Enthalpies of formation of Cr3+ (aq) and the inner sphere complexes CrF2+Qaq), CrC12+(aq), CrBr2+(aq), and CrSO,+ (aq)

Transcription

1 Enthalpies of formation of Cr3+ (aq) and the inner sphere complexes CrF2+Qaq), CrC12+(aq), CrBr2+(aq), and CrSO,+ (aq) INGEMAR DELLIEN~ AND LOREN G. HEPLER Departmetlt ofcl~etnist,:l., Ut~iuersity of Letl~bridge, Letlrbridge, Alberta TIK 3M4 Received October 20, 1975 INGEMAR DELLIEN and LOREN G. HEPLER. Can. J. Chem. 54, 1383 (1976). We have carried out calorimetric measurements leading to AHfO = -60 kcal mol-1 for Cr3+(aq). Further calorimetric measurements have led to enthalpies of reaction of Cr3+(aq) with HF(aq), C1-(aq), Br-(aq), and SO4'-(aq) to form the 'inner sphere' complexes CrF2+(aq), CrCI2+(aq), CrBr2+(aq), and CrS04+(aq). Results of our measurements lead to AH,O = ( ) kcal mol-1 for Cr3+(aq), AH,O = kcal mol-1 for CrF2+(aq), AHfO = kcal mol-i for CrC12+(aq), AH? = kcal mol-1 for CrBr2+(aq), and AH? = kcal mol-1 for CrS04+(aq). ~NGEMAR DELLIEN et LOREN G. HEPLER. Can. J. Chem. 54, 1383 (1976). On a effectuc des mesures calorimitriques permettant de diterminer que le AH? du Cr3+(aq) est -60 kcal mol-1. D'autres mesures calorimctriques ont permis d'cvaluer les enthalpies des rhctions du Cr3+(aq) avec HF(aq), C1-(aq), Br-(aq) et S042-(aq) conduisant B des complexes de "sphkre interne" CrFZ+(aq), CrC12+(aq), CrBr'+(aq) et CrS04+(aq). Les rcsultats de nos mesures conduisent aux valeurs de AH? = (-60.0 f 1.5) kcal mol-1 pour Cr3+(aq), AHfO = kcal mol-i pour CrFZ+(aq), AHfO = kcal mol-1 pour CrC12+(aq), AHfO = kcal mol-i pour CrBrTaq) et AHfO = kcal mol-1 pour CrS04+(aq). [Traduit par le journal] Introduction The National Bureau of Standards Technical Note (1) lists AH; = kcal mol-i for Cr(H~o)~~+(aq), which corresponds to AH; = ( ) = kcal mol-i for Cr3+(aq) in which no water of hydration is explicitly included. Dellien et al. (2) have recently reviewed seven different paths to this enthalpy of formation and have calculated AH; values ranging from - 51 to - 62 kcal mol-i for Cr3+(aq). We (2) selected AH; = -57 kcal mol-' for Cr3+(aq) and the corresponding AH; = ( ) = -467 kcal mol-i for Cr(H20)63+(aq) as 'best' values. Neither the selection of ref. 2 nor that in ref. 1 can be defended as accurate or reliable. We have therefore undertaken calorimetric measurements to resolve the substantial (17 kcal mol-l) discrepancy between 'reasonable' interpretations of previously published results. There are also significant gaps and uncertainties in the presently available thermochemical data for some important halide and sulfate complexes of Cr(II1) in aqueous solution. We have therefore made calorimetric measurements on some of these species. ]On leave from Chemical Center, Physical Chemistry I, University of Lund, Lund, Sweden, It is likely that the substantial discrepancies between the results of earlier investigators are mostly due to chemical difficulties rather than calorimetric errors. We have therefore taken considerable care to identify the chromium species involved in the various calorimetric reactions we have investigated. Experimental All calorimetric measurements were made with the LKB 8700 Precision Calorimetry System. The standard 100 ml LKB glass reaction vessel was used with 1 ml glass ampoules for some of the measurements; other measurements were made with a stainless steel bomb calorimeter (from which we could exclude oxygen) identical to that described by Olofsson, Sunner, Efimov, and Laynez (3). All of our calorimetric results refer to OC and are reported in terms of the defined thermochemical calorie (1 cal = J). Solutions of chromous perchlorate were prepared by electrolytic reduction of solutions of chromic perchlorate, as described by Pecsok and Schaefer (4+ Concentrations of Cr2+(aq) in final solutions ranged from to M, as determined by reaction with excess 1: followed by titration with thiosulfate solution. Our preparations of ferric perchlorate solutions began with FeC13.6H,0 (BDH Analar), which was dissolved in aqueous perchloric acid. The 'ferric hydroxide' that was precipitated on addition of NH,(aq) was filtered off, washed, redissolved in perchloric acid, reprecipitated with NH3(aq), etc., until the resulting ferric perchlorate solution showed no test for chloride with silver nitrate.

2 1384 CAN. I. CHEM. VOL Solutions were standardized with KMnO, solution after reduction of Fe3+(aq) to Fe2+(aq) with zinc. A solution of cupric perchlorate was prepared by dissolving CuO (BDH) in perchloric acid. After the solution was filtered, it was standardized by reaction with iodide and thiosulfate. Stock Ce(IV) perchlorate solution was prepared by dissolving (NH4)2Ce(N03), in warm HClO,. After the solution was cooled and the precipitated ammonium perchlorate removed by filtration, Ce(IV) concentration was determined against K4Fe(CN),.3H20 with ferroin indicator. Solutions of CrF2+(aq) were prepared according to the procedure of Swaddle and King (5), except that we used somewhat lower concentrations than they did. Spectra of our solutions agreed well with those reported by Swaddle and King (5). Solutions were stored in a refrigerator, with all calorimetric runs and analyses being completed within 36 h of the original preparation. Solutions of CrC12+(aq) were prepared and handled in similar fashion, as also described by Swaddle and King (5). Solutions of CrBr2+(aq) were prepared as described by Guthrie and King (6), except that we began with electrolytically prepared solutions of Cr2+(aq) as described above so that we had no Zn2+(aq) in our solutions. Extinction coefficients of our solutions were about 4% larger than values previously reported by Taube and Myers (7). Solutions were stored in the refrigerator, with samples taken out for analyses and calorimetric measurements within a few hours of completion of the preparation. Solutions of Cr(SO,)+(aq) were prepared by reducing cold solutions of K2Cr207 and H2S04 with H202, followed by ion exchange separation with Biorad AG 50W X 8 resin. The spectra of the resulting solutions were similar to that reported by Fogel, Tai, and Yarborough (8), but our extinction coefficients (X = 590 nm, e = 19.0 M-1 cm-1; X = 420 nm, E = 18.9 M-1 cm-1) were larger than theirs. In this connection we note that our extinction coefficients for Cr3+(aq) agree with those of several earlier investigators. Solutions containing the various inner sphere complexes of Cr(II1) were analyzed for chromium spectrophotometrically after oxidation with H202 in alkaline solution,, as described by Haupt (9). A Cary 14 spectrophotometer was used for these and other spectrophotometric measurements. The same instrument was used for observation of various calorimetric solutions to insure that appropriate reactants and products were identical as required for combination of various reaction AH values. Reduction of Cr03 with H202 in HC10, solution led to solutions of chromic perchlorate from which we obtained hydrated crystals of chromic perchlorate after several weeks' storage with concentrated H2S04 in a desiccator. Solutions of Cr3+(aq) prepared by dissolving these crystals in water and perchloric acid were free of dimers as judged by the spectrum around the 267 nm peak and also Iower wavelengths. Results and Calculations We have measured the enthalpy of reaction of Cr2+(aq) with Fe3+(aq). Our choice of Fe3+(aq) as oxidizing agent was partly based on the suggestion of Ardon and Plane (10) that monomeric Cr3+(aq) is the principal product when Cr2+(aq) is oxidized in one electron transfer reactions. We carried out test tube reactions followed by spectrophotometric analysis of the product solutions to establish that more than 95% of the chromium product was present as the desired mononleric Cr3+(aq). Ardon and Plane (10) had previously used an ion exchange method (probably better than our spectrophotometric method) to show that more than 99% of the chromium was present as monomeric Cr3+(aq) in similar solutions. We therefore represent the calorimetric reaction by Our calorimetric measurements on reaction 1 were carried out with weighed amounts of standardized concentrated ferric perchlorate solution in the ampoule and a slight excess of dilute chromous solution in the bomb calorimetric vessel, with both solutions being 0.5 M in HC104. Seven measurements led to a total AH = kcal mol-i (average deviation = 0.6 kcal mol-l) for reaction 1 plus the enthalpy of dilution of the ferric perchlorate solution. Separate determination of this enthalpy of dilution (0.31 kcal mol-l) permits us to select AH0 = kcal mol-i for the reaction represented by [I]. Because of the electrical symmetry of this reaction, it is reasonable to assume that the effect of the 0.5 M HC104 on the enthalpy of reaction is small coinpared to the uncertainty indicated by the average deviation of our results cited above; we have therefore neglected further heats of dilution in arriving at our standard enthalpy of reaction represented by AH0. Stout and Chisholm (11) have reviewed earlier investigations and have calculated an apparently reliable AH: = kcal mol-i for CrClz(c). Gregory and Burton (12) have measured the enthalpy of solution of CrClz(c) in 1.0 M C1-(aq), with a result in fair agreement with an earlier (13) measurement. Combination of these results with our estimated enthalpies of dilution and the AH: of CrC12(c) cited above leads to AH: = kcal mol-i for Cr2+(aq). These AH: values for CrClz(c) and Cr2+(aq) are the same as listed in ref. 1. We therefore use these values for calculations with our AH0 for reaction 1.

3 DELLIEN AND HEPLER 1385 The difference in AH: values listed in ref. 1 for Fe2+(aq) and Fe3+(aq) amounts to 9.7 kcal mol-'. We use this value for subsequent calculations, although it should be noted that there is some evidence (14) that this difference is larger than 9.7 kcal mol-'. Use of the AH: values cited above with our AH0 for reaction 1 leads to AH: = kcal mol-l for Cr3+(aq). We suggest that the total uncertainty in this value is about -t 1.5 kcal l. Choosing a larger difference between AH? values for Fe2+(aq) and Fe3+(aq) would lead to AH: of Cr3+(aq) being less negative than the kcal mol-l above. We have also made calorimetric measurements on the enthalpy of reaction of excess Cr2+(aq) (in the bomb) with Cu2+(aq) (in the ampoule), all in 0.5 M HC104 solution. Duplicate test tube experiments followed by ion exchange separation of products established that the principal calorimetric reaction can be represented by with about 4% of the Cr(II1) present as hydrolytic dimers or polymers. Five determinations (adjusted for enthalpy of dilution of cupric perchlorate solution) lead to AH0 = kcal mol-l (average deviation = 1.8 kcal mol-l) for reaction 2. Reference 1 lists AH: = kcal mol-l for Cu2+(aq) and AH: = kcal mol-i for Cu-'-- (aq). Use of these values with the AH: for Cr2+(aq) cited above and our AH0 for reaction 2 leads to AH? = kcal inol-i for Cr3+(aq). We suggest that the uncertainty in this value is about + 2 kcal mol-l. Use of slightly different (15) AH: values for Cu+(aq) and Cu2+(aq) leads to an insignificantly different AH: of Cr3+(aq). Oxidation of Cr2+(aq) with Agf(aq) was tried but found to be unsuited for our purposes because a considerable fraction of the Cr(II1) formed was in the form of dimers or hydrolytic polymers rather than the desired Cr3+(aq). Similarly, reduction of Cr(V1) in acidic solution by H202(aq) leads to solutions containing substantial fractions of Cr(II1) in the form of dimeric or larger species. We also note that the species formed by reaction of me'tallic chromium with aqueous hydrochloric acid depend on purity of the metal, presence or absence of oxygen, and possibly other factors, all sufficiently complicated that we did not choose such reactions as promis- ing for detailed calorimetric investigation. We have also made calorimetric ineasurements of the enthalpy of oxidation of monomeric Cr3+(aq) with Ce(IV) in 0.5 M HC104 solution as represented by [3] Cr3+(aq) + 3Ce(IV) = Cr(V1) + 3Ce(III) Our ineasurements lead to AH = -2.2 kcal mol-l (average deviation = 0.7 kcal mol-l) for this reaction. We have also measured the enthalpy of oxidation of Fe2+(aq) with Ce(IV) in 0.5 M HC104 and found AH = kcal mol-l (average deviation = 0.06 kcalmol-') for the reaction that we represent by Finally, we have also carried out calorimetric measurements to find that AH = -2.1 kcal mol-l (average deviation = 0.4 kcal mol-l) for dissolving K2Cr04(c) in our Ce(IV) calorimetric solution and AH = kcal mol-i for adding water to our Ce(IV) solution, as represented by reactions 5 and 6: Combination of our enthalpies of reactions 3-6 leads (neglecting enthalpies of dilution) to ;lho = kcal mol-l (average deviation = 0.8 kcal mol-l) for the reaction that we represent by [7] Cr3+(aq) + 3Fe3+(aq) + 2K+(aq) + 4H20(liq) = K2Cr04(c) + 3Fe2+(aq) + 8H+(aq) We use this result with AH: = kcal mol-' for K2Cr04(c) from our recent review (2), AH: values for Fe2+(aq) and Fe3+(aq) froin ref. 1, and AH: values for Kf(aq) and HlO(1iq) from ref. 16 to obtain AH: = kcal mol-l for Cr3+(aq). Use of a larger difference between enthalpies of formation of Fe2+(aq) and Fe3+ (aq) leads to AH: of Cr3+(aq) more negative than kcalmol-l. We also point out that the AH; for K2Cr04(c) is related (2) to AH? values for (NH4)2Cr207(c), Cr03(c), and Cr203(c), for all of which there may be non-negligible uncertainties. It is therefore impractical to provide an estimate of the uncertainty to be associated with the above AHO = kcal mol-i for Cr3+(aq). On the basis of uncertainties in our calorimetric results and in various AH: values that we

4 1386 CAN. I. CHEM. VOL. 54, 1976 have used, we suggest that AH? = -60 kcal mol-i for Cr3+(aq) is the best value that is presently available (as compared to the range from -51 to kcal mol-i cited in the Introduction). We also suggest that the uncertainty in this value is about kcal mol-i. Because some enthalpies of complex formation are known with accuracy considerably better than kcal mol-i (as discussed later in this paper), we suggest that the value above be written as AH? = kcal mol-i. We there- fore also adopt AH? = kcal mol-' for Cr(H~0)6~+(aq) in which we have explicitly included water of hydration. Now we turn to our investigations of various aqueous complexes of Cr(II1). All of our work has been done with 'inner sphere' complexes, such as CrF(H20)52+(aq). We choose to describe all of our results concisely without specifically indicating the water of hydration; thus we represent the chromic fluoride complex by CrF2+(aq), and similarly for other complexes. We have measured the enthalpy of oxidation of CrF2+(aq) with Ce(IV) in 0.5 M HC104 to be kcal inol-i (average deviation = 0.1 kcal mol-i) and the enthalpy of oxidation of solutions of Cr3+(aq) and HF(aq) to yield an identical final solution to be kcal mol-i (average deviation = 0.3 kcal mol-i). Combination of these two results yields AH = kcal mol-i for the reaction The only earlier result we can compare with is AH = 1.3 kcalmol-i at 86OC reported by Swaddle and King (5) on the basis of their d In K/dT results for 1 M LiC104 solutions. We have ineasured the enthalpy of oxidation of CrC12+(aq) with Ce(IV) in 0.5 M HC104 to be kcal mol-i (average deviation = 0.2 kcal mol-i) and the enthalpy of oxidation of solutions of Cr3+(aq) and C1-(aq) with Ce(IV) to yield identical final solutions to be kcal mol-i (average deviation = 0.04 kcal mol-i). Combination of these values leads to AH = 6.29 kcal mol-i for the reaction Related earlier investigations have been carried out by King and co-workers (17); our earlier assessment (2) of their results led to AH = 5 kcal mol-i for reaction 9, but it is also reasonable to select a larger value in close agreement with our new result. We have measured the enthalpy of oxidation of CrBr2+(aq) with Ce(IV) in 0.5 M HC104 to be kcal mol-i (average deviation = 0.14 kcal mol-i) and the enthalpy of oxidation of solutions of Cr3+(aq) and Br-(aq) to yield identical final solutions to be kcal mol-i (average deviation = 0.07 kcal mol-i). Combination of these values leads to AH = 8.93 kcal mol-i for the reaction Our AH for oxidation of CrBr2+(aq) includes a correction for decomposition of the complex. The amount of such decomposition during the time between analysis and calorimetric reaction was estimated by way of the rate data of Guthrie and King (6); the magnitude of the correction was less than 0.6 kcal mol-i for all runs. Earlier d In K/dT results of Espenson and King (18) lead to an enthalpy of reaction 10 (taken to be 5 kcal mol-i in our review (2)) that is significantly smaller than the value we have obtained above. We have measured the enthalpy of oxidation of CrS04+(aq) (inner sphere complex) by Ce(IV) in 0.5 M HC104 solution to be kcal mol-i (average deviation = 0.10 kcal 1nol-l) and the enthalpy of oxidation of solutions of Cr3+(aq) and (S042-(aq) and HSOi-(aq)) to yield the same final solution to be kcal mol-' (average deviation = 0.03 kcal inol-i). Combination of these results leads to AH = 3.65 kcali~~ol-~ for the reaction we represent by in which a is the fraction of S(V1) that is in the HS04-(aq) form. For the reaction we have taken log K = and AH = -5.4 kcal mol-i (both for 0.5 M HC104 solution) on the basis of inany results summarized by SillCn and Martell (19). We combine all of these results to obtain AH = 7.6 kcal mol-i for [I31 Cr3+(aq) + SO4'-(aq) = CrS04+(aq) (inner sphere) Kinetic results from Fogel, Tai, and Yarborough (8) show that dissociation of Cr(S04)+-- (aq) complexes is negligible in our solutions

5 DELLIEN AND HEPLER 1387 TABLE 1. Enthalpies of formation 2. I. DELLIEN, F. M. HALL, and L. G. HEPLER. Chem. (298 K) Rev. In press. 3. G. OLOFSSON, S. SUNNER, M. EFIMOV, and J. LAYNEZ. A H,o J. Chem. Thermodyn. 5, 199 (1973). Ion (kcal mol-1) 4. R. L. PECSOK and W. P. SCHAEFER. J. Am. Chem. SOC. 83, 62 (1961). 5. T. W. SWADDLE and E. L. KING. Inorg. Chem. 4, 532 (1965). 6. F. A. GUTHRIE and E. L. KING. Inorg. Chem. 3, 916 (1964). 7. H. TAUBE and H. MYERS. J. Am. Chem. Soc. 76,2103 (1954). 8. N. FOGEL, J. M. J. TAI, and J. YARBOROUGH. J. Am. during the time between completion of the Chem. Soc. 84, 1145 (1962). preparation and completion of the calorimetric 9. G. W. HAUPT. J. Res. Natl. Bur. Stand. 48, 414 (1952). measurements. Their results (8) also show that 10. M. ARDON and R. A. PLANE. J. Am. Chem. Soc. 81, outer sphere association of Cr3+(aq) with 3197 (1959). S042-(aq) is negligible (less than 0.2%) in our 11. J. W. STOUT and R. C. CHISHOLM. J. Chem. Phys. 36, solutions. Fogel et al. (8) have previously re- 979 (1962). ported AH = 7.2 kcal mol" for this reaction: 12. N. W. GREGORY and T. R. BURTON. J. Am. Chem. SOC. 75, 6054 (1953). based on their equilibrium constants over the 13. F. R. BICHOWSKY and F. D. ROSSINI. The thermotemperature range 48 to 84 "C in 1 M NaC104 chemistry of the chemical substances. Reinhold solution. Publishing Corp., New York Our enthalpies of reactions 8-10 and 13 have 14. J. W. LARSON, P. CERUTTI, H. K. GARBER, and L. G. been combined with our AH: of Cr3+(aq) and HEPLER. J. Phys. Chem. 72, 2902 (1968). 15. L. M. GEDANSKY, E. M. WOOLLEY, and L. G. HEPLER. AH: values for HF(aq), C1-(aq), Br-(aq), and J. Chem. Thermodyn. 2, 561 (1970). S042-(aq) from ref. 16 to obtain the AH: values 16. D. D. WAGMAN, W. H. EVANS, V. B. PARKER, for CrF2+(aq), CrC12+(aq), CrBr2+(aq), and 1. HALOW, S. M. BAILEY, and R. H. SCHUMM. CrS04+(aq) (all inner sphere complexes) that are National Bureau of Standards Technical Note U.S. Government Printing Office, Washington, D.C. listed in Table C. F. HALE and E. L. KING. J. Am. Chem. Soc. 71, Acknowledgments 1779 (1967); R. J. BALTISBERGER and E. L. KING. J. We are grateful to the National Research Am. Chem. Soc. 86, 795 (1964); H. S. GATES and E. L. KING. J. Am. Chem. Soc. 80, 5011 (1958); Council of Canada for support of this research. K. SCHUG and E. L. KING. J. Am. Chem. Soc. 80, In addition, I.D. thanks Bokelunska resestipen (1958). diet and Per Westlings minnesfond for travel 18. J. H. ESPENSON and E. L. KING. J. Phys. Chem. 64, grants. 380 (1960). 19. L. G. SILLBN and A. E. MARTELL. Stability constants 1. D. D. WAGMAN, W. H. EVANS, V. B. PARKER, of metal-ion complexes. Special Publ. No. 17. The I. HALOW, S. M. BAILEY, and R. H. SCHUMM. Chemical Society, London. 1964; L. G. SILLBN and National Bureau of Standards Technical Note A. E. MARTELL. Stability constants of metal-ion U.S. Government Printing Office, Washington, D.C. complexes, Supplement No. 1. Special Publ. No The Chemical Society, London