1896
J . Phys. Chem. 1986, 90, 1896-1899 612 GI2
= ( 1 - k,z)(tllrzz)'/2
= (1
+j,J(GIl
( 14)
+ 'T2?)/2
( 5,
where k 1 2a n d j , , are deviation parameters to the geometric and arithmetic mean rules, respectively, which are usually obtained by fitting to suitable experimental values. The calculated excess enthalpies are very sensitive to the value of k I 2 . However, for Kr + Xe there is disagreement between the available experimental sets of results of and it seemed difficult to choose one of them to obtain k l z . W e decided instead to use the value k i 2= 0.019 used by Singer and Singer' in Monte Carlo simulations and by Gibbons25in perturbation theory calculations (25) Gibbons, R. M. J . Chem. SOC.,Faraday Trans. 2 1975, 71, 1929.
for Kr + Xe liquid mixtures, obtained in both cases by fitting to the experimental GEvalues of Calado and S t a ~ e l e y The . ~ deviation to the arithmetic mean rule was then chosen to give the best agreement of theory with our high pressure @ results a t 190.01 K. We obtained j , , = 0.004. Calado et aI.l3 used several theoretical models to compare with their vapor-liquid equilibrium results. Their j , , are in the range 0.0006-0.060. On the other hand, our calculations for Ar Kr mixtures4 using the vdw-l model give j , 2 = o.ooj, In view of the similaritiesof the two systems, Ar + Kr and Kr + Xe, our to be a reasonable result, j , , = o.oo4 Figures 3 and 4 show the kind of agreement we obtain between the vdW-l calculation and experiment, The good agreement is especially striking for AH' in Figure 4 . Registry No. K r , 7439-90-9; Xe, 7440-63-3.
+
Polyacene Dianion Heats of Generation and Solvation Gerald R. Stevenson* and Ramli Tamby Hashim Department of Chemistry. Illinois State University, Normal, Illinois 61 761 (Received: October I O , 1985; In Final Form: December 13, 1985)
-
Heats of hydration and heats of reaction with iodine have been used to experimentally determine the enthalpies of generation of a series of polyacene dianions in THF from sodium metal and the solvated hydrocarbon [AH' for A(THF) + Na(a) A2-,2Na+(THF)]. These heats of generation are all very close to -40 kcal/mol, indicating that entropy considerations, not electron affinities, account for the difficulty of formation of the smaller polyaromatic dianions. The heats of generation have been used in a thermochemical cycle to determine the enthalpies of solvation, including ion association, of these polyacene A2-,2Nat(THF)] in tetrahydrofuran (THF). These enthalpies dianions plus two sodium cations [AHofor A2-(g) + 2Nat(g) are all very large and negative and vary from -408 kcal/mol for A = pentacene to -444 kcal/mol for A = anthracene. These solvations are all more than twice as exothermic as those of the respective anion radicals. Further, a plot of the dianion solvation enthalpy vs. the anion radical solvation enthalpy is linear and has a negative slope. This plot predicts that the dianions of naphthalene and benzene in THF (both of which are unknown) would have been more exothermic heats of solvation than those of the other polyacenes.
-
Introduction Hydrocarbon dianions are unknown in the gas phase, and only one uncontested report of an organic dianion remains in the literature.' The reason that two electrons cannot be added to a 7~ electronic system is due to the very strong electron-electron (Table I). The values for Erepare identical repulsion energy (Erep) with the gas-phase disproportionation enthalpies for the corresponding anion radicals (A-.) (reaction l ) . 2 The enthalpy required 2A-*(g) + A2-(g) + A(g) AH,' = Erep (1)
-
to add two electrons to the neutral molecule (A) (reaction 2) is AH2' = Erep- 2EA A(g) + 2e-(g) A2-(g) (2) simply EFep minus twice the electron affinity (EA) of the neutral molecule. The best literature values for the electron affinities of a number of polyarornatics have been previously ~ e l e c t e dand ;~ when these are combined with the values for Erep, we can clearly see how very thermodynamically unfavorable it is to add two electrons to an aromatic hydrocarbon (Table I). If the gas-phase dianions were to be generated from the capture of an electron from sodium metal (reaction 3), the process would be 2 X 118.4 A(g) 2Na(g) A*-(@ + 2Nat(g) AH,O = Erep- 2EA 21P (3)
+
-
+
kcal/mol more endothermic than reaction 2 due to the ionization potential of sodium metaL4 O n the other hand, tetrahydrofuran (1) Bowie. J. €3.; Stapleton, B. J. J . Am. Chem. SOC.1976, 98, 6480. (2) Dewjar. M. J. S.: Harget. A,; Haselbach, E. J . Am. Chem. SOC.1969, 91. 7521. (3) Stevenson. G. R.: Schock, L. E.; Reiter, R. C. J . Phys. Chem. 1983, 87. 4004.
0022-3654/86/2090-1896$01.50/0
TABLE I: Thermodynamic Parameters for Polyaromatic Hydrocarbons and Their Anions (in kcal/mol)'
hydrocarbon benzene naphthalene anthracene tetracene pentacene pyrene perylene benzo[a]pyrene
EA -26.6 3.5 12.7 16.0 19 13.3 21.1 19.1
E,en AH', 162 127 117 107 99 108 100 I01
215 120 92 75 61 81.4 57.8 62.8
AH', 452 357 329 312 298 318 295 300
AH'sub
8.09 17.4 23.4 28.9 35 22.5 30 28.3
-3.2 -1 7
-I 2.5 --I 5 --2.7 --15 -1 5
"The values for EA and heats of hydrogenation were taken from ref 3 and those for EIepfroin ref I O . (THF) solutions of these dianions are thermodynamically and kinetically stable relative to the solid metal and solvated A as evidence dby their spontaneous formation and persistence. Clearly the solvation energy (including solvation) of the dianion plus that for the two cations must be exothermic enough to overcome Erep, IP, and the sublimation enthalpies. This statement is especially true considering the negative entropy change of reaction 3. The immense effect that solvation has upon the chemistry of dianions coupled with the fact that solvation enthalpies of organic dianions are completely unknown (except for that of the [8]annulene dianion)5 prompted us to carry out a study of the solvation of the polyacene dianions. Further, since the solvation enthalpies of the corresponding anion radials have already been r e p ~ r t e d the ,~ (4) Lotz, W. J . Opt. SOC.Am. 1967, 57, 873. ( 5 ) Stevenson, G. R.: Schock, L. E.; Reiter, R . C. J . Phqs. C h e m 1984, 88, 5417.
0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 9, 1986 1897
Polyacene Dianion Heats of Generation and Solvation 40
j
/
SCHEME I'
l
-+ - -
+ +
+
AH2(s) 2NaOH(aq) A2-,2Na+(THF) 2H20(1) -AHo,,, 2Na(s) 2H20(I) 2NaOH(aq) H2(g) -88.2 AHOh A(s) + Hz(g) AH2(s) A(THF) A(s) W O I " A(THF)
2Na(s)
+
A2-,2Na*(THF)
AHOgen
@Valuesin kcal/mol. SCHEME II'
+ + - -
2I-,Na+(THF) A(THF) Ids) IATHF) 12(s) 2Na(s) 2NaI(s) 2I-,Na+(THF) 2Nal(s) A(THF) 0
1
2
3
4
5
6
7
+ 2Na(s)
-
A2-,2Na+(THF)+ 12(THF)
AH',,,,, -4.2 h 0.2 -69.28 -2.4 h 0.5
A2-,2Na+(THF)
AHOgen
'Values in kcal/mol.
(Millimoles of Salt) x 10
70
Figure 1. Representative plots of the heat due to the reaction of the T H F dianion solvated salts with water (reaction 4) vs. the millimoles of salt in the glass bulbs. The slopes of these lines yield enthalpies of -64.9 f 1 . 9 , - 6 2 . 9 f 2 . 1 , - 5 9 . 6 i 2 . 1 , - 5 0 . 7 f 1 . 1 , 3 3 . 4 i 1 . 6 , a n d - 5 7 . 8 & 1.5 kcal/mol for the salts of anthracene, tetracene, pentacene, pyrene, perylene, And benzo[a]pyrene, respectively. These heats represent the enthalpies of reaction 4.
measurements of dianion solvation enthalpies would complete the picture that relates the neutral molecules, anion radicals, and dianions thermodynamically (disproportionation). It is well-known that the dianion of neither naphthalene nor benzene can be generated via sodium reduction in T H F . It is generally thought that this is due to the fact that these two compounds have the lowest EA'S and highest electron-electron repulsion energies of the polyacenes, and the dianion solvation energy is simply not great enough to overcome these two destabilizing effects. here, we wish to report that the solvation enthalpy of these two dianions is, indeed, large enough to overcome these intrinsic effects and that entropy considerations are responsible for the elusive nature of these two dianions. It has been previously found that the solvation enthalpies of the separated polyacene anion radicals and sodium cations become In fact, less negative as the size of the anion radical is decrea~ed.~ a nearly linear relationship has been found between the total R energy of the polyacene and the solvation enthalpy of the gas-phase anion radical and sodium ~ a t i o n . We ~ were interested to see whether we could find a relationship between the anion radical solvation enthalpies and that for the dianions. Such a relationship was found, but it was not the expected result. It should be pointed out here that the term anion radical (or dianion) plus cation solvation enthalpy refers to the heat generated upon plunging the separated gas-phase anion and cation into a solvent and allowing the system to come to equilibrium. The state of the resulting solvated ions often consists of ion associated species. Thus, in this sense, the solvation enthalpy of the gas-phase separated ions includes the heat of ion association.
Results and Discussion Crushing thin-walled glass bulbs containing T H F solutions of the sodium salts of polyacene dianions under 100 mL of water in our calorimeter system resulted in an immediate rise in the temperature of the calorimeter. After the heat generated from the aquation of the H F was subtracted, plots of the change in the heat content of the calorimeter vs. the millimoles of dianion salt were constructed. These plots were found to be linear (Figure l), and the slopes represent the enthalpies of reaction 4 ( A P r m ) . A2-,2Na+(THF)
+ 2H20(1)
-
AH,(s)
+ 2NaOH(aq)
(4)
These enthalpies of reaction can be combined with the heat of reaction of sodium metal with water (-44.1 kcal/mol),6 the heat of hydrogenation of the polyacene (AHoh),'and the heat of so(6) Gunn, S. R. J . Phys. Chem. 1967, 71, 1386.
A
60 50
-
411
L 0
36 20 10
E (water)
0
0
1
2
3
4
5
6
7
mmoles of d l a n l o n
Figure 2. Plots of the heat of the change in the heat content of the calorimeter for the reaction between the T H F solvated dianion of perylene with water (smaller slope) and with iodine (larger slope). The slopes of these lines (-33.4 and -97.2 kcal/mol, respectively) represent the enthalpies of reactions 4 and 6, respectively. Although the two reactions have very different enthalpies, they both yield the same enthalpy (within experimental error) of generation of the dianion from the metal and solvated hydrocarbon.
lution of the hydrocarbon in THF, as shown in Scheme I, to yield the heat of generation of the solvated dianion from the metal and solvated polyacene (reaction 5). A(THF)
+ 2Na(s)
-
A2-,2Na+(THF)
AHogen(5)
These heats of generation can also be obtained by crushing the glass bulbs under 100 mL of dry THF containing 0.6 g of I,. This reaction results in a much more dramatic increase in the temperature of the calorimeter (Figure 2), which is due to reaction 6. A2-,2Na+(THF) + 12(THF)
-
21-,Naf(THF)
+ A(THF) (6)
When the heat of reaction 6 is combined with the heat of formation of Na18 and the heats of solution of NaI and I, in T H F as shown in Scheme 11, the heats of generation of the T H F solvated dianions are generated (Table 11). It is clear from Table I1 that the heats of generation that are calculated from reaction 4 and Scheme I are well within experimental error of those determined from reaction 6 and Scheme 11. All of the polyaromatic dianions used in this study have heats of generation that are very similar in magnitude. Further, these enthalpies are about the same as the heat of reaction of sodium metal with water. Since the generation of the gas-phase dianion salts is extremely endothermic (7) Shaw, R.; Golden, D. M.; Bensen, S . W. J . Phys. Chem. 1977, 81, 1716. (8) Suttle, J. F. In "The Alkali Metals", Comprehensiue Inorganic Chemistry; Sneed, C . , Brasted, R. C., Eds.; Van Nonstrand: New York, 1957; Vol. VI.
1898 The Journal of Physical Chemistry, Vol. 90, No. 9, 1986
Stevenson and Hashim
TABLE II: Enthalpies of Reaction (AH",,) of THF Solvated Dianions with Water and Iodine and the Heats of Generation (j.Hogen) of These Dianions in THF from Na and the THF Solvated Neutral Hydrocarbon (in kcal/mol)
__
AH',,, uith
AHogenfrom rxn w i t h
water
- - __ iodine
-64.9 f 1.9
--99.5 f 4.4
dianion
._ --
-50.7 f 1.1
-101.4 f 3.1
--40.2 f 1.2
-41.1 f 3.2
-33.4 f 1.6
-97.2 f 2.7
-46.1 f 1.7
-47.1 f 2.8
A2-,2Nat(THF) AHoaub
-
-44.5 f 1.7
TABLE III: Enthalpies of Dianion Solvation ( AHololv,2-), Dianion and Dianion Solution (AHo,h,2-), Hydrocarbon Solution (AHoloIn,J, Generation from the Solvated Hydrocarbon and Solid Metal -51.8" -236.gb -(Erep- 2EA)
+ A2-(g)
-41.6 f 4.6
-40.3 f 2.2
2Na(g) 2Na(s) 2Na(g) 2Na+ 2e-(g) A(g) + 2e-(g) A2%J 2Na+(g)
-40.3 f 2.0
-59.6 f 2.1
A(s) -* A(THF) A(g) -* A(s)
- + -
iodine
-37.8 f 2.2
SCHEME IIId
+ 2Na(s) --
water
--62.9 f 2.1
-57.8 f 1.S
A(THF)
.
I
AZ-,2Na+(THF)
AH0sol".2-C
"Reference 15. Reference 16. When these gas-phase ions are put into T H F and allowed to equilibrate, the resulting solution contains the dianion associated with two cations. Thus, this ion association is part of the solvation process. Values in kcal/mol.
due to the large ionization potential of sodium and the strong electron-electron repulsion in the resulting dianions, the solvation enthalpies of these dianion salts must be very negative. The actual solvation enthalpies of these gas-phase salts can be calculated with reasonable reliability by including reaction 3 in a thermochemical cycle with the heats of generation (Scheme 111). The heat of reaction 3 is based, in part, upon the calculation of Erep.The calculation of Erepis based upon the method of Hush and Blackledge, which is now three decades old.9 However, since the idea is so simple, the only contributions are the electron distribution of the first added electron and the Coulombic repulsion exerted by it on the incoming second electron; it does yield values that are almost identical with those obtained via much more sophisticated means as M I N D 0 II.2%10 From Table I11 it is clear that the magnitudes of the solvation decrease with the size of enthalpies for the dianions (AHosolv,Z-) (9) Hush, N. S.; Blackledge, J. J . Chem. Phys. 1955, 23, 514. (10) (a) Stevenson, G. R.; Zigler, S. S.;Reiter, R. C. J . Am. Chem. SOC. 1981, 103, 6057. (b) The structures of the organic reaction products for the
reaction products of the perylene (I) and pyrene dianions (11) with water are abbreviated in ref 10. They should be as follows:
(AH"..Ja ~
AHasolv.2 ~ H 0 s o , n2-
hydrocarbon naphthalene anthracene tetracene pentacene pyrene perylene benzo[a]pyrene
-444 -410 -408 -432 -439 -424
f3 i3 f3 f2 f2 f3
~HO,,,n A AHOgen +O 52 f 0 03 -14f4C +O91fO04 -4034~15 -13 f 4 +Ob -37 8 f 1 4 -8 f 3 Ob -40 3 f 1 6 -16f4 +O19fO02 -4024~12 -9 f 3 +Ob 46lf15 12 f 4 Ob 445f11
"Errors were propagated from the standard errors in the slopes of the lines obtained from Figure 2, and the errors were reported in the measurements in the literature values used. bThe solubilities and enthalpies for these neutral compounds were too close to zero to be measured. 'These heats of solution are small quantitites that result from the difference between two large numbers (the solvation enthalpies and crystal lattice e n e r g i e ~ ) ~Thus, , ' ~ they do have relatively large errors.
__
~. -.
._
- - - ...
,> . 4 4
E
440
w L
0 b5
>
0 _1 (o
420
L
0 z Q
e
400 170
180
190
2016
-(ANION RADICAL SOLVATION ENTHALPY)
Figure 3. Plot of minus the dianion solvation enthalpies vs. minus the anion radical solvation enthalpies for a series of polyacene substrates. The slope and the intercept of the lines are -2.8 f 0.2 and 951 f 1 I , respectively, and the correlation coefficient is 0.9856.
I
I1
the hydrocarbon. Surprisingly, this is exactly the opposite of that observed for the anion radicals of these same polya~enes.~ Indeed, a simple plot of the enthalpy of solvation of the dianion vs. that
Polyacene Dianion Heats of Generation and Solvation
The Journal of Physical Chemistry, Vol. 90, No. 9, 1986 1899
under high vacuum as previously described.I0J3 The heats of reaction of these dianion solutions with both H 2 0 and with I2 were measured. Reaction of Dianions with Water. The dianion solutions were then placed into glass bulbs,I0 which were broken under 100 mL of water in the ca10rimeter.I~ The output from the calorimeter was fed directly into a 64K computer system by Digital. After the reaction (reaction 4; they are all listed in Ref 10) the contents of the calorimeter were titrated with standardized HCl to obtain the amount of dianion in the bulbs. To obtain the heats due to the reactions of the dianions with the water, it was first necessary to subtract out the heat due to the aquation of the solvent. This process has been previously described along with the calibration kcal/mo13 suggests that the dianion solvation enthalpy is -465 of the ~ a l o r i m e t e r . ~The ~ , ' ~dianion of the lithium salt of naphkcal/mol. With this solvation enthalpy, we can utilize Scheme thaleneI4can be readily generated in T H F via exhaustive reduction 111 in reverse to obtain the heat of generation of this unknown with the metal. However, exhaustive reduction of naphthalene dianion-ion pair. This simple calculation leads to a value of -37 with N a in T H F does not yield detectable amounts of the dianion. kcal/mol for reaction 7. These results are consistent with the For the large polyacenes, we carried out the metal reduction until earlier statement that all of the generation heats are about -40 the ESR signal was lost, indicating complete reduction of the anion kcal/mol, but they leave use with the surprising fact that the radical to dianion. The narrow N M R lines for the dianions (all NP2-,2Na+(THF) does not form spontaneously despite its very of the dianions reported here have well-characterized N M R exothermic heat of generation. spectra), the lack of an ESR signal, and the fact that the only It appears that the smaller polyacene dianions have more organic compound found in the calorimeter after the reaction was negative solvation enthalpies and simultaneously more positive the dihydropolyacene convinced us of the integrity of the dianion values for the enthalpy of addition of two electrons (AH",).These solutions. Further, the addition of water to either the solvated two effects, one stabilizing and the other destabilizing, cancel each dianions or the solid dianion salts does not yield detectable amounts other leaving the heat of generation almost independent of the of hydrogen gas. substrate. The reason that the dianions of the smaller polyacenes Reaction of Dianions with Zodine. The same calorimeter system (those of benzene and naphthalene) do not form spontaneously was charged with 100 mL of dry T H F containing 0.6 g of I,. The with sodium in THF is due to the very negative entropy for glass bulbs containing the THF-dianion solutions were crushed reaction 5 . This entropy of generation grows more negative as under this solution in the calorimeter. The increase in the temthe size of the electron host decreases. For both the benzene and perature of the calorimeter was due to the reaction of the dianion naphthalene dianions, the entropy term dominates. Similarly, the with the iodine (reaction 6). Plots of the change in the heat content solvation enthalpy for the benzene dianion is established to be -482 of the calorimeter vs. the millimoles of dianion in the bulbs are kcal/mol. linear (Figure l), and the slopes of these lines represent the Keeping in mind that AHosolv,2incorporates two processes, enthalpy of reaction 6. For each separate dianion generation reaction 8 and 9, it would be nice to known what fraction of this several bulbs were sealed from the apparatus containing the bulk dianion solution. One of these bulbs was broken under water in AZ-(THF) + Na+(THF) (8) A2-(g) + 2Na+(g) a beaker. Titration of the beaker contents with HC1 yielded the A'-(THF) Na+(THF) A2-,2Na+(THF) (9) amount of dianion in the bulb. The concentrations of the dianion solution in this bubl was considered to be the same in each of the value is accounted for by these two processes. The enthalpies for bulbs harvested from the same bulk solution. these reactions are unknown, and at present there is no experiAny protic material, as water, contaminating the T H F and I, mental technique for obtaining them. Howver, Streitwieser and in the calorimeter would result in the presence of the dihydroSwanson" have shown that the close proximity of the two positive polyacene in the calorimeter after the reaction. When freshly charges can compensate for a major portion of the electrondistilled T H F (distilled from the benzophenone ketyl) was utilized electron repulsion. and the calorimeter was maintained under a N 2 atmosphere prior Finally, it should be shown that the results given in Figure 2 to and during the reaction, only the polyacene itself was formed also allow the determination of the anion radical disproportionation in the calorimeter. enthalpies (AHodisp) in T H F . Since the only difference between Heats of Solution. The heats of solution of NaI, I,, and the disproportionation in the gas and solvated states is the heats of dianion (AHosolv,~), polyacenes in T H F were measured by simply breaking sealed bulbs solvation of the anion radical (AHosolv,-.), containing these substances under THF in the calorimeter system. and neutral molecule (AHosolv,A), eq 10 yields these disproporThe change in the heat content of the calorimeter was considered tionation enthalpies. A major problem with eq 10 is that the result to be due to the dissolution of the substance. Since all of the enthalpies of solution and of reactions 4 and 6 result from the slopes of linear plots, the errors reported represent the standard conies from a small difference between very large numbers, which deviation in the slopes of these lines. These lines were generated should lead to considerable error. Despite this consideration, from solutions that ranged from 0.09 to 0.14 M in dianion. AZ3OdiSpis predicted to be 6 and 12 kcal/mol for the anthracene and perylene dianions. The reported values for these disproAcknowledgment. We thank the National Science Foundation portionation heats are 7 and 27 k ~ a l / m o l . ' ~ J ~ ~ (Grant No. CHE-8411827) for support of this work.
of the anion radical (AHowlv,-.)is close to linear and has a negative slope of -2.8 and a y intercept of -951 (Figure 3). This result is coupled with the fact that all of the heats of generation of the dianions from the solvated polyacenes and solid metal (reaction 5) are very close to -40 kcal/mol. The dianion of naphthalene cannot be formed via sodium reduction in T H F . However, the relationship exhibited in Figure 2 allows the determination of the solvation enthalpy for this unknown dianion. The anion radical solvation enthalpy of -172.5
+
-
-+
Experimental Section The polyacene dianion solutions were generated via exhaustive reduction of the polyacene in THF with a sodium metal mirror (1 1 ) Streitwieser, Jr., A,; Swanson, J. T.J . Am. Chem. SOC.1983, 105, 2502. (12) (a) Jachimowicz, H. C.; Wang, G. L.; Szwarc, M. J . Pkys. Chem. 1978,82, 1378. (b) Wang, H. C.; Levin, G.; Szwarc, M. J . Am. Chem. SOC. 1977, 99, 5056. (13) (a) Stevenson, G. R.; Forch, B. E. J . Am. Chern. SOC.1980, 202, 5985. (b) Stevenson, G. R.; Williams, Jr., E.; Caldwell, G . J. Am. Chem. Soc. 1979, 101, 520.
Registry No. THF, 109-99-9; I,, 7553-56-2; Na, 7440-23-5; NaI, 7681-82-5; [anthraceneI2-2Na+, 11065-56-8; [tetraceneI2-2Na+,1 106761-1; [pentaceneI2-2Na+, 67073-58-9; [pyreneI2-2Na+, 60836-61-5; [pery1enel2-2Na+, 11068-26-1; [ben~o[a]pyrene]~-2Na+, 7941 2-1 1-6; naphthalene, 91-20-3; anthracene, 120-12-7; tetracene, 92-24-0; pentacene, 135-48-8; pyrene, 129-00-0; perylene, 198-55-0; benzo[a]pyrene, 50-32-8. (14) Smid, J. J . Am. Chem. SOC.1965, 87, 655. (15) Hicks, W. T.J . Chem. Phys. 1963, 38, 1873. (16) Lotz, W. J . Opt. SOC.Am. 1967, 57, 873.
