Communications to the Editor
The Journal of Physical Chemistry, Vol. 83, No.
paper than in terms of 3d orbital participation.
Molecular Orbital Theory of Organic Chemistry", McGraw-Hill, New York, N.Y., 1969. The energy variation associated with the interaction of a doubly occupied MO, pl, with a singly occupied MO, p2,usually amounts to a stabilization energy when the energy difference between the two interaction MO's is small; however upon increasing the energy gap, the stabilizlng effect decreases becomingeventually destabilizing when the energy gap is large. For details see F. Bemardi, N. D. Epbtis, W. Cherry, H. B. Schlegel, M. H. Whangbo, and S. Wolfe, J . Am. Chem. SOC.,98, 469 (1976). See N. D. Epiotis, J. Am. Chem. Soc., 95, 3087 (1973), and references therein. F. Bernardi, A. Mangini, N. D. Epiotis, S. Shaik, and J. R. Larson, J . Am. Chem. Soc., 99, 7465 (1977). C. C. Price and S. Oae, "Sulfur Bonding", Ronald Press, New York, 1962. For a recent review of this problem see A. Mangini, Mem. Accad. Lincei, 14, Sez. I1 (1977). F. Bernardi, I. G. Csizmadia, A. Mangini, H. 8. Schlegel, M. Whangbo, and S.Wolfe, J . Am. Chem. Soc., 97, 2209 (1975). E. L. Wehry, J . Am. Chem. Soc., 89, 41 (1967).
(8)
References and Notes (1) H. Forest and 6. P. Dailey, J. Chem. Phys., 45, 1736 (1966); T. Pedersen, N. W. Larsen, and L. Nygaard, J. Mol. Struct., 4, 59 (1969); H. D. Bisi and D.R. Williams, Bull. Am. Phys. Soc., 11, 826 (1966). (2) N. W. Larsen and F. M. Nicolaisen, J . Mol. Struct., 22, 29 (1974). (3) W. J. Hehre, L. Radom, and J. A. Pople, J . Am. Chem. SOC.,94, 1496 (18172). (4) W. J. E. Parr and T. Schaefer, J . Magn. Reson., 25, 171 (1977). (5) F. Bernairdl, N. D Epiotis, R. Yates, and S. Wolfe, J . Am. Chem. Soc., 98, 5435 (1976). (6) F. Bernardi, M. Guerra, and G. F. Pedulli, Tetrahedron,34, 2141 (1978). (7) The energy stabilization associated with the interaction of an occupied MO, p,, with a vacant MO, (p2, is given by
(9) (10) (11)
AqZ = NHiz - c~Hid*/(ci- 4
(12)
where ndenotes the orbital occupation, el and c2 the orbital energies of the two interacting MO's, S,,their overlap integral, and HI, their matrix element. For details, see for instance M. J. S. Dewar, "The
(13) (14)
5, 1979 643
COMMUNICATIONS TO THE EDITOR Anion Radical Solvation Enthalpies Publication costs assisted by the Petroleum Research Fund
Sir: The capture of a free gas phase electron by a gaseous acceptor (A) to yield the solvated anion radical (A*-) is much more exothermic than the same reaction to form the gas phase anion radical, the difference being the enthalpy of the anion radical. The comof solvation (Dslosolv) manding role of anion solvation in controlling the thermodynamic stabilities of organic anions was demonstrated by the classic observations of Brauman and B1air.l Despite the obvious importance of solvation enthalpies in controlling the stabilities and chemistry of organic anion radicals, no experimental solvation enthalpies for these species have lbeen reported except for a single attempt to correlate the threshold of photoejection of an electron from a rhodium electrode into hydrocarbon solutions of acceptors with their solvation energiesa2 However, Hush and Blackledge3 carried out a series of MO calculations which were used in conjunction with Born-type interaction terms to estimate the solvation heats for several anion radicals, including anthracene, which in tetrahydrofuran (THF) yielded a value of --18 kcal/mol for AHosolv.Here, we report an experimental determination of the solvation enthalpies of the anthracene anion radical in T H F and hexamethylphosphoramide (HMPA) and show that the estimations of Hush and Blackledge are very high. Since it is well established that the exclusive organic reaction product resulting from the addition of water to the anthracene anion radical in a variety of solvents is 9,10-dihydroanthra~ene,~ this reaction was utilized to obtain the relative heats of formation of the anthracene anion radical in the gas phase and solvated in T H F and HMPA. The possibility of the evolution of hydrogen gas from the reaction of the solvated anthracene anion radical with water was eliminated by pumping any gaseous products into a calibrated gas buret with a Toepler pump as previously d e ~ c r i b e d . The ~ fact that no gas phase products could be detected means that at least 99.9% of the reaction leads to protonation of the anthracene anion radi~al.~ 0022-3654/79/2083-0643$0 1.OO/O
TABLE I: Calorimetric Data for t h e R e a c t i o n of AN', in HMPA with Watera AT AT HMPA due t o due t o amount , [AN-.], HMPA, AN-., A Ttot , mmol "C "C "C g ~0.871 1.389 1.462 0.894 0.818 0.709 1.183 1.069 1.280 0.936
0.475 0.785 0.806 0.483 0.460 0.339 0.561 0.310 0.372 0.276
0.582 0.918 0.976 0.596 0.543 0.470 0.780 0.655 0.770 0.573
0.467 0.740 0.779 0.479 0.439 0.381 0.632 0.571 0.680 0,501
0.115 0.178 0.197 0.117 0.104 0.089 0.148 0.084 0.090 0.072
a The calibration factor for the calorimeter is -119.3 kcal/deg. Multiplying this factor by the slope yields the enthalpy.
T H F and HMPA solutions of the anthracene anion radical were sealed into evacuated thin-walled glass bulbs, which were placed into the cell of a Parr solution calorimeter and broken under 100 mL of deoxygenated water with a push rod. The change in the temperature of the calorimeter is due to the heat of reaction of the anion radical with water and the heat of aquation of the HMPA or THF. The heat of aquation of the HMPA and T H F can be subtracted out after carrying out the measurements with pure HMPA or T H F in the glass bulbs (Table I). The remaining heats are due to the reactions with wellestablished stoichiometries4depicted in eq 1 and 2, where 2AN-.,Na+ + 2H20 AN + ANHz 2Naaq++ 20H,;
-
-
+
(1)
2AN-- + 2Na'+ + 2Hz0 AN + ANHz + 2Naaq++ 20Haq- (2) the only hydrocarbons present in the calorimeter are anthracene (AN) and 9,lO-dihydroanthracene (ANHz). It must be remembered that in HMPA the anthracene anion radical is free from counterion association, and in the THF it is ion paired with the counterion (Na+).6 0 1979 American
Chemical Society
The Journal of Physical Chemistry, Vol. 83,No. 5, 1979
644
0.4
Communications to the Editor
of solution of the sodium cation in this solvent is -108 kcal/mol,12 the single ion heat of solvation of the anthracene anion radical can be obtained. Subtracting -108 from the enthalpy of the reaction shown in eq 4 yields a value of -60 kcal/mol for the solvation enthalpy of AN-. in HMPA, eq 5. This is much more exothermic than was
1
AN-.,
0.6
0
1.2
m o l e s of anion radical
Flgure 1. Plots of the change in the temperature of the calorimeter vs. the mmoles of salt sealed in the glass bulbs. The temperature change due to the water-THF and water-HMPA interaction has been subtracted out. The mmoles of anion radical salt in the bulbs were determined by titrating the calorimeter contents with standardized HCI solution. The line given by 0 represents the HMPA solutions, and the line given by 0 represents the THF solutions. The slopes of the two lines are within experimental error of each other.
TABLE 11: Enthalpies of Reaction
AH", reaction
ANH,
kcal/mol
t ANsomt 2NaOHaq -+ ~ A N - * H M ~ A~ N ~ + H M tP 2H,0uq A 2Nao,u t 2H,0xq-+ 2NaOHaq t H, 2Nag -+ 2Na0,m 2Na+, t 2e-g-+ 2Nag ANsolid t H2g* A"zsolid 2 A N g -+ 2ANs01i, 2AN-., -+ 2AN, t e-,
AN-*, t Na+,+
+
AN-.HMPA
+ Na'HMpA
-88.2 -51.8 - 236.8
- 17 - 23,4 t 25.4 -168.1
*
Plots of the change in the temperature of the calorimeter, minus that due to the solvent (AT due to AN-.), vs. the mmoles of anion radical in the glass bulbs are linear (Figure l),and the slopes of the lines are proportional to the enthalpy of the reactions shown in eq 1 and 2. The enthalpies for the reactions depicted in eq 1 and 2 are -28.9 f 0.3 and -27.8 f 0.5 kcal/mol of anion radical, respectively. If these two enthalpies are combined with the heat of reaction of sodium metal with water,7 the heat of vaporization of sodium metal,8 the ionization potential of s ~ d i u mthe , ~ heat of hydrogenation of anthracenelO the heat of vaporization of AN,11 and the electron affinity of AN1* in a thermochemical cycle, the enthalpies for the reactions shown in eq 3 and 4 are found to be -167.0 and -167.0 kcal/mol, respectively (Table 11). AN-., + Na+, AN--,Na+THF (3) AH" = -167.0 f 3 AN-., + Na+, AN-*HMpA + Na'HMpA (4) AH" = -168.1 f 3 It is of interest to note that despite the large difference in the two solvent systems and the fact that the ions are in different states of aggregation, the two enthalpies are within experimental error of each other. Since the ions are free from association in HMPA and the single ion heat +
AN-sHMpA
AHo = -60 f 6
(5)
expected. Although HMPA is known to be an excellent solvent for anion radical formation with alkali metals due to its ability to solvate cations,13it has long been believed that anions remain practically unsolvated in this solvent due to steric hindrance around the electropositive phosphorus center.14 This is clearly not the case. In fact, the heat of solvation of the anthracene anion radical in HMPA is about 56% of that for the sodium cation. From our study, it is not possible to determine single ion heats of solvation for the anthracene anion radical in THF, as AN-. is always associated with the cation. However, from the work of Hirota15 and others it is clear that the ion association enthalpy for the anthracene anion radical with Na+ in T H F is no larger than 10 kcal/mol. Thus the sum of the solvation heats for AN-. and Na+ must be less than -157 kcal/mol. We do not have a strong argument as to why the estimation of the solvation energy of Hush and Blackledge appear to be much to high, but it would appear that the polarization of the T H F molecule in the proximity of the anion radical is much greater than can be accounted for by their simple electrostatic model.
t 55.6
a By propagating t h e errors in t h e various measurements, t h e f i n a l error is estimated t o b e a b o u t 3 k c a l / m o l .
-
+
Acknowledgment. We thank the Donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this work.
References and Notes (1) J. I. Braumann and L. K. Blair, J. Am. Chem. Soc., 92, 5986 (1970). (2) A. Prock, M. Djobelian, and S. Sullivan, J . fhys. Chem., 71, 3378 (1967). (3) N. S. Hush and J. Blackledge, J . Chem. fhys., 23, 514 (1955). (4) (a) A. Rainis, R. Tung, and M. Szwarc, J. Am. Chem. Soc., 95, 659 (1973); (b) E. R. Minnich, L. D. Long, J. M. Ceraso, and J. L. Dye, ibid., 95, 1061 (1973); (c) S. Bank and B. Bockrath, ibid., 94, 6076 (1972). (5) G. R. Stevenson, I. Ocasio, and A. B. Bonilla, J . Am. Chem. Soc., 98, 5469 (1976). (6) A. Cserhegyi, S. Kume, J. Jagur-Grodzinski, and M. Szwarc, J . Am. Chem. Soc., 89, 7129 (1967). (7) S. R. Gunn, J . fhys. Chem., 71, 1386 (1967). (8) W. T. Hicks, J . Chem. fhys., 38, 1873 (1963). (9) W. Lotz, J . Opt. Soc. Am., 57, 873 (1967). (10) (a) The heat of hydrogenation of anthracene was calculated from the heats of combustion of anthracene and 9,lOdihydroanthracene. The enthalpy for AN 4- H, ANH, is -17.0 kcal/mol.8b (b) J. D. Cox and G. Pilcher, "Thermochemistry of Organic and Organometallic Compounds", Academic Press, London, 1970. (11) (a) L. H. Thomas, J . Chem. Soc., 2132 (1959); (b) R. S. Becker and E. Chen, J . Chem. fhys., 45, 2403 (1966). (12) (a) Based upon an extrathermodynamic assumption (TATB assumption) the single ion heat of solvation for the potassium cation in HMPA is -93.6 kcal/mol.'Ob By firing both the potassium and sodium salts in the calorimeter, the single ion heat of solvation of Na' can be calculated.'& (b) B. G. Cox and A. J. Parker, J. Am. Chem. Soc., 95, 402 (1973); (c) W.Martir, A. E. Alegria, and G. R. Stevenson, ibid., 98, 7955 (1976). (13) G. Levin, J. Jagur-Grodzinski, and M. Szwarc, J . Am. Chem. Soc., 92, 2268 (1970). (14) H. Normant, Angew. Chem., Int. Ed. Engl., 6, 1046 (1967). (15) N. Hirota, J . fhys. Chem., 71, 127 (1967). (16) E. M. Arnett, D. E. Johnston, and L. E. Small, J . Am. Chem. Soc., 97, 5600 (1975).
-
Department of Chemistry Illinois Sfa te University Normal, Illinois 6 176 1
Gerald R. Stevenson" Gary Caldwell Elmer Wllllams, Jr.
Received August 8, 1978; Revised Manuscript Received November 7, 1978
