The electrochemical reduction of octafluorocycl ohexadienes: Polarographic studies of the relative stabilities of a pair of isomers and their verification

ELECTROANALYTICALCHEMISTRYAND INTERFACIALELECTROCHEMISTRY Elsevier Sequoia S.A., Lausanne- Printed in The Netherlands

23

THE ELECTROCHEMICAL R E D U C T I O N OF OCTAFLUOROCYCLOHEXADIENES: POLAROGRAPHIC STUDIES OF THE RELATIVE STABILITIES OF A PAIR OF ISOMERS AND THEIR VERIFICATION

A. M. DOYLE, C. R. PATRICKANDA. E. PEDLER Department of Chemistry, The Universityof Birmingham, P.O. Box 363, Birmingham,B15 2TT (England) (Received 30th March 1971)

There have been few reports in the literature of a correlation of rate constants determined by d.c. polarography with thermodynamica data. We have determined the position of the equilibrium between octafluorocyclohexa-l,3 and 1,4-dienes and related this to the half-wave potentials for reduction of the dienes 1. The complete equation for a polarographic wave, applicable to both reversible and irreversible processes where mass transfer is effected solely by diffusion is2:

ia-i (nF(E-E°)~ 1.14 (D) ~ (omFE~ i - expk R T- -J + k~exp \ ~ - /

(1)

where kf° is the velocity constant for the forward (reduction) reaction at a potential E and E ° is the hypothetical standard electrode potential for the reversible reaction (the other symbols having their usual polarographic significance). For a reaction involving two electrons, provided that E ° is less negative than E by more than 60 mV, the first term ofeqn. (1) may be neglected and the current flow is given by the equation for a completely irreversible reaction. At the half-wave potential, eqn. (1) then becomes: kr° = 1.14 ( D y exp k ~ -

J

(2)

It is our purpose to compare the rate coefficients measured for the electrochemical reduction of the isomeric octafluorocyclohexadienes. The two rate coefficients must be compared at a common value of the potential, but it may not easily be apparent that there is some difficulty in choosing the potential at which the comparison should be made. If the two reactions for which the rate coefficients are to be compared have the same value of ct, then it is sufficient that the comparison be made at a common value of the potential (provided that the measurements are made in the same electrode-solvent system), but the condition regarding ~ is not fulfilled in the present cases. In consequence the ratio of the two rate coefficients, when compared at a common potential E, which is measured in practice with respect to some conveniently chosen, but arbitrary, zero potential Eo, contains a term of the type exp [(cq - 0 t 2 ) n F ( E - Eo)/R T], and is therefore dependent on the choice of E and E o. The question therefore arises of whether, in a particular system, there is a potential that may be chosen such that the ratio of the rate coefficients contains no term

,J. Electroanal. Chem., 33 (1971)23-30

24

A . M . DOYLE, C. R. PATRICK, A. E. PEDLER

representative of the electrical energy. This question also arises in comparing of the effectiveness of different metals in bringing about reactions at electrodes 3,4. The electrical contribution to the factors determining a rate constant might be eliminated if it were possible to extrapolate experimental observations at other potentials to such a potential of the electrode as is accompanied by no change in potential, even local, in passing through the electrode-solution interface. It does not follow that because there is no potential difference between points well within the electrode and solution that there is no variation in potential in the immediate vicinity of the interface, caused by the distribution of ions and the orientation of dipolar solvent molecules. However, the effects of these variations in potential are minimized at the potential of zero charge (p.z.c.), although even at this special potential it can only be asserted that the effects are minimal rather than absent. There remains at the p.z.c, a potential difference between the phases made up of a component due to the dipolar orientation of molecules of solvent, and one due to the solvent-electron interaction across the boundary. Both contributions are unmeasurable but are often assumed smalP. In the absence of more information it is reasonable to suppose that extrapolation to the p.z.c, gives a minimal residual electrical contribution in making any comparison. By the theory of absolute rates 6, velocity constants may be written in the form : kf = ~ - exp

(_

/3/

RT/

(assuming a transmission coefficient of unity), and kr may be identified with k°, the velocity constant at the p.z.c., where AG° becomes the standard chemical free energy of activation (with no electrical contribution). Thus from eqns. (2) and (3):

kT

-h- exp

(_AG°~ = 1.14 ( D ~ exp ~_nFEi~

RT/

~t /

~--R-T-]

(4)

In order to calculate AG° from eqn. (4) the values of an and E~ employed must of course include a double layer correction, which affects both experimental quantities 7. Previous papers 1 have described the polarographic behaviour of octafluorocyclohexa-l,3- and -1,4-dienes in an ethanol-water (3:2) solvent using tetramethylammonium chloride (0.4 M) as electrolyte. Controlled potential reduction of the dienes gave a quantitative yield of hexafluorobenzene according to the overall equations : V F

F + 2e

F

F F

F

F

+ 2F ®

(ii)

F

F

F + 2e

F

(i)

F

F

F

+ 2F @

F F

J. Electroanal. Chem., 33 i1971) 23-30

F

F

F

F

.,

F

POLAROGRAPHY AND STABILITY OF ISOMERS

25

A mechanism for the reaction was put forward in which reactions (iii) and (iv) were rate controlling diene + e . . . . . . ~ (diene-)

(iii)

F F diene-

- . . . .

-',- F F

(iV)

F F

the subsequent one-electron reduction of the C6F} radical formed in (iv) being extremely rapid. Both perfluoro-dienes react to give the same radical in reaction (iv) the structure of which may be assumed to approximate to that of the transition state. For two reactions which proceed via the same transition state the difference between the free energies of activation is equal to the difference between the free energies of formation of the two species. The second of these quantities may be obtained from the equilibrium constant for the interconversion of the two species. Application of the considerations outlined above leads to a value of(AG°)l.4 (AG°)I.3 = 0.97 kcal mol-1 (1 cal = 4.1840 J) in excellent agreement with the value obtained from equilibrium measurements (1.10_+0.22 kcal mol-1). Neglect of the double layer correction to both E~ and an leads to a value of 0.94 kcal mol- 1 for the difference in the free energies of formation, and a variation in the value selected for the p.z.c, of +0.1 V varies the free energy difference by -+0.39 kcal mol-1 respectively. In order to test the plausibility of the assumptions underlying the analysis of the polarographic study just described, a study has been made of the equilibrium between the isomeric octafluorocyclohexadienes at higher temperatures. If either of the isomeric octafluorocyclohexadienes is heated to temperatures in the range 250-600°, in the absence of a metal surface, it is transformed slowly to the other isomer until an equilibrium is reached 8. In glass ampoules, in the absence of a catalyst, the isomerisations proceed very slowly, but the addition of a catalyst, such as potassium fluoride, which was used in this study, enables equilibrium to be reached in about 100 h at 250°, and more rapidly at higher temperatures. The composition of reaction mixtures was determined by gas chromatography. At each temperature the composition of the equilibrium mixture produced from either of the pure dienes was determined separately. The attainment of equilibrium was verified by the analysis of ampoules that had been heated to the required temperatures for different periods of time. Equilibrium was judged to have been attained when two ampoules, each having been heated for a significantly different, but long, period of time, contained mixtures of the same composition (within experimental error). The equilibrium constants, defined as K = [1,3-diene]/[1,4-diene] determined from such experiments are presented in Table 1. It is evident that the 1,3-diene becomes more stable as the temperature is raised, although only slowly. The results were fitted by the least squares procedure 9 to the equation log K = - 0.1233 - 203.6/T which is of the form of the van't Hoff isochore, In K = B - A H / R T which would be expected to obtain for the variation of an equilibrium constant with J. Electroanal. Chem., 33 (1971) 23-30

26

A . M . DOYLE, C. R. PATRICK, A. E. PEDLER

TABLE 1 Equilibrium constants in column 1 were deduced from the equilibration of octafluorocyclohexa-l,4-diene, and those in column 2 from the equilibration of octafluorocyclohexa-1,3-diene

Temp.

Equilibrium constants 1

K = [ l ,3-diene] / [ l,4-diene] 2

250 300 350 400 450

0.299 0.310 0.348 0.352 0.405

0.337 0.322 0.368 0.370 0.406

temperature, provided that the heat of reaction, AH, and the term B are independent of temperature. From the equation for log K it follows that AH is 0.932 kcal mol- 1 for the conversion of octafluorocyclohexa-l,4-diene to octafluorocyclohexa-l,3-diene. This value is associated with a standard error of 0.11 kcal mol- a or more realistically with a 95 ~o confidence range of 0.25 kcal m o l - 1. The heat ofisomerisation for the pair of analogous hydrocarbons has not been reported. Amongst hydrocarbons a conjugated diene is generally more stable than its unconjugated isomer. This is demonstrated by the heat of hydrogenation of several acyclic hydrocarbon dienes, the results of which suggest that, for example, the heat of formation of a (conjugated) 1,3-diene will be more negative than the heat of formation of the isomeric 1,4-diene by about 3.5 kcal mol-1. This difference is sometimes attributed 1° to the involvement of resonance in the more stable isomer, but may more plausibly be attributed to the different states of hybridization of the carbon atoms. In passing from the 1,4-diene to the 1,3diene the bond between carbon atoms in the hybridised state sp3-sp 3 is replaced by one between atoms that are hybridised in the state sp2-sp 2. In the present case the "conjugated" isomer appears to be the less stable, contrary to experience with hydrocarbons. This might be an indication that the rule with hydrocarbons does not hold for fluorocarbons, which show some characteristic thermochemical behaviour in other respects1 ~. Unfortunately, no other data relating to fluorocarbons are available for comparison. On the other hand it should be kept in mind that the data available for hydrocarbons relate to acyclic dienes, in which the two double bonds may, in the 1,3-diene system, take up a trans configuration relative to one another. This configuration is likely to be favoured on energetic grounds. In a cyclic system, such as in cyclohexa-l,3-dienes, the double bonds are constrained to assume a cisoid configuration, and in so doing the thermochemical advantage that is available in acyclic systems may be lost. Such an effect may explain in part the reversal of the anticipated relative stabilities of the octafluorocyclohexadienes. If it is accepted that the equation for log K may be extrapolated to room temperature, which supposes that the heat and entropy of reaction are constant over a range of 250° outside the range of experimental observations (which is not unreasonable) we find that the free energy of isomerisation of octafluorocyclohexa-l,4diene to the isomeric 1,3-diene is, at 25°, 1.10 kcal mol- 1 with an error, for 95 ~o confidence limits, of +0.22 kcal mol- 1 .J, Electroanal. Chem., 33 (1971) 23-30

POLAROGRAPHY AND STABILITY OF ISOMERS

27

EXPERIMENTAL

Electrochemistry

Values of an for the reduction of octafluorocyclohexa-l,3- and 1,4-dienes, obtained from E vs. log [(i d - i)/i] have previously been reported 1 as 0.67 and 0.51 respectively. These TaM plots must be corrected for the existence of the double layer potential q~2 (the potential in the outer plane of closest approach). For the reduction of a neutral substance the required correction is given by the equation 7 i

~n F

RT

/

~cb. \ [1 - - ' ~ = slope of the Tafel plot ~ ~tl /

Values of the potential q~2 for solutions of (CH3)¢N+C1 are not available, although the results of Devanathan and Fernando ~3 suggest that the specific absorption of tetramethylammonium ions is less than that of K + ions. We have, therefore, corrected an using values of q~2 US. applied potential for NaF in aqueous solution 14 (in general this is the maximum correction since values of ~b2 will generally be less negative than those for Na + due to residual absorption of the larger ion). These results show that t])2 ~ - - 0 . 0 7 3 and -0.087 V, with ~b/Oq= +0.0516 and +0.0417 for octafluorocyclohexa-l,3 and 1,4-diene respectively, at the half-wave potentials giving corrected values for c~nof 0.704 and 0.537 for the 1,3- and 1,4-diene. The validity of assuming linearity for the corrected Tafel plots (constant value of the transfer coefficient) over a voltage range of up to 1.0 V may be open to question (excluding the anticipated curvature close to the reversible electrode potential), although examples of linear Tafel plots ranges of 0.44).5 V are known 4. Consideration of potential energy curves and the relationship of these to the transfer coefficient indicates that at high overpotentials ~ may no longer be constant (or that at least the slope of the Tafel plot will differ from the slope found at low overpotentials). However, it is difficult to estimate the overpotential at which this effect becomes pronounced. For the examples we are considering, changes in ~ with overpotential and the consequent errors in the free energy differences calculated may not be significant due to the similarity of the compounds concerned. The half-wave potentials were measured against a saturated calomel electrode (SCE) and were - 1.19 V and - 1.49 V, which become, after correcting for q52, -0.684 V and -0.970 V vs. the potential at the p.z.c, for the 1,3- and 1,4-diene respectively. The potential chosen is that of aqueous sodium fluoride viz. -0.472 vs. NCE 15. No corrections have been made for the presence of alcohol and gelatine, although these would be similar in magnitude for each diene. Values of D~-, determined from id VS. concentration curves and the Ilkovic equation were 1.50 x 10- 3 cm s -~ and 1.35 x 10 3 cm s ½for octafluorocyclohexa-l,3 and 1,4-dienes respectively (assuming n = 2, according to reactions (i) and (ii)). Thermal equilibration of the isomers of octafluorocyclohexadiene (with C. S. Carvo)

Octafluorocyclohexa-l,3-diene (b.p. 63°) and octafluorocyclohexa-l,4-diene (b.p. 58°) were prepared as previously described 1. Samples of about 1 g of the chosen diene, together with 1 g of powdered potassium fluoride were sealed in vaeuo (< 10-3 mm Hg) into small glass ampoules J. Elearoanal. Chem., 33 (1971) 23-30

28

A.M. DOYLE, C. R. PATRICK~ A. E. PEDLER

(60 mm × 18 mm, i.d. 12 mm). The ampoules were placed for a suitable time, sufficient to obtain equilibrium (96 h decided upon after use of shorter times) in a furnace whose temperature was regulated to within _ 3° at the chosen temperature. At the end of the period the ampoule was withdrawn, cooled in ice, and when open, samples of the liquid were withdrawn and analysed by gas-liquid chromatography. Gas-liquid chromatography was carried out using a Perkin-Elmer Vapour Fraktometer. The column (length 6 ft)* was packed with dinonyl phthalate (15~o w/w) on celite (80-120 mesh) and was operated at 55°. The mixtures were analysed using the relative peak heights, and on the basis of calibration experiments. APPENDIX

The thermodynamics of the reduction of octafluorocyclohexadiene to hexafluorobenzene The reduction processes which are described in the text may be written formally as ;

c-C6Fs+2e ~ C 6 F 6 + 2 F -

A(i)

The overall processes may be written in two parts, namely : C 6 F 8 "-~ C 6 F 6 + F 2 F 2 + 2 e ~ 2F-

A(ii)

A(iii)

The thermodynamics of the latter are embodied in the standard potential for the fluoride ion. The thermodynamics of the first part require attention. The heat of formation of neither of the isomeric octafluorocyclohexadienes has been determined. The equilibrium studies presented in this paper show that the heats of formation do not differ greatly, so that in view of the magnitudes of the quantities involved, and of our present interest in them, we may regard them as equal. Reliable values of heats of formation of highly fluorinated organic compounds are sparse. We have based our considerations upon values tabulated recently by Cox and Pilcher 16. The standard heats of formation (at 25°C) of gaseous decafluorocyclohexene and hexafluorobenzene are ( - 462.7 and - 228.5 kcal mol- 1 respectively). The heat of dodecafluorocyclohexane has not been determined, but may be estimated as - 584_+ 7 kcal mol- 1 by using bond energy relationships similar to those given by Good and others 17, but using the more recently selected values of heats of formation of fluorocarbons. The heat of fluorination of octafluorocyclohexene to give dodecafluorocyclohexane is therefore 122 _+7 kcal mol- 1. The heat of fluorination of hexafluorobenzene to give decafluorocyclohexene is -234.2 kcal mol-1, corresponding to an average value of -117 kcal mo1-1 for the fluorination of the two double bonds involved in the overall process. If, with respect to resonance or other stabilisation factors, the fluorocarbon system were to follow the same pattern as with hydrocarbons, one would expect that the heat of fluorination of octafluorocyclohexadiene to give decafluorocyclohexene would be more nearly equal to that of the fluorination of decafluorocyclohexene to give dodecafluorocyclohexane than to that of the fluorination of * 1 ft~0.3048

m.

J. Electroanal. Chem., 33 (1971) 23-30

POLAROGRAPHY AND STABILITY OF ISOMERS

29

hexafluorobenzene to give an isomer of octafluorocyclohexadiene. It is reasonable to suppose, therefore, that the heat of reaction A(ii) (the obverse of fluorination) is unlikely to exceed about 120 kcal tool -~ and may be smaller by so much as 10-15 kcal mol- 1. In order to estimate the free energy of reaction A(ii) we need also to know the entropy of reaction. The principles underlying many group-additive methods for the estimation of entropies of compounds TM 19 require that the entropies of saturation of members of a set of olefins with a particular reagent, such as fluorine, will be similar in magnitude, but will show small differences dependent upon the symmetries of the olefins and of the saturated compounds formed from them and, to a lesser extent, upon other factors. Few values are available for the entropies of gaseous fluorocarbons or fluoro-olefins. The entropies (for the gas state, p = 1 arm.) of some simple fluoro-olefins and fluorocarbons are known, or have been reliably estimated 2°*. From these quantities it may be shown that the entropies of fluorination of tetrafluoroethylene and of hexafluoropropene are both - 4 1 __+1 cal K-1 mol-1. Because we are dealing with a substance of higher molecular weight we might expect the entropy of fluorination of hexafluorobenzene to give an octafluorocyclohexadiene to be a little greater than this, and propose an estimate of - 45 + 5 cal K - 1 mol- 1 for the latter quantity. It should be recalled that in these considerations, as in those for the heat of reaction, we recognise that the thermodynamic properties of the isomeric octafluorocyclohexadienes differ, but suppose the differences to be small, as indicated by the results of the equilibrium studies. We are now in a position to write an expression for the standard free energy change for reaction A(ii) for the hypothetical gas state at 25°, with p = 1 atm., as AG (cal mole- 1) = 298.2 ( - 4 5 + 5) + (110,000-120,000) = 108-118 kcal mol 1. We are interested in the reaction when carried out in solution. In view of the large magnitude of free energy involved it will not be altered materially by any corrections that might be made for the condensing of the hypothetical vapours (at p= 1 atm.) to the liquid state and dissolving these in a solvent. The reversible electrode potential for reaction A(iii) is given 15 as +2.85 V or - 131,500 cal tool -1, so that AG° for reaction A(i) is - 23,500- - 13,500 cal mol- 1. Thus E °, the hypothetical reversible electrode potential for reaction A(i) is + 0.29 to + 0.51 V. ACKNOWLEDGEMENTS

Thanks are due to S.R.C. and the British Council for maintenance awards to A.M.D. and C.S.C., respectively. SUMMARY

The thermal equilibration and polarographic reduction of octafluorocyclohexa-l,3- and 1,4-dienes has been studied. The difference between the free energies of formation of the two species obtained from thermal measurements was 1.10__+0.22 kcal mol-1 which compared with 0.97 kcal tool-~ calculated from polarographic reduction potentials, the 1,4-diene being the most stable. * Note that the value for the entropy of hexafluoroethane should be 79.4 cal K -~ mol -I, as quoted in ref. 18.

J. Electroanal. Chem., 33 (1971) 23-30

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A . M . DOYLE, C. R. PATRICK, A. E. PEDLER

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A. E. PEDLER,J. Chem. Soc. (C), (1971) 282. 2 R. BRDICKA,Collect. Czech. Chem. Commun., 19 (1954) $41. 3 J. O'M. BOCKR1SANDE. C. POTTER,J. Electrochem. Soc., 99 (1952) 169; B. E. CONWAY,E. M. BEATTY AND P. A. D. DE MAINE, Electrochim. Acta, 7 (1962) 39. 4 B. J. PmRSMAAND E. GILEADI,in J. O'M. BOCKRIS(Ed.), Modern Aspects of Electrochemistry No. 4, Butterworths, London, 1966, pp. 47 et seq. 5 J. O'M. BOCKRlSANDA. K. N. R.EDDY,Modern Electrochemistry, MacDonald, London, 1970, p. 1145. 6 H. EYRING, S. GLASSTONEAND K. J. LAIDLER,J. Chem. Phys., 7 (1939) 1053. 7 P. DELAHAY,Double Layer and Electrode Kinetics, Interscience, New York, 1965, p. 198 et seq. 8 B. GETHING, C. R. PATRICK,J. C. TATLOW,R. E, BANKS,A. K. BARBOURAND A. E. TIPPING, Nature, 183 (1959) 586. 9 0 . L. DAVIES,Statistical Methods in Research in Production, Oliver and Boyd, London, 1961. 10 G. W. WHELAND, Resonance in Organic Chemistry, Wiley, New York, 1955, p. 132. ll M. J. S. DEWARAND H. N. SCHMEISING,Tetrahedron, 5 (1959) 166; 11 (1960) 96. 12 C. R. PATRICKin M. STACEY,J. C. TATLOWANDA. G. SHARFE(Eds.), Advances in Fluorine Chemistry, Vol. 2, Butterworths, London, 1961, p. 1. 13 M. A. V. DEVANATHANAND M. J. FERNANDO, Trans. Faraday Soc., 58 (1962) 368. 14 C. D. RUSSELL,J. Electroanal. Chem., 6 (1963) 486. 15 B. E. CONWAY,Electrochemical Data, Elsevier, Amsterdam, 1952, pp. 221-232; D. C. GRAHAME, Chem. Rev., 41 (1947) 441. 16 J. D. Cox AND G. PILCHER, Thermochemistry of Organic and Organometallic Compounds, Academic Press, London and New York, 1970. 17 W. D. GOOD, D. R. DOUSLIN, D. W. SCOTT, A. GEORGE, J. L. LACINA, J. P. DAWSONAND G. WADDINGTON,J. Phys. Chem., 63 (1959) 1133. 18 S. W. BENSONAND J. H. BUSS,J. Chem. Phys., 29 (1958) 546. 19 S. W. BENSON,Thermochemical Kinetics, Wiley, New York, 1968. 20 W. M. D. BRYANT,J. Polym. Sci., 56 (1962) 277.

J. Electroanal. Chem., 33 (1971) 23-30