J . Phys. Chem. 1986, 90, 1892-1896
1892
Thermodynamic Properties of Liquid Mixtures of Krypton and Xenon J. C. G. Calado, H. J. R. Guedes, M. Nunes da Ponte,* L. P. N. Rebelo, and W. B. Streettt Centro de Quzmica Estrutural, Complexo 1 , 1096 Lisboa Codex, Portugal (Received: August 27, 1985, In Final Form: December 9, 1985)
The equations of state of liquid krypton and liquid xenon and of approximately equimolar mixtures were measured at four temperatures between 180 and 195 K, from just above the saturated vapor pressure up to 70 MPa. Similar studies were performed at 190 K for two other mixtures of krypton mole fraction 0.319 and 0.707. The excess volumes p are negative at low pressures, but increase rapidly with pressure, becoming almost zero at high pressures. There is a very asymmetric dependence of p on composition at low pressures, with a minium in the vs. x curves displaced to the krypton-rich side. As pressure is applied, these curves become more symmetric. The changes of the excess thermodynamic properties with pressure were calculated at 185 and 190 K. The excess Gibbs energies GE are much less sensitive to pressure and temperature than the excess enthalpies HE or the product of temperature by the excess entropies TSE.The experimental results are well reproduced by conformal solution theory (van der Waals one-fluid model).
Introduction The measurements reported in this paper were obtained in the course of a program to investigate the effect of pressure on the thermodynamic properties of liquid mixtures of condensed gases. Previous studies of the binary systems nitrogen methane,l argon methane,* argon n i t r ~ g e n argon ,~ k r y p t ~ n krypton ,~ methane,5 and carbon monoxide methane6 have already been published. Mixtures of krypton and xenon are of considerable fundamental importance. Consisting of simple, monatomic molecules, their properties should be accurately predicted by any successful theory of liquid mixtures. Several theoretical and computer studies of this system include the Henderson and Barker' perturbation theory calculations of the excess thermodynamic properties, at 161.38 K, and the Singer and Singer* Monte Carlo computer simulations. Experimental studies on liquid mixtures of krypton and xenon are the following: the excess Gibbs energy GE and excess volume p measurements of Calado and Staveley9at 161.39 K; the results of Chiu and Canfield,Io at the same temperature; the excess enthalpy HE results of Staveley, quoted by Azevedo et al.," and of Adams;' the vapor-liquid equilibrium measurements of Calado et aI.,I3 at temperatures close to the critical region. As far as we know, no high-pressure density measurements have been attempted for this system. We performed pVT measurements on pure krypton, pure xenon, and approximately equimolar mixtures at four temperatures between 180 and 195 K and on two other mixtures of krypton mole fraction 0.319 and 0.707, at 190 K. These provide information on the asymmetry of the vs. composition curve, while the measurements at four different temperatures allow for an accurate calculation of the derivative ( 6 p / 6 T ) , necessary for the calculation of the effect of pressure on the excess enthalpy and the excess entropy SE. Conformal solution theory in the van der Waals one-fluid form of Leland et aI.l4 gave good agreement with our experimental results.
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Experimental Section The apparatus used for the pVT measurements was described by Barreiros et aL4 The krypton and xenon used in this work were supplied by Air Liquide, with purities guaranteed to be 99.995 mol %. Temperatures were read by a platinum resistance thermometer, with an accuracy of fO.01 K, and pressures were measured with a Ruska dead-weight gauge, with an accuracy of at least fO.01 MPa. The accuracy of the molar volumes reported here is estimated to be fO.1 %. 'Present address: School of Chemical Engineering, Olin Hall, Cornell University, Ithaca, N Y 14853.
0022-3654/86/2090-1892$01.50/0
Results In our experimental method, pressure, temperature, and quantity of substance inside the cell are measured, while the molar volumes are calculated. We need therefore to calibrate the volume of the cell, and the accuracy of our results depends critically on the accuracy of the density data used for this purpose. Our calibration procedures were described by Albuquerque et aI.l5 They give the cell volume at 130 K. Using the results of Rhodes et for the thermal expansion of 301 stainless steel, and correcting also for the effect of pressure, we obtained the cell volumes at our working temperatures and pressures. Molar volumes were then calculated from our raw experimental data. Comparison with the results of Streett and Staveleyl' for krypton and of Streett et al.18for xenon gave an average deviation of 0.41%. As explained by Albuquerque et al.15 the expected deviation would be 0.4%, due to a systematic difference between the density data used by Streett et al. and by ourselves as calibration sets. The pVT results given in this paper are therefore consistent with our values for other simple liquid mixtures.'-5 It should be said, however, that somewhat more dispersion than usual was noticeable in our results for krypton xenon. This may have been a consequenceof difficulties of mixing, due to the high density of liquid xenon. Unusual discrepancies between results of several
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(1) Nunes da Ponte, M.; Streett, W. B.; Staveley, L. A. K. J . Chem.
Thermodyn. 1978, 10, 151.
(2) Nunes da Ponte, M.; Streett, W. B.; Miller, R. C.; Staveley, L. A. K. J . Chem. Thermodyn. 1981, 13, 767. (3) Calado, J. C. G.; Palavra, A. M. F.; Streett, W. B. Proc. 72nd Annu. Meet. AlChE, San Francisco, 1979. (4) Barreiros, S. F.; Calado, J. C. G.; Clancy, P.; Nunes da Ponte, M.; Streett, W. B. J . Phys. Chem. 1982, 86, 1722. ( 5 ) Barreiros, S.F.; Calado, J. C. G.; Nunes da Ponte, M.; Streett, W. B. J . Chem. Soc., Faraday Trans 1 1983, 79, 1869. (6) Calado, J. C. G.; Guedes, H. J. R.; Nunes da Ponte, M.; Streett, W. B. Fluid Phase Equilib. 1984, 16, 185. (7) Lee, J. K.; Henderson, D.; Barker, J. A. Mol. Phys., 1975, 29, 429. (8) Singer, J. V. L.; Singer, K . Mol. Phys. 1972, 24, 357. (9) Calado, J. C. G.; Staveley, L. A. K. Trans Faraday Soc. 1971,67,289. (10) Chiu, C. H.; Canfield, F. B. Trans Faraday Soc. 1971, 67, 2933. ( 1 1) Azevedo, E. J. S.G.; Lobo, L. Q.; Staveley, L. A. K . ; Clancy, P. Fluid Phase Equilib. 1982, 9, 267. (12) Adams, W. M.S.C. Thesis, Cornell University, 1984. (13) Calado, J. C. G.; Chang, E.; Streett, W. B. Physicu A (Amsterdam)
1983, 117A, 127. (14) Leland, T. W.; Rowlinson, J. S.; Sather, G . A. Trans. Furaday Soc. 1968, 64, 1447. (15) Albuquerque, G. M. N.; Calado, J. C. G.; Nunes da Ponte, M.; Palavra, A. M. F. Cryogenics 1980, 20, 601. (16) Rhodes, B. L.; Moeller, C. E.; Hopkins, V.; Marx, T. 1. Adc. Cryog. Eng. 1963, 8, 278. (17) Streett, W . B.; Staveley, L. A. K. J . Chem. Phys. 1971, 55, 2495. ( 1 8) Streett, W. €3.: Sagan, L. S.; Staveley, L, A. K. J . Chem. Thermodyn. 1973. 5 , 633.
0 1986 American Chemical Society
Properties of Liquid Mixtures of Krypton and Xenon TABLE I: Experimental Values of the Molar Volume V , at Pressure p and Temperature T , for Krypton, Xenon, and Four Mixtures v/ (cm3 V/(cm3 T/K P/MPa mol-’) T/K P/MPa mol-‘) 0.556Kr 0.444Xe Kr 179.99 3.74 44.612 179.99 8.12 43.360 13.06 42.801 7.49 43.230 23.41 41.753 7.96 43.119 40.50 40.413 10.95 42.291 49.74 39.802 25.19 39.823 185.00 8.05 44.234 39.066 3 1.67 39.39 17.75 42.835 38.164 28.09 41.710 37.762 44.77 38.43 40.860 37.276 50.14 59.80 39.455 46.182 3.97 185.00 7.24 190.01 6.10 45.274 44.680 7.44 14.35 43.865 44.558 31.54 41.887 43.883 9.24 14.38 41.88 41.000 42.461 52.22 40.278 41.076 21.20 63.52 39.602 40.964 21.72 28.37 73.45 39.049 39.969 39.049 35.95 0.546Kr 0.454Xe 63.93 36.699 195.03 5.90 46.149 47.735 4.66 190.01 15.82 44.276 7.41 46.143 22.99 43.307 43.491 14.51 27.63 42.832 21.72 4 1.663 37.46 41.699 40.069 31.60 48.77 41.147 40.15 39.017 37.639 54.97 0.319Kr 0.681Xe 70.13 36.569 190.01 7.60 45.488 47.484 7.93 195.03 10.86 45.083 11.59 45.527 17.75 44.265 44.649 13.98 31.54 42.999 42.470 22.09 41.88 42.238 40.852 30.91 52.22 41.584 37.46 39.968 62.56 41.011 38.324 52.62 73.59 40.406 37.477 63.24 0.707Kr 0.293Xe Xe 190.01 12.10 43.848 45.102 179.99 11.20 18.99 42.764 43.620 33.61 34.15 40.931 42.831 48.09 73.58 38.104 45.895 185.00 7.51 45.921 7.69 45.340 14.72 44.259 29.47 42.790 56.36 46.465 190.01 7.83 44.326 34.99 42.529 69.46 47.194 195.03 6.08 45.892 18.58 45.192 27.10 43.448 56.25 42.862 68.49
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The Journal of Physical Chemistry, Vol. 90, No. 9, 1986 1893
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authors for krypton xenon liquid mixtures, which will be referred to later, might have the same cause. In Table I, we present our pVT results for pure krypton and pure xenon at 179.99, 185.00, 190.01, and 195.03 K, for the
37 20
0
I
p/MPa Figure 1. Experimental (p, V) points at 190.01 K for the following liquids: (a) Xe; (b) 0.319Kr 0.681Xe; (c) 0.556Kr 0.444Xe; (d) 0.707Kr + 0.293Xe; (e) Kr.
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+
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mixture 0.556Kr 0.444Xe at the three lower temperatures, for 0.546Kr + 0.454Xe at 195.03 K, and for 0.319Kr + 0.681Xe and 0.707Kr + 0.293Xe at 190.01 K. In Figure 1 we plot the experimental isotherms a t 190.01 K. The calculation of the molar excess volumes at rounded values of pressure and temperature follows eq 1, where the sub-
P(P,T,x) = V,(P,T,x)- xVi(P,n - (1 - X ) I / z ( P , T )
(1)
scripts 1, 2, and m refer to krypton, xenon, and the mixture, respectively, and x is the mole fraction of krypton. The molar volumes of krypton and of the mixtures were calculated from a volume-explicit equation of state, eq 2, fitted V=
v, + A In [ ( B + P , ) / ( B + PI1
(2)
separately to each experimental isotherm, where p , is the saturated vapor pressure, V, is the orthobaric liquid molar volume, A and B are constants, and V is the molar volume at pressure p . As for xenon, and due essentially to financial reasons and the high price of gas, we decided to measure only a few p,V points at each temperature. We subsequently used these results to calculate the average difference to the equation fitted by Streett et a1.18 to their pVT results. This equation, corrected for that difference, was then used to obtain V,, and calculate the excess volumes with eq 1. They are given in Table II at rounded values of pressure.
TABLE 11: Excess Molar Volumes VE at Rounded Values of Pressure p , for Krypton + Xenon Liquid Mixtures of Mole Fraction of Krypton xKr, at Temperature T T = 190.01 K T = 195.03 K, T = 179.99 K, T = 185.00 K, P/MPa x K r = 0.556 X K ~= 0.556 x K r = 0.319 x K r = 0.556 xKr = 0.707 xKr= 0.546 2 -1.417 -1.623 -1.774 -2.684 -3.292 -4.525 5 -1.003 -1.092 -1.132 -1.682 -2.016 -2.289 10 -0.593 -0.664 -0.649 -0.964 -1.105 -1.238 15 -0.356 -0.451 -0.413 -0.625 -0.682 -0.808 20 -0.209 -0.327 -0.278 -0.432 -0.446 -0.564 30 -0.050 -0.190 -0.138 -0.223 -0.207 -0.281 40 0.020 -0.117 -0.072 -0.1 14 -0.098 -0.105 50 0.048 -0.070 -0.037 -0.046 -0.044 0.025 60 -0.035 -0.018 -0.000 -0.016 70 -0.007 0.036 -0.002
1894 The Journal of Physical Chemistry, Vol. 90, No. 9, 1986 TABLE 111: Constants in
1 -
Ea 3-8"
B, 7.323084 X lo-' -1.728636 X 10" 1.633321 X lo-' 2.081 814 X lo-' 1,130354 1.171 017 1.794 098
2 3 4
S 6
I
0
1
4
8 9 10 11 12 13
-1.845244 8.404090 X IO-* 4.414308 X -7.110582 X 4.655457 X lo-' 2.676693 X IO-'
1 --.____I_
1
Calado et al.
c
L
!i
"E
s>
r" in cm3 mol-l, P in MPa, and T in K.
-1
-2
I
0 0
20
10
70
40
60
50
-3
dMPa
Figure 2. Excess volumes temperatures, of krypton eq 3
+ xenon equimolar mixtures, calculated from
Singh and Milleri9 proposed an equation for the pressure, temperature, and composition dependence of p.It is based on the Redlich-Kister expansion r/F-(p,T,x)= ~ ( -lx ) [ A B(2x - 1) + C(2x - I)*] (3)
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where x is the mole fraction of krypton, and A , B, and C are functions of pressure p and temperature T A = B1 Fl F2 (4) B = B,(F1 + Bi2F2) (5)
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C = B A F , + BIT,) F , = B , exp{-B3p + B,(T- 160) - B , p [ ( T - 160)/160])
(6)
(7) 160) - B , , p [ ( T - 160)/160]) (8) where B , to B , , are adjustable parameters. We fitted eq 3-8 to our results, including also the results of Chiu and Canfieldlo at 161.39 K and (essentially) zero pressure. The resulting values of the parameters are given in Table 111. The root mean square deviation of the fit was 0.059 cm3 mol-'. Figure 2 shows the pressure dependence of the excess volume p of an equimolar mixture, at our four working temperatures, calculated from eq 3-8. Figure 3 gives p at 190.01 K as a function of composition (mole fraction of krypton) and at several pressures. The circles correspond to the experimental p,obtained with eq 1 and given in Table 11, while the full lines were calculated from eq 3-8. The effect of pressure on the excess Gibbs energy GE, the excess enthalpy H E ,and the excess entropy SEare given by
F2 = B8 exp(-B,p
0
r" as a function of pressure p , at the indicated
XKr
Figure 3. Excess volumes as a function of composition at several pressures and at 190.01 K. The circles are experimental values given by eq 1, the full lines correspond to eq 3, and the dotted lines to the vdW-1 calculations, with methane as reference fluid. TABLE I V Effect of Pressure p (Relative to Zero Pressure) on the Excess Enthalpy, AHE,Excess Cibbs Energy, ACE, and Excess Entropy Multiplied by Temperature, TASE, of a 0.556Kr + 0.444Xe Mixture
T/K
P/MPa
AHE/ (J mol-')
AGE/ (J mol-')
TUE/ (J mol-')
185.00
0 2 5 10 20 40 70
0 67 120 165 208 243 254
0 -4 -8 -12 -17 --I9 -20
0 71 128 177 235 262 274
190.01
0 2 5 10 20 40 70
0 145 228 28 5 348 406 430
0 -6 -1 2 -1 8 -24 -28 -29
0 151 240 303 372 434 459
+ B,,(T-
4 G E = G E ( T , x , p )- GE(T,x,po)=
l&c"
dp
(9)
AHE = H E ( T , x , p )- HE(T,x,pn)=
TASE = AHE - AGE (1 1) where po is some reference pressure, taken as zero in this work. (19) Singh, S. P.; Miller, R. C. J . Chem. Thermodyn. 1979, 1 1 , 395
1
0.5
e,
Values of AGE, and TASE,calculated with eq 3-8 at 185.00 and 190.01K, for 0.556Kr + 0.444Xe, are given in Table IV. .
Discussion As far as we known, the only available data on densities of krypton + xenon liquid mixtures were obtained by Calado and Staveley' and by Chiu and CanField,'O at essentially zero pressure and close to the xenon triple-point temperatare (161.39 K). The two sets of results are not in good agreement, Calado's VE results being more negative and more symmetric around the x = 0.5 axis, as shown in Figure 5 . We preferred to include the values of Chiu and Canfield in our fit of p data by eq 3-8 because they show a minimum shifted to the krypton-rich side, similar t o our low pressure p at higher temperatures. The full line in Figure 5 , corresponding to eq 3-8, is accordingly closer to the results given in ref 10. Our results show marked similarities with the results previously obtained for other simple mixtures, notably argon
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Properties of Liquid Mixtures of Krypton and Xenon TABLE V: Size ( u ) and Energy ( e ) Parameters of the Intermolecular Potential Used To Apply the Equation of State of Methanez3as a Reference in the vdw-1 Theorv CH, Kr Xe (e/k)/K u/nm
151.81 0.3737
165.8 0.3628
230.2 0.3952
k r y p t ~ n .Excess ~ volumes are large and negative at low pressure, become less negative as pressure is applied, and reach a limiting value very close to zero at high pressures. The asymmetry around the x = 0.5 axis of the vs. x curves is pronounced at low pressures, with a minimum shifted to the side richer in the more volatile component (krypton, in this work). As pressure increases, the curves become more symmetric. Finally, the effect of pressure and temperature on the excess enthalpy HE is much stronger than on the excess Gibbs energy GE. The argon + krypton system exhibits a curious feature at high pressures, where vs. x curves have an incipient S shape. For krypton xenon mixtures, due to the fewer number of experimental pVT points measured, it was not possible, however, to obtain a precise picture of vs. x curves at high pressures, where the excess volumes are very small and the relative experimental errors are large. Vapor-liquid equilibrium measurements reported in the literature were performed by Calado and S t a ~ e l e yChiu , ~ and Canfield,I0 and Calado, Chang, and Streett.13 The first two studies were performed at the same temperature and agreement between them can be considered reasonably good. Calado and Staveley give CE(x= 0.5) = 114.5 f 1.3 J mol-', while Chiu and Canfield obtained 101.8 J mol-'. An earlier value of Seemeyer, quoted by Rowlinson,20 145 J mol-', is probably too large. Calado, Chang and, StreettI3 calculated GEvalues from their subcritical, high-pressure vapor-liquid equilibrium isotherms. A plot of CE/T vs. 1/ T should, in principle, give information about the excess enthalpy HE. However, if we plot the result of Calado et al. together with those of ref 9 or 10, for an equimolar mixture, the scatter in the points obtained prevents any meaningful conclusion. On the other hand, there are two sets of direct (calorimetric) measurements of the excess enthalpies. One was obtained in Oxford by Staveley and callaborators and was quoted by Azevedo et al.," and the other one by AdamsI2 at Cornell University. Although the Cornell calorimeter is a refined version of the Oxford one and agreement between results obtained in both calorimeters is very good for other mixtures, as for instance C O CH4,Z'the two sets of results for Kr Xe are quite different. Staveley gives p ( x = 0.5,T = 165 K) = 48.5 J mol-' while Adams obtained H E ( x = 0.5,T = 163.0 K) = 109.1 J mol-l. The discrepancies referred to above underline the difficulties found by several workers when working with krypton + xenon mixtures. The order of magnitude of the GE and HE values at low pressures is, anyway, firmly established, and shows how much stronger is the relative effect of pressure on H E than on GE.
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The Journal of Physical Chemistry, Vol. 90, No. 9, 1986 1895 I
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200
100
0
A G ~
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I
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20
40
I 60 PhPa
Figure 4. Changes of the excess Gibbs energy, AGE, the excess enthalpy, A@, and the excess entropy (multiplied by temperature), T S E ,with pressure for 0.556Kr 0.444Xe mixtures at 185.00 K. -, experimental values calculated from eq 3, 9, 10, and 11; - - - ,vdW-1, methane reference, AHE; vdW-1, L-J(6,12) reference, ATrE.
+
-.-
\
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Comparison with Theory As for our previous papers on the equation of state of simple liquid mixtures,& we used the conformal solution theory of Leland et aI.,l4 the well-known van der Waals one-fluid model, to try and reproduce our experimental results. This model requires an equation of state to characterize a reference fluid. Preliminary calculations with the equation of state of the (12,6) Lennard-Jones given by Nicolas et a1.22showed poor agreement with experimental excess enthalpies, as shown in Figure 4. We decided to concentrate on a more realistic equation of state and used the Sievers and Schu1zZ3equation for methane in reduced
0
0.5
1
XKr
.,
Figure 5. Excess volumes at essentially zero pressure and at the triplepoint temperature of xenon (161.39 K): 0 , Chiu and Canfield;Io Calado and S t a ~ e l e y-, ; ~ eq 3.
form. The energy and size parameters of the intermolecular potential for methane, krypton, and xenon are given in Table V. For methane we used the same as Calado et a1.,6 while those for krypton and xenon were chosen to give the best fit to the p V T data obtained in this work. They are in good agreement with the parameters given for the same liquids by McDonald and Singer.24 For the mixtures, the parameters are obtained in the vdW-1 model by use of the van der Waals mixing rules:
To calculate these parameters, the cross interaction parameters (20) Rowlinson, J. S. 'Liquids and Liquids Mixtures", 2nd ed.: Butterworth: London, 1969; p 130. (21) Zollweg, J., personal communication. (22) Nicolas, J. J.; Gubbins, K. E.; Streett, W. B.; Tildesley, D. J. Mol. Phys. 1979, 37, 1429.
are given by (23) Sievers, U.; Schulz, S. Fluid Phase Equilibia 1980, 5 , 35. (24) McDonald, I. R.; Singer, K. Mol. Phys. 1972, 23, 29.
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 . ~ deviation the experimental GEvalues of Calado and S t a ~ e l e y The 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.
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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)
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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.
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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 repulsion energy (Erep) (Table I). The values for Erepare identical 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)
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to add two electrons to the neutral molecule (A) (reaction 2) is AH2' = Erep- 2EA A(g) + 2e-(g) A2-(g) (2) minus twice the electron affinity (EA) of the neutral simply EFep molecule. The best literature values for the electron affinities of a number of polyarornatics have been previously ~ e l e c t e dand ;~ we can clearly when these are combined with the values for Erep, 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 EA E,en AH', AH', AH'sub
benzene naphthalene anthracene tetracene pentacene pyrene perylene benzo[a]pyrene
-26.6 3.5 12.7 16.0 19 13.3 21.1 19.1
162 127 117 107 99 108 100 I01
215 120 92 75 61 81.4 57.8 62.8
452 357 329 312 298 318 295 300
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
