Bonner, J. Amer. Chem. SOC., 1954,76, 3826. 10 Ardon and Plane, J. Amer. Chem. SOC., 1959, 81, 3197. 11 Haupt, J. Res. Nut. Bur. Stand., 1952, 48, 414. 12 Allen, Anal. Chem., 1958, 30,447. 13 Dodgen and Rollefson, J. Amer. Chem. SOC., 1949,71,2600. 14 Palmer and Elliot, J. Amer. Chem. SOC., 1938, 60, 1852. 15 Harris, Wood and Ritter, J. Amer. Chem. SOC., 1951, 73, 3151. 16 Kruse and Taube, J. Amer. Chem. Sac., 1960,82,526. 17 Benson, J. Amer. Chem. SOC., 1958,80,5151. Orgel, Report Tenth Solvay Conference (Brussels, 1956), p. 289.