Estimation of Enthalpy Data for Reactions Involving Gas Phase Ions

Inorg. Chem. 2003, 42, 2886−2893

Estimation of Enthalpy Data for Reactions Involving Gas Phase Ions Utilizing Lattice Potential Energies: Fluoride Ion Affinities (FIA) and pFValues of mSbF5(l) and mSbF5(g) (m ) 1, 2, 3), AsF5(g), AsF5‚SO2(c). Standard Enthalpies of Formation: ∆fH°(SbmF5m+1-,g) (m ) 1, 2, 3), ∆fH°(AsF6-,g), and ∆fH°(NF4+,g)† H. Donald Brooke Jenkins* and H. K. Roobottom Department of Chemistry, UniVersity of Warwick, CoVentry, CV4 7AL, West Midlands, U.K. Jack Passmore* Department of Chemistry, UniVersity of New Brunswick, Fredericton, New Brunswick, Canada, E3B 6E2 Received November 4, 2002

Fluoride ion affinity (FIA) values (and the associated pF- values) are difficult to establish experimentally for pentafluorides of arsenic and antimony. Our approach, utilizing estimated lattice potential energies, provides a further opportunity to establish this data for liquid (and gaseous) SbF5 and gaseous AsF5 which compliments values obtained using ab initio routes for monomeric gas phase molecules and adds to results based on rigorous methods. A strategy is developed whereby construction of (multiple) Born−Fajans−Haber cycles centered around the (target) FIA reaction of interest yield a plethora of estimates for the enthalpy change of interest. This general approach is illustrated here by specific estimation of some experimentally based FIA values of SbF5 and AsF5. FIA values/kJ mol-1 and pF- values estimated in this paper are FIA(SbF5,l) ≈ −475 (±63), pF-(SbF5,l) ) 11.4 (±1.5); FIA(SbF5,g) ≈ −506 (±63), pF-(SbF5,g) ) 12.4 (±1.5); FIA(2SbF5,l) ≈ −609 (±63), pF- (2SbF5,l) ) 14.6 (±1.5); FIA (2SbF5,g) ≈ −671 (±63), pF- (2SbF5,g) ) 16.0 (±1.5); FIA (3SbF5,l) ≈ −635 (±39), pF- (3SbF5,l) ) 15.2 (±0.9); FIA (3SbF5,g) ≈ −728 (±39), pF- (3SbF5,g) ) 17.4 (±0.9); FIA (AsF5,g) ≈ −421 (±22), pF- (AsF5,g) ) 10.1 (± 0.5); and FIA (AsF5‚SO2,s) ≈ −390 (±22), pF- (AsF5‚SO2,s) ) 9.3 (±0.5). Related standard enthalpies of formation (in kJ mol-1) are also assigned: ∆fH°(SbF6-,g) ≈ −2075 (±52); ∆fH°(Sb2F11-,g) ≈ −3520 (±63); ∆fH°(Sb3F16-,g) ≈ −4874 (±39); ∆fH° (NF4+,g) ≈ 903 (±32); ∆fH° (AsF6-,g) ≈ −1907 (±22).

Introduction

* Authors to whom correspondence should be addressed. H.D.B.J.: tel, +44-2476-523265 or +44-24-76-466747; fax, +44-2476-524112 or +442476-466747; e-mail, [email protected]. J.P.: tel, 506-453-4781; fax, 506-453-4981; e-mail, [email protected]. † This paper is dedicated to the affectionate memory of Dr. Donald Frank Charles Morris, who died in Oxford on 10 June 2000 and was buried at St. Mary’s Church, Denham Village, Buckinghamshire, on 26 June 2000 and who made a significant contribution to the study of thermochemstry. He was friend and colleague of H.D.B.J.

established ancillary enthalpy data if the maximum precision in the target data is to be ensured. We establish a procedure for the estimation of the enthalpy change, ∆H, for selected reactions involving gas phase ions for which certain of the enthalpies of formation of the species involved have not been experimentally determined and so are unavailable. Absence of such data prevents establishment of ∆H, by direct calculation. The approach described is a general one. It is illustrated here by derivation of a series of specific and important fluoride ion affinity (FIA) values that utilize our recently developed method of estimating lattice enthalpies.1 Our approach provides a way to obtain experimental FIA

2886 Inorganic Chemistry, Vol. 42, No. 9, 2003

10.1021/ic0206544 CCC: $25.00

Extending the scope of methods to estimate elusive, uncertain, or difficult to measure thermodynamic data has always represented a challenge. Any strategy needs to involve thermochemical cycles employing, whenever possible, well-

© 2003 American Chemical Society Published on Web 04/08/2003

Enthalpy Data for Reactions InWolWing Gas Phase Ions

values other than from mass spectrometry measurements such as those from ion cyclotron2 measurements. The FIA values obtained from the methods described in this paper can be used as benchmarks for calculated FIAs also. Ancillary thermochemical data used is listed in Appendix 1 of this paper. A strategy, often employed, in an attempt to stabilize a new or novel inorganic or organic cation in the form of a salt is to employ a strong Lewis acid (e.g., SbF5,l) in order to extract a fluoride ion from a suitable precursor. Stabilization is more likely if, among other things, the FIA shows a good degree of exothermicity, and so such quantities are of interest to synthetic chemists. This work complements recent progress in the estimation of fluoride ion affinities by ab initio methods3,4 for gas phase species (as exemplified by Christe and Dixon’s initiative in the derivation of a pF- scale of values.5a) and other methods. It can provide additional experimentally based values of the FIA of SbF5(l) for comparison with the ab initio values obtained for SbF5(g) (see, for example, Krossing and Goussor,4 Seppelt,6 or footnote 117 and Table 9 in ref 3). Fluoride Ion Affinities of Antimony Pentafluoride. Fluoride Ion Affinity of SbF5(l), FIA(SbF5,l), and Standard Enthalpy of Formation of Gaseous SbF6- Ion, ∆fH° (SbF6-,g): The fluoride ion affinity, FIA, of m mol of SbF5, in the liquid state, corresponds to the process7 FIA(mSbF5,l)

mSbF5(l) + F-(g) 98 SbmF5m+1-(g)

(1)

for which FIA (mSbF5,l) represents the associated enthalpy change of reaction 1. The stepwise procedure to determine this enthalpy change, ∆H, for reaction 1, for the case where m ) 1, is as follows. Step 1: Target Reaction Defined. For our first example: FIA(SbF5,l)

F-(g) + SbF5(l) 98 SbF6-(g)

(2)

Figure 1. Cycle developed around target reaction for the estimation of FIA(SbF5,l) showing two modes of closure based (i) on complexation enthalpy (upper inner cycle) and (ii) on standard enthalpies of formation (peripheral outermost cycle).

Step 2: Construction of a Subsidiary Cycle. In such circumstances the basic tenet of our approach consists of modification of the target reaction by the stratagem of adding the same “partner” ion (counterion) to both sides of the target reaction such that the oVerall enthalpy change is unaltered. Once partnered with the ions already present, these counterion additions form the constituent gaseous ions of ionic salts (and hence enable the incorporation of lattice enthalpy steps within the cycle being developed around the target reaction to provide an alternative route equivalent, enthalpically, to the direct reaction). These steps must involve salts for which standard enthalpies of formation (or other thermodynamic data) are available; then the cycle loop is closeable and the target enthalpy change is quantifiable. The appropriate ions to use for addition are selected with several considerations in mind. The pairs of ions created should, ideally, give rise to simple salts (e.g., alkali metal halides) or ones for which reliable enthalpy of formation data is available. In the example, gaseous alkali metal cations M+ form ideal partner ions for the F- and SbF6- and are able to generate a series of individual thermochemical cycles, one for each selected M+, according as M+ ) Li+, Na+, K+, Cs+, O2+, Ag+ etc.:8

since ∆fH° (SbF6-,g) is unavailable from experimentally based data so direct estimation of FIA(SbF5,l) is not possible. (1) (a) Jenkins, H. D. B.; Roobottom, H. K.; Passmore, J.; Glasser, L. Inorg. Chem. 1999, 38, 3609. (b) Jenkins H. D. B.; Tudela, D.; Glasser, L. Inorg. Chem. 2002, 41, 2364. (c) Jenkins H. D. B.; Glasser, L. Inorg. Chem. 2002, 41, 4358. (2) See, for example: (a) Larson, J. W.; McMahon, T. B. J. Am. Chem. Soc. 1983, 105, 2944. (b) Larson, J. W.; McMahon, T. B. J. Am. Chem. Soc. 1985, 107, 766. (3) Cameron, T. S.; Deeth, R. J.; Dionne, I.; Du, H.; Jenkins, H. D. B.; Krossing, I.; Passmore J.; Roobottom., H. K. Inorg. Chem. 2000, 39, 5614. (4) Krossing, I.; Gonsior, M.; Mitzel, N. Z. Anorg. Allg. Chem. 2002, 1821. (5) (a) Christe, K. O.; Dixon, D. A.; McLemore, D.; Wilson, W. W.; Sheehy, J. A.; Boatz, J. A. J. Fluorine Chem. 2000, 101, 151. (b) Krespan, C. G.; Dixon, D. A. J. Fluorine Chem. 1996, 77, 117. (6) Hwang, I.-C.; Seppelt, K. Angew. Chem. 2001, 3690. (7) Process 1 is exothermic and thermodynamically represented by a negatiVe number, i.e., FIA(mSbF5,l) < 0. A convention exists in the literature whereby FIA values are cited as positiVe Values. Since, in this paper, we will employ our values always in the thermodynamic context, we shall follow the strict thermodynamic convention and so avoid confusion. Thus, all FIA values cited in this paper are less than zero and defined in accordance with a process analogous to process 1.

Step 3: Closure of Cycle Loop. The partially completed cycle loop above can now be closed either (i) by using the experimentally determined complexation enthalpy, ∆compH°(MF,c), as measured by Burgess et al.9a for the reaction MF(s) + SbF5(l) f MSbF6(s) (upper cycle in Figure 1), or (ii) by using tabulated standard enthalpies of formation data for MF(8) In principle any cation M+ could be involved. Multiply charged cations, e.g., Ba2+, with suitable modification of eq 2, are also included: Ba2+(g) + 2F-(g) + 2SbF5(l) f Ba2+(g) + 2 SbF6-(g) and leads to an estimate of 2 FIA(SbF5,l). However, as we move away from the alkali metal cation salts, the reliability of the thermochemical standard enthalpies of formation of the salts etc. falls off considerably. (9) (a) Burgess, J.; Peacock R. D.; Sherry, R. J. Fluorine Chem. 1982, 20, 541. (b) We attribute this to a mistake in sign used in ref 9a. (c) Bougon, R.; Bui Huy, T.; Burgess, J.; Christe, K. O.; Peacock, R. D. J. Fluorine Chem. 1982, 19, 263.

Inorganic Chemistry, Vol. 42, No. 9, 2003

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Jenkins et al. PF-

Table 1. Crystal Structure Data and Lattice Potential Energies Estimated from Eq 3 for SbF6- Salts hexafluoro antimonate salts MSbF6 and M[SbF6]2 LiSbF6

a

NaSbF6 KSbF6 a CsSbF6 AgSbF6 O2SbF6 Ba[SbF6]2

crystal structureb parameters/nm, deg hexagonal; a ) 0.518, c ) 1.360, Z ) 1 cubic; a ) 0.8184, Z ) 4 cubic; a ) 1.014, Z ) 8 rhombohedral; a ) 0.533, R ) 56.9, Z ) 1 cubic; a ) 0.985, Z ) 8 V(O2+)/nm3 ) 0.015c V(SbF6-)/nm3 ) 0.121c triclinic; a ) 0.489, b ) 0.507, c ) 0.863, R ) 104.7, β ) 100.3, γ ) 116.5, Z ) 1

UPOTe/ Vd/nm3 kJ mol-1 0.1360

560

0.1370 0.1303 0.1298

558 567 571

0.1195 0.1360

580 560

0.1750

1799

a It should be noted that Burgess et al.9a predicted the lattice energies of the corresponding hexafluoroantimonate salts to be in the ranges 617 < UPOT(LiSbF6)/kJ mol-1 < 754 and 549 < UPOT(KSbF6)/kJ mol-1 < 590. The precise values were uncertain because the charge distributions on the hexafluoroantimonate anions were not established in their paper. While our value of UPOT (KSbF6) ()568 kJ mol-1) lies within the specified range, the value for UPOT (LiSbF6) ()560 kJ mol-1) does not. b Reference 14. c Estimated, in the absence of crystal structure data, from addition of single ion volumes using Tables 5 and 6, ref 1a. d Represents the molecular formula unit V ) Vcell/Z. e UPOT values are calculated using eq 3 with the values1a of R/kJ mol-1 nm ) 117.3 β/kJ mol-1 ) 51.9 and I ) 1 for MSbF6 salts and R/kJ mol-1 nm ) 133.5 β/kJ mol-1 ) 60.9 and I ) 3 for M[SbF6]2 salts. UPOT )2I(RV-1/3 + β) (3)

(s), SbF5(l), and MSbF6(s) (peripheral cycle in Figure 1). Figure 1 shows these two alternative closure routes. Step 4: Evaluation of Lattice Potential Energies. Lattice potential energies are obtained either from established literature values,10 or are estimated from their crystal structure volume1a,c or their measured density1b or else by using our database of single ion volumes.1a For simple alkali metal fluorides, lattice energies, UPOT(MF), are already available in the literature11 and are taken directly from there. For the SbF6- salts, the crystal structures and derived volumes of the salts are available and are listed in Table 1 while the value of V(O2SbF6), its crystal structure volume not being available, can be estimated additively from our ion volume database (see Table 1 in ref 1). Using the upper cycle of Figure 1 and the data in Table 2, we obtain an estimate FIA(SbF5,l)/kJ mol-1 ) -473 ((75). We comment, at this point, regarding the large standard deviations that are reported throughout this paper. This arises usually from the broad spread of estimated values for FIA yielded by the thermochemical data. This is, in turn, attributed, at least in part, to the experimental difficulties experienced by researchers in working with SbF5 and its salts and often in determining the exact nature of the products in thermochemical reactions. One view might be to discard extreme values. However, we believe that by including as many estimates as possible (e.g., 14 in the case of FIA(SbF5,l)) in our analysis the averaged value obtained will be more reflective of the actual value we are seeking to (10) See, for example: Lide, D. R. Lattice Energies. Handbook of Chemistry and Physics, 80th ed.; CRC Press: Boca Raton, FL, 2000; Section 12, pp 12-22. (11) Jenkins, H. D. B.; Pratt, K. F. Proc. R. Soc. London 1977, A356, 115.


Table 2. FIA(SbF5,l) and Obtained from Upper Cycle of Figure 1 Using Enthalpies of Complexation of SbF5(l) with Alkali Metal and Silver Fluorides (Table 5, Ref 9a)a hexafluoro antimonate salt

UPOTb (MSbF6)/ kJ mol-1

UPOTc (MF)/ kJ mol-1

∆compH° d/ kJ mol-1

FIA(SbF5,l)/ kJ mol-1

pFvalue

LiSbF6 NaSbF6 KSbF6 CsSbF6 AgSbF6

560 558 567 571 580

1030 910 808 744 953

-116 -147 -182 -217 -106

-584 -497 -421 -388 -477

14.0 11.9 10.1 9.3 11.4

a Average value of FIA(SbF ,l)/kJ mol-1 ) -473 ((75); pF- ) 11.3 5 ((1.8). b Obtained from crystal structure data (Table 1) using eq 3.1a c Obtained from refs 10 and 11. d Reference 9a.

Table 3. FIA(SbF5,l) and PF- Obtained from Outer (Peripheral) Cycle of Figure 1 Using ∆fH°(MSbF6,s) from Richards and Woolfa Corrected by Burgess et al.b,c hexafluoro UPOTd UPOTe ∆fH° ∆fH° FIA antimonate (MSbF6)/ (MF)/ (MSbF6,s)/ (MF,s)/ (SbF5,l)/ pF-1 -1 -1 -1 kJ mol salt kJ mol kJ mol kJ mol-1 value kJ mol NaSbF6 KSbF6 AgSbF6

558 567 580

910 808 953

-2058 -2092 -1622

-573.6 -567.3 -204.6

-510 -439 -464

12.2 10.5 11.1

a Reference 13. b Reference 9a. c Average value of FIA(SbF ,l)/kJ mol-1 5 ) -471 ((36) and pF- ) 11.3 ((0.9). d Obtained from crystal structure data (Table 1) using eq 3.1a e Obtained from refs 10 and 11.

Table 4. FIA(SbF5,l) and PF- Obtained from Outer (Peripheral) Cycle of Figure 1 Using ∆fH°(MSbF6,s) from Burgess et al.a,b hexafluoro UPOTc UPOTd ∆fH° e ∆fH° FIA antimonate (MSbF6)/ (MF)/ (MSbF6,s)/ (MF, s)/ (SbF5,l)/ pFsalt kJ mol-1 kJ mol-1 kJ mol-1 kJ mol-1 kJ mol-1 value LiSbF6 NaSbF6 KSbF6 CsSbF6 AgSbF6

560 558 567 571 580

1030 910 808 744 953

-2062 -2054 -2086 -2082 -1622

-615.7 -573.6 -567.3 -553.5 -204.6

-590 -506 -433 -375 -464

14.1 12.1 10.3 9.0 11.1

a Reference 9a. b Average value of FIA(SbF ,l)/kJ mol-1 ) -473 ((66) 5 and pF- ) 11.3 ((1.6). c Obtained from crystal structure data (Table 1) using eq 3.1a d Obtained from refs 10 and 11. e Reference 9a.

Figure 2. Cycle for the estimation of ∆fH°(SbF6-,g).

determine. It should be noted also that other workers are similarly obliged to quote quite large standard deviations for their values (e.g., ref 12), although ab initio routes are, generally speaking, less able to provide error limits. Using the peripheral cycle of Figure 1, we obtain FIA(SbF5,l)/kJ mol-1 ) -471 ((36) using data from Richards and Woolf13 in Table 3 (as corrected by Burgess9a) or FIA(SbF5,l)/kJ mol-1 ) -473 ((66) using data by Burgess,9a Table 4. Using Figure 2 we can now estimate that ∆fH°(SbF6-,g)/kJ mol-1 ) -2075 (+52) from the data in Table 5.

(4)

Enthalpy Data for Reactions InWolWing Gas Phase Ions Table 5. ∆fH°(SbF6-,g) Calculated Using Burgess et al.a Recommended Values for ∆fH°(MSbF6,s)b

correspond to the process ∆vapH°(SbF5,l)

hexafluoro antimonate salts

UPOTc (MSbF6)/ kJ mol-1

∆fH° d (MSbF6,s)/ kJ mol-1

∆fH° (M+,g)/ kJ mol-1

∆fH° (SbF6-,g)/ kJ mol-1

(SbF5)3(l) 98 (SbF5)3(g)

LiSbF6 NaSbF6 KSbF6 CsSbF6 AgSbF6 O2SbF6 Ba[SbF6]2

560 558 567 571 580 560 1800

-2062 -2054 -2086 -2082 -1622 -1468 -4174

686 609 574 457 1019 1172 1660

-2184 -2104 -2094 -1969 -2068 -2081 -2026

based on electron diffraction studies16a which show that gaseous SbF5 consists principally of a trimer which also contains tetramer. The enthalpy of depolymerization16b,c for the process

-,g)/kJ

b

1

/4(SbF5)4(g) f SbF5(g)

mol-1

Reference 9a. Average value of ∆fH°(SbF6 ) -2075 ((52). c Obtained from crystal structure data (Table 1) using eq 3.1a d Reference 9a. a

a

-2075 ((52)

∆fH°(SbF5,l)/kJ mol-1 ∆fH°(F-,g)/kJ mol-1 FIA(SbF5,l)/kJ mol-1 pF-(SbF5,l)

-1328 -249 -498 (+52) 11.9 ((1.2)

SbF5(l) f SbF5(g, monomer)

Finally using this value to estimate FIA(SbF5,l) directly, we obtain (Table 6) a value -498 (+52) kJ mol-1 leading to an overall average value, from the 14 estimates made, of

-

(5)

FIA(SbF5,g)/kJ mol-1 ) -506 (+63)

(10)

and hence that pF-(SbF5,g) ) 12.4 (+1.5)

(11)

5a

which corresponds to a pF value defined by -

(9)

to be 30.9 kJ mol-1. This latter combined value for the enthalpy of depolymerization and evaporation of the liquid SbF5 is the currently accepted value.9c Our value of FIA(SbF5,l) when combined with this value leads to the prediction that

Obtained from Table 5.

FIA(SbF5,l)/kJ mol-1 ) -475 (+63)

(8)

has been estimated to be 18.5 kJ mol-1 and a value for the overall process16c

Table 6. FIA(SbF5,l) and pF- Estimated from ∆fH°(SbF6-,g) Data Obtained in This Paper ∆fH°(SbF6-,g)/kJ mol-1 a

(7)

-1

pF (SbF5,l) ) [-FIA(SbF5,l)/kcal mol ]/10

(6)

and having a value 11.4 ((1.5). Obtaining thermochemical data for some of these materials, it must be said, offers experimentalists a considerable challenge. For example, LiSbF6 is nontrivial to work with due to its hygroscopic nature (especially prior to the routine availability of high-quality, commercial dryboxes). Liquid SbF5 presents a different problem being highly reactive as well as viscous and polymeric in nature. This makes the underlying thermochemistry difficult to study. In view of such difficulties we might anticipate (and indeed find) quite large standard deviations arising in the FIA values estimated from thermochemical data recorded for these materials. There are, in addition, occasional anomalies in the data presented. For example, Burgess, Peacock, and Sherry’s values9a of FIA for SbF5(l) (-418 kJ mol-1) and SbF5(g) (-390 kJ mol-1) would predict a negatiVe enthalpy of conversion of SbF5(l) to SbF5(g).9b The chemistry involved with this conversion process is extremely complicated: the experimental15 ∆vapH°(SbF5,l) values of 43.4 and 45.2 kJ mol-1 respectively (12) Mallouk, T. E.; Rosenthal, G. L.; Muller, R.; Brusasco, R.; Bartlett, N. Inorg. Chem. 1984, 23, 3167. (13) Richards, W. W.; Woolf, A. A. J. Fluorine Chem. 1971, 129. (14) Landolt-Bo¨rnstein, New Series; Hellwege, K.-H., Ed.; Group III: Crystal and Solid State Physics, Vol. 7, Crystal Structure Data and Inorganic Compounds; Springer-Verlag: Berlin, 1973. (15) (a) Kemmitt, R.; Sharp, D. W. A. AdV. Fluorine Chem. 1965, 4, 142. (b) Shaw, R. C. Stroog, W. Ind. Chem. Eng. 1961, 43, 1624.

Chemically it is recognized that SbF5(g) represents a stronger F- ion acceptor (Lewis acid) than AsF5(g) and should therefore have the lower (in thermodynamic terms)7 FIA. Our value satisfies this expectation when compared with the value of FIA(AsF5,g)/kJ mol-1 () -423) recorded later in this paper, and this value for SbF5(g) is also close to that reported (-499 kJ mol-1) for FIA(SbF5,g) by Krespan and Dixon5b based on MP2 calculations and isodesmic reactions and is within 0.6% of that estimated by Christe and Dixon5a (-503 kJ mol-1) derived from correlated MP2/DPZ level of theory obtained also using isodesmic reactions. Fluoride Ion Affinity of 2 mol of SbF5(l), FIA(2SbF5,l), and Standard Enthalpy of Formation of Gaseous Ion, Sb2F11-, ∆fH°(Sb2F11-,g). Antimony pentafluoride exhibits a propensity for polymeric ion formation, and this is reflected in the formation of polyanions, as, for example, in the salt I2Sb2F11.17,18 The formation of the Sb2F11- anion is driven (16) (a) Brunvoll, J.; Ischenko, A. A.; Miakshin, I. N.; Romanov, G. V.; Spiridonov, V. P.; Strand, T. G.; Sukoverkhov, V. F. Acta Chem. Scand. 1980, A34, 733. (b) Fawcett, J.; Holloway, J. H.; Peacock, R. D.; Russell, D. R. J. Fluorine Chem. 1982, 20, 9. (c) Christe, K. O.; Hoge, B.; Boatz, J. A.; Prakash, G. K. S.; Olah, G. A.; Sheehy, J. A. Inorg. Chem. 1999, 38, 3132. (17) Brownridge, S.; Krossing, I.; Passmore, J.; Jenkins H. D. B.; Roobottom, H. K. Coord. Chem. ReV. 2000, 197, 397 (18) (a) Kemmitt, R. D. W.; Murray, M.; McRae, V. M.; Peacock, R. D.; Symons, M. C. R.; O’Donnell, T. A. J. Chem. Soc. A 1968, 862. (b) Gillespie, R. J.; Morton, M. J. J. Mol. Spectrosc. 1969, 30, 178. (c) Davies, C. G.; Gillespie, R. J.; Ireland, P. R.; Sowa, J. M. Can. J. Chem. 1974, 52, 2048. (d) Wilson, W. W.; Thompson, R. C.; Aubke, F. Inorg. Chem. 1980, 19, 1489. (c) Passmore, J.; Richardson, E. K.; Taylor, P. J. Chem. Soc., Dalton Trans. 1976, 1006.


2889

Jenkins et al. FIA(2SbF5,l) ) UPOT(XeFSb2F11) - UPOT(XeFSbF6) + ∆compH2° - ∆compH1° + FIA(SbF5,l) (17) It is seen that the term “UPOT(XeF2)” and the RT terms are thus eliminated, leaving only the terms UPOT (XeF+SbF6-) and UPOT (XeF+Sb2F11), which are known21b to be Figure 3. Cycle developed around target reaction for the estimation of FIA(mSbF5,l) showing mode of closure based on complexation enthalpy.

UPOT(XeF+SbF6-)/kJ mol-1 ) 537

(18)

UPOT (XeF+Sb2F11-)/kJ mol-1 ) 470

(19)

and by the exothermic (estimated to be -144 kJ mol-1)19 reaction SbF6-(g) + SbF5(g) f Sb2F11-(g)

(12)

in which the negative charge is delocalized over 11 as opposed to six fluorine atoms. The value of FIA(2SbF5,l) is calculated below, while the related FIA(Sb2F10,g) has been calculated to be -555.6 kJ mol-1 20 along with that for FIA(Sb3F15,g) ) -570.3 kJ mol-1,20 where Sb2F10(g) and Sb3F15(g) are molecular species in the gas phase. We can obtain (absolute) estimates of FIA(2SbF5,l), corresponding to the process 1 with m ) 2, and of the closely related ∆fH°(Sb2F11-,g): ∆fH°(Sb2F11-,g)

Sb(c) + 11/2F2(g) 98 Sb2F11-(g)

leading to the assignment of FIA(2SbF5,l)/kJ mol-1 ) -609 (+63)

(20)

pF-(2SbF5,l) ) 14.6 (+1.5)

(21)

and

Using this datum, we can then, further, estimate the standard enthalpy of formation, ∆fH°(Sb2F11-,g), of the Sb2F11gaseous anion (Figure 3, m ) 2), since ∆fH°(Sb2F11-,g) ) FIA(2SbF5,l) + 2∆fH°(SbF5,l) + ∆fH°(F-,g) (22)

(13)

using data for measured complexation enthalpies ∆compHm°/ kJ mol-1 (eq 14) ∆compHm°

XeF2(s) + mSbF5(l) 98 XeFSbmF5m+1(s) (m ) 1,2) (14) for the salts:9a XeFSbF6 (∆compH1°/kJ mol-1 ) -32) and XeFSb2F11 (∆compH2°/kJ mol-1 ) -99).9a We can regard reaction 1, which determines FIA(mSbF5,l), as being the target reaction and follow the stepwise procedure, this time adding XeF+ ions (instead of alkali metal ions) to both sides of the target reaction. This course is followed, since their exists no standard enthalpy of formation data for alkali metal Sb2F11- salts. The cycle of Figure 3 is then created for which the closure loop is reaction 14. We can write

giving ∆fH°(Sb2F11-,g) /kJ mol-1 ) -3520 (+63)

(23)

Fluoride Ion Affinity of 3 mol of SbF5 (l), FIA(3SbF5,l), and Standard Enthalpy of Formation of Gaseous Ion, Sb3F16-, ∆fH° (Sb3F16-,g). Using similar procedures (although restricted by paucity of data) to those outlined earlier (Figure 4) we can determine FIA(3SbF5,l) (corresponding to process 1 having m ) 3) by adding the Cs+(g) ion as the partner ions. We use the data UPOT(CsF) ) 744 kJ mol-1; UPOT(CsSb3F16), determined using eq 31a taking V(Cs+) ) 0.01882 nm3 (Table 4, ref 1a), V(Sb3F16-) ) 0.317 nm3 (Table 6, ref 1a),22 to be UPOT(CsSb3F16)/kJ mol-1 ) 441

(24)

FIA(SbF5,l) ) UPOT (XeFSbF6) + /2RT + ∆compH1° - “UPOT(XeF2)” (15)

with the experimental value of ∆fH°(CsSb3F16,s) as determined by Burgess, Peacock, and Sherry9a (Appendix 1) and also their value of ∆complex H° ) -304 kJ mol-1 for the reaction

FIA(2SbF5,l) ) UPOT(XeFSb2F11) + 3/2RT + ∆compH2° - “UPOT(XeF2)” (16)

CsF(c) + 3SbF5(l) 98 CsSb3F16(c)

3

A further strategy that can be employed, often to real advantage, in order to eliminate unknown or uncertain terms, is to (effectiVely) subtract one cycle from another (i.e., Figure 3 (for m ) 1) from Figure 3 (for m ) 2)). This corresponds to subtraction21a of eq 15 from eq 16 and leads to (19) Using the results obtained in this paper. (20) Dixon, D. A.; Christe, K. O. Private communication with H.D.B.J., October 2000.


∆complexH°

(25)

From the upper left-hand cycle in Figure 4 we find FIA(3SbF5,l)/kJ mol-1 ) -603, while the left-hand peripheral (21) (a) The XeF salts have strong interaction with the anion and so may have substantial covalent contribution so that the use of an essentially ionic model may not be totally applicable. However, since differences are taken, these contributions may, at least in part, cancel out. (b) Jenkins, H. D. B.; Schrobilgen, G. J.; Lehman, J. Manuscript in preparation. (22) Note misprint in ref 1a: Volume cited for the ion Sb3F14- should be for Sb3F16- (Table 6, column 1).


Figure 5. Cycle for NF4MFn salts. Table 7. Crystal Structure, Lattice Potential Energy, and Standard Enthalpy of Formation for NF4MFn Salts salt NF4BF4 Figure 4. Cycle developed around target reaction for the estimation of FIA(3SbF5,l) showing two modes of closure based (i) on complexation enthalpy (right-hand upper inner cycle) and (ii) on standard enthalpies of formation (right-hand peripheral inner cycle). The cycle for estimation of ∆fH°(Sb3F16-,g) is the right-hand cycle.

NF4SbF6

NF4AsF6

cycle leads to FIA(3SbF5,l)/kJ mol right-hand cycle predicts that ∆fH°(Sb3F16-,g)/kJ

mol

-1

-1

) -627. Use of the

) -4874 (+39)

a

(26)

The latter value used directly, with data from Appendix 1, predicts FIA(3SbF5,l) to be FIA(3SbF5,l)/kJ mol-1 ) -635 (+39)

(27)

and a value pF-(3SbF5,l) ) 15.2 (+0.9)

(28)

This is an interesting result, which has consequences for the predicted stability of Sb3F16- salts. Comparison of the difference between successive values of FIA(mSbF5,l) as m goes from 1 to 3 shows that, while the values for m ) 2 and m ) 1 differ by 103 kJ mol-1, those for m ) 3 and m ) 2 differ by only 26 kJ mol-1. The implication is that the values decrease asymptotically as m increases.23 Often a strategy used for the synthesis (and therefore stabilization) of a given cation in the form of a salt is to employ a strong Lewis acid to extract a halogen atom from a suitable precursor material. Comparison of FIA(pF-) values can aid the choice of suitable reagents.24 We shall consider values for FIA(4SbF5,l) and FIA(5SbF5,l) etc. in a following publication.25 Fluoride Ion Affinity of Arsenic Pentafluoride, FIA(AsF5,g). To estimate FIA(AsF5,g), we rely on the standard enthalpy of formation of NF4AsF6, which in turn means that we need to determine ∆fH°(NF4+,g). Estimation of the Standard Enthalpies of Formation of Gaseous NF4+, ∆fH°(NF4+,g). NF4BF4 and NF4SbF6 have (23) A similar effect was reported by Christe, K. O., and Dixon, D. A., at the 16th ACS Winter Fluorine Conference, “Discovering New Roles for Fluorine: From Enzymes to Microlithography”, January 12-17, 2003, TradeWinds Island Grand Beach Resorts and Conference Centre, St. Pete Beach, Fl (Abstract 53). (24) See, for example: Bernhardi, I.; Drew, T.; Seppelt, K. Angew. Chem., Int. Ed. 1999, 38, 2232. (25) Jenkins, H. D. B.; Passmore, J.; Krossing, I. Manuscript in preparation.

crystal structure a, c/nm, Za tetragonal, a ) 0.992, c ) 0.523 Z)4 tetragonal, a ) 0.796, c ) 0.584 Z)2 tetragonal, a ) 0.770, c ) 0.573 Z)2

V/nm3

UPOT/ kJ mol-1

∆fH° b/ kJ mol-1

0.129

568 ( 25

-1410 ((5)

0.185

516 ( 25

-1674 ((12) -1669 ((12)

0.170

527 ( 25

-1538 ((11)

Reference 14. b Reference 26a, 34.

been prepared, and the corresponding experimental standard enthalpies of formation, ∆fH°(NF4BF4,s), ∆fH°(NF4AsF6,s), and ∆fH°(NF4SbF6,s), have been measured26 (Appendix 1). The thermochemistry of this trio of salts provides us with a means of estimating the fluoride ion affinity of AsF5(g), FIA(AsF5,g). The standard enthalpy of formation of gaseous NF4+, ∆fH°(NF4+,g), is first estimated employing Figure 5, incorporating into the cycle appropriate lattice potential energy steps. Crystal structure data and results for estimates made, on this basis, for UPOT (NF4MFn) where MFn- is BF4-, SbF6-, or AsF6- are listed in Table 7. ∆fH°(NF4+,g), is predicted to lie in the range 879 (+25) e ∆fH°(NF4+,g)/kJ mol-1 e 927 (+59)

(29)

averaging to 903 (( 32) kJ mol-1, which can be compared to a previously published27 ab initio local density functional (LDF; scaling as N3)28 value of 881 kJ mol-1; a calorimetrically determined value26a (of 784 ((30) kJ mol-1) which, using the lattice energies in this paper, revises to +884 ((30) kJ mol-1; and a value derived26b from the calorimetric value of ∆fH°(NF4BF4,s)26c (of 854 ((40) kJ mol-1) and based on a lattice energy, UPOT(NF4BF4)/kJ mol-1, of 494, which revises to a value of +928 ((40) kJ mol-1 using the lattice energy value derived in this paper.26d,e Finally this can be compared with a roughly estimated value29 of 975 kJ mol-1. (26) (a) Bougon, R.; Bui Huy, T.; Burgess, J.; Christe, K. O.; Peacock, R. D. J. Fluorine Chem. 1982, 19, 263. (b) Goetschel, C. J.; Campanile, V. A.; Curtis, R. M.; Loos, K. R.; Wagner, D. C.; Wilson, J. N. Inorg. Chem. 1972, 11, 1696. (c) Sinke, G. C. Dow Chemical Co., private communication referenced in 26a. (d) It should be noted that the average of the ab initio result and the two calorimetric results gives ∆fH°(NF4+,g)/kJ mol-1 ) 898 ((50), close to the present value estimated. (e) Wilson, J. N. AdV. Chem. Ser. 1966, No. 54, 30. (27) Dixon, D. A.; Christe, K. O. J. Am. Chem. Soc. 1992, 114, 2978. (28) Parr, R. G.; Yang, W. Density Functional Theory of Atoms and Molecules; Oxford University Press: New York, 1989.


2891

Jenkins et al. Estimation of the Standard Enthalpy of Formation of Gaseous AsF6-, ∆fH°(AsF6-,g), and of the Fluoride Ion Affinity of Gaseous AsF5, FIA(AsF5,g). The standard enthalpy of formation ∆fH°(NF4AsF6,s) has been determined26a to be -1538 kJ mol-1 (Table 7). Using this value in Figure 5 (with MFn- ) AsF6-) leads to an estimate for the enthalpy of formation of the gaseous AsF6- ion, -1920 e ∆fH°(AsF6-,g)/kJ mol-1 e -1898

-412 e FIA(AsF5‚SO2,s)/kJ mol-1 e -368

(36)

averaging to be FIA(AsF5‚SO2,s)/kJ mol-1 ) -390 (+22) kJ mol-1 (37) and corresponding to a value pF-(AsF5‚SO2,s) ) 9.3 (+0.5)

(30)

(38)

Discussion

averaging to give ∆fH°(AsF6-,g)/kJ mol-1 ) -1907 (+22)

(31)

This value corresponds to a value for the FIA of AsF5 gas, FIA(AsF5,g), FIA(AsF6-,g)

AsF5(g) + F-(g) 98 AsF6-(g)

(32)

to be in the range -443 e FIA(AsF5,g)/kJ mol-1 e -399

(33)

averaging to FIA(AsF5,g)/kJ mol-1 ) -421 (+22)

(34)

pF-(AsF5,g) ) 10.1 (+1.5)

(35)

and

This is in reasonably close agreement with the MP2/PDZ values obtained by Christe and Dixon5a,20 (FIA(AsF5,g) ) -443 kJ mol-1; pF-(AsF5,g) ) 10.6) and reported earlier by ourselves3,30 (FIA(AsF5,g) ) -422 kJ mol-1; pF-(AsF5,g) ) 10.1) and with the value cited in Table 9 of ref 3 (FIA(AsF5,g) ) -419 kJ mol-1; pF-(AsF5,g) ) 10.0). Fluoride Ion Affinity of Arsenic Pentafluoride Solvate, AsF5‚SO2. FIA(AsF3‚SO2,s). Experimentally the AsF6anion precursor is often used in the solvent SO2.31, In this situation, an adduct is formed between the AsF5 and the SO2, to give a solid material AsF5‚SO2 that will accept a fluoride anion to yield the complex anion AsF6-. To reflect this experimental observation thermodynamically, it is necessary to consider the FIA of this solid adduct AsF5‚SO2, FIA(AsF5‚ SO2,s). The thermochemical cycles in Figure 6 are employed to estimate this parameter, which is found to be (29) As a check on the value obtained for ∆fH°(NF4+,g) we can consider the reactions NF3(g) f N(g) + 3F(g), for which ∆H/kJ mol-1 ) 3E(N-F) ) ∆fH°(N,g) + 3∆fH°(F,g) - ∆fH°(NF3,g) ) 472.704 + 3(78.99) - (-124.7) ) 834.4, giving E(N-F)/kJ mol-1 ) 278.1, where E(N-F) is the bond energy of the N-F bond; and NF2(g) f N(g) + 2F(g), for which ∆H/kJ mol-1 ) 2E(N-F) ) ∆fH°(N,g) + 2∆fH°(F,g) - ∆fH°(NF2,g) ) 472.704 + 3(78.99)-(43.1) ) 666.5, giving E(N-F)/kJ mol-1 ) 333.3. Thus, for the process NF4+(g) f N+(g) + 4F(g), ∆fH°(NF4+,g)/kJ mol-1 ) ∆fH°(N+,g) + 4∆fH°(F,g) - 4E(N-F) ) 1882.139 + 4(78.99) - 4E(N-F), leading to 864 e ∆fH°(NF4+,g)/kJ mol-1 e 1086, averaging to ∆fH°(NF4+,g)/kJ mol-1 ) 975 ((111). (30) See footnote 117 and Table 9 in ref 3. (31) Passmore, J.; Sutherland, G.; White, P. S. Inorg. Chem. 1981, 20, 2169.


Aside from the clear need to establish definitive quantitative data for the fluoride ion affinities considered in this paper, there is an important secondary interest. An important role is played by the halide ion affinity, HIA, in stabilizing salts. The more negative this term, the more thermodynamically favorable will be the target synthesis. The relative magnitude of the lattice energy term compared to HIA is also an important consideration. Accordingly, if the anion selected to stabilize a given Lewis acidic cation is relatively small in Volume (so having a relatively large lattice energy) and this is paired with an anion whose precursor has a large (exothermic) FIA, then the selected cation is more likely to be stabilized. The FIA data estimated in this paper can be used in this way to assess the thermodynamics governing the likelihood of being able to prepare and stabilize salts containing highly Lewis acidic cations with AsF6- and SbmF5m+1- and other anions. Our hope is that these principles will find use as part of the toolkit of every inorganic synthetic chemist. While the examples considered within this paper have been exclusively directed at the estimation of FIA data, it was stated in the Introduction that the techniques presented could be used to estimate other data. Electron affinity data, EA(X,g), of X(g) and corresponding to the process X(g) + e f X-(g); enthalpy of formation data, ∆fH°(X2-,g), of X2-(g) and corresponding to the process 1/2X2(ss) f X2-(g) where ss represents the standard

Figure 6. Cycles for the evaluation of FIA(AsF5SO2,s).


state of X2; and data for the double halide ion affinity, DHIA(MXn,p), of MXn(p) in phase p for the process MXn(p) + 2X-(g) f MXn+2-(g) can all be estimated using the approach described in this paper in a manner similar to the examples already cited. In the three cases, addition of one, two, and two A+(g) partner ion(s) in the respective cases and incorporation of lattice energy step(s) leads respectively to the following relationships: EA(X,g) ) UPOT(AX) + ∆fH°(AX,s) - ∆fH°(A+,g) ∆fH°(X,g) (39) ∆fH°(X2-,g) ) UPOT(A2X) + ∆fH°(A2X, s) 2∆fH°(A+,g) (40) DHIA(MXn,p) ) UPOT(A2MXn+2,s) - 2UPOT(AX,s) + ∆fH°(A2MXn+2, s) - 2∆fH°(A+,g) - ∆fH°(MXn,p) (41) which, in turn, permit estimation of the data. Thermodynamic Data Employed. In certain cases in this paper thermochemical values employed do not always correspond to those in the NIST database32 (see Appendix 1). This arises from the fact that in the original papers the thermodynamic data used (particularly in older references) relies on sources other than ref 32 (for example, that in ref (32) NIST Chemistry Webbook: http://webbook.nist.gov./chemistry/. (33) Wagman, D. D.; Evans, W. H.; Parker, V. B.; Schumm, R. H.; Harlow, I.; Bailey, S. M.; Churney, K. L.; Nutall, R. L. Tables of Chemical Thermodynamic Properties. J. Phys. Chem. Ref. Data 1982, 11, Suppl. 2. (34) Liass, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J. Phys. Chem. Ref. Data 1988, 17, Suppl. 1. (35) Karapet’yants, M. Kh.; Karapet’yants, M. L. In Thermochemical Constants of Inorganic and Organic Compounds; Schmarck, Ed.; J. Transl. Ann ArborsHumphrey Science Publ.: Ann Arbor and London, 1970. (36) (a) O’Hare, P. A. G.; Hubbard, W. N. J. Phys. Chem. 1965, 69, 4358. (b) Barin, I.; Knacke, O.; Kubaschewski, O. Thermodynamic Properties of Inorganic Substances; Springer-Verlag: Berlin, 1977; suppl. (37) See ref 17, page 473.

33), and consistency demands that we should use this data as the most appropriate set to use. The differences that arise by adopting this policy are, in any event, very small (especially considering the often large standard deviations it is necessary to quote in work of this kind). Appendix 1. Thermochemical Data Employed species AgSbF6(c) Ba[SbF6]2(c) CsSbF6(c) KAgBr4(c) KSbF6(c) LiSbF6(c) NF4AsF6(c) NF4BF4(c) NF4SbF6(c) Na+SbF6-(c) O2+(g) AsF3(l) AsF5(g) AsF5‚SO2(c) Ba2+(g) BF4-(g) SbF3(c) SbF5(l) SbF5(g) SO2(g)

∆fH°/kJ mol-1 -1622,13

S°298/J K-1 mol-1

-16229a

-426713 -20829a -96933 -2143,13 -20869a -206213 -153826a,34 -141026a,34 -167426a,34 -2110,13 -20549a 117133,35 -82133,35 -123736 -156537 166033 -1716,35 -1770,26b -178226e -91613 -13289a,26a -1301 (( 15)9a -29733,35

181.2133

105.435 26534 248.133

Acknowledgment. H.D.B.J. thanks David Dixon (Richland, WA), Leslie Glasser (Johannesburg, now Perth), and John S. O. Evans (Durham) for helpful discussions during the course of this work. H.K.R. thanks the EPSRC for their provision of a studentship and J.P. and the Department of Chemistry, University of Warwick, is thanked for a travel bursary. J.P. thanks the National Science and Engineering Research Council of Canada for an operating grant. H.D.B.J. acknowledges, with grateful thanks, EPSRC support. Ingo Krossing (Karlsruhe) is thanked for helpful discussions during the course of this work. IC0206544


2893

Estimation of Enthalpy Data for Reactions Involving Gas Phase Ions

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