NOTES
2053
eter, after applying the appropriate corrections. It is hard therefore to account for the discrepancy of about 20% between our results and those of Dawes and Back. The absolute precise value of Gexchis crucial only when a quantitative evaluation of the energetics of the exchange process can decide in favor of a certain mechanism, in comparison with others. At first glance it appears as if Dawes and Back have achieved this goal and have accounted (in Table V of their paper) for the different pathways of exchange. They have used the known number of ions formed in nitrogen per 100 ev (2.88) and the number of nitrogen molecules undergoing dissociative excitation per 100 ev (1.54). A critical review of the arguments presented in their paper reveals, however, serious inconsistencies between their proposed mechanism and their own experimental results. Dawes and Back propose that an isotopic exchange takes place between the nitrogens of the N4+ ion on neutralization by an electron.* Such a reaction would accordingly yield an exchanged nitrogen molecule plus two nitrogen atoms N2**+ N2+
N4+**
N4+**
(1)
+ e- -+N2* + N + N*
(2)
where N2* is an exchanged nitrogen molecule. It is obvious that reaction 2 will yield Nz* only in half of the cases (the other half will yield Nz** 2W and Nz 2N*). This factor of 0.5 exists in addition to the factor of 0.5 which originates from the interactions of isotopically identical nitrogen molecules, which was taken into account by the authors. This additional factor of 0.5 upsets the balance of Gexehreported by Dawes and Back by 1.44, and the contribution of the dissociative excitation has to be increased accordingly from 1.54 to 2.98. We shall now compare the behavior of the system in the presence of additives as determined by the two groups of investigators. Dawes and Back carried out two series of experiments using NO as scavenger. I n N214J4series G(N214J5)was 2.57, whereas the N150 N140 N2 14,14+ N215J6experiment in the Ni50 G(N214J5) was 2.85. We have repeated the NO experiments using a mixture of 98.4% N215J5 1.6% N140 and obtained G(N214,15)= 2.56 f 0.13,5in excellent agreement with Dawes and Back. This agreement in the presence of NO suggests that the discrepancy in Gexchbetween our results and those of Dawes and Back can hardly be attributed to dosimetry. A comparable value for Gexchwas also observed in both studies’pz for nitrogen containing 0.4-0.570 0 2 . This may suggest that the lower value for Gexch in “pure”
+
+
+
+
+
+
nitrogen reported by Dawes and Back is due to a trace impurity. A critical review of our previous communication also reveals certain points which require a revision. First, it should be pointed out that our value of Gexch can hardly be accounted for in view of the high dissociation energy of N2. Second, our conclusion that excited nitrogen molecules do not undergo isotopic exchange with nitrogen molecules at their ground state is open to criticism. This conclusion, which was reached on the basis of the results of Back and is valid only for the two lowest triplet states of Nz which are generated by N atom recombination downstream from the discharge. Other shorter lived Nz (excited) could not be found outside the discharge tube used in that study. In fact, the reaction
x2l4,I4 (excited) + Nz15,15+2x214,15
(3)
is energetically feasible’ even for the lower excitation levels of Nz,down to 6 ev above ground level. It may be concluded that the mechanisms leading to the N214314-N215915 exchange suggested in both previous reports do not fully account for the observed exchange reaction and the system still requires further study. (4) The occurrence of an intramolecular isotope exchange in Na+ prior t o neutralization is excluded by the fact that the equilibrium Np+ N*$ N,+ would then lead t o a chain reaction which would imply a dose rate dependence of Gexoh.It has been suggested* that the rate of dissociation of Na+ -L N r + N3 is slow compared with the rate of its neutralization. Considering the equilibrium constant of Na+ NZ = Na+, this cannot be true for the lower dose rates studied. As no increase in Gexehwas observed at lower dose rates, it is unlikely that isotopic exchange takes place in the Nz+ i- Nt e Na + reaction. (5) We have also examined the other products of the “ 4 0 Nz15r15system and found G(N150) = 0.1 (by 0 N ) , G(NaL6~160) = 0.04 (by Na O), G(Na14,150) = 0.1 (by N NO, ?), G(On) = 0.8 (by 0 O), and G(N0a) < 0.01. (6) R. A. Back and J. I. Y. Mui, J. Phys. Chem., 66, 1362 (1962). (7) J. D. Hirschfelder, J. Chem. Phys., 9, 645 (1941); K. Otozai, Bull. Chem. SOC.Japan, 24, 218, 257, 262 (1951).
+
+
+
+
+
+
+
+
Solvent Shifts of Electronic Energy Levels of Acetone and Benzene
by K. Keith Innes va’anderbilt University, Nashville, Tennessee (Received November 16, 1965)
Solvent shifts of electronic transitions seem always to have been discussed as if it were not possible to determine the shifts separately for the two energy levels giving rise to each transition.’,2 Volume 70, Number 6
June 1966
2054
NOTES
1
120-
110-
10-
I
1
100-
I I
I
(kca I/m o IB)
T Electronic Energy
O-
(kcalhole)
1
I I
f
1
I
Electronic Energy
I
10.0
I
to-
6.3
T I
i
I
I I
0-
VAPOR
VAPOR
Figure 2. Effect of phase change on electronic energy levels of acetone. T h e scale for the excited states cannot be joined exactly to that of the lower states but the excited states lie a t approximately 105 kcal/mole.
LIQUID
Figure 1. Effect of phase change on electronic energy levels of benzene.
Here, it is shown how the separate shifts may be determined experimentally. That is, it is shown how energy levels in figures such as 1 and 2 of the present note or Figure 1 of an earlier paper by Bayliss and b‘lcRae3 may be made quantitative. Although the idea and the theories of the shifts of individual electronic states are old, we have not found experimental numbers for the individual levels in any earlier work. Availability of solvent shifts for each electronic state should make testing of theories somewhat more straightforward. The simplest case is considered, namely that in which a substance acts as its own solvent: The spectrum of the pure vapor is compared with that of the pure liquid. We consider the 2600-A absorption of benzene as illustrative of a*-a transitions for which the effect of condensation is a shift of absorption to longer wavelengths (a “red shift”). Similarly, the 3000-A absorption of acetone is taken as representative of a*-n transitions and “blue shifts.” For each molecule, the vapor spectrum is summarized by Pearse and Gaydon4 and the liquid spectrum has been measured by Mitzner.5 We take an arbitrary zero on each electronic energy level diagram (Figures 1 and 2) corresponding to the pure liquid at 20”. To make this clear we write 0
= EL2Q30K =
+
ELooK
293OK
CLvdT
and
+ S,
293OK
A E V a P 2 g 3 0 ~= E V 2 g 3 0 ~= E V O o g
The Journal of Physical Chemistrp
LIQUID
CVvdT
In these expressions the superscript vap means vaporization, the superscripts L and V mean liquid and vapor, respectively, and CV is the heat capacity a t constant volume. Now for purposes of locating the ground electronic states of the vapors of Figures 1 and 2, we seek good approximations to the four terms on the right-hand sides of the equations. (1) For each phase, we take EOOK as the electronic energy and take it as independent of temperature (that is, we include the zeropoint vibrations in our electronic levels and we assume that electronic energy is not excited at room temperature). (2) For each phase we divide the integral into one heat capacity term contributed by medium-tohigh-frequency vibrations and a second term contributed by low-frequency motions of all kinds. We assume that the first of these is the same for the two phases and that the second can be fitted by the classical equipartition approximation, viz., CVT. On these assumptions, when the first equation is subtracted from the second, we find on rearranging melectronic
=
- (cvv- cLv)!f?
AEVaP2g30~
(1) J. N. Murrell, “The Theory of Electronic Spectra of Organic Molecules,” John Wiley and Sons, Inc., New York, N. Y., 1963. (2) H.H.Jaff6 and M. Orchin, “Theory and Applications of Ultraviolet Spectroscopy,” John Wiley and Sons, Inc., New York, N. Y., 1962. (3) N.S. Bayliss and E. G. McRae, J. Phys. Chem., 58, 1002 (1954). (4) R. W. B. P e y e and A. G. Gaydon, “The Identification of Molecular Spectra, 3rd ed, Chapman and Hall, Ltd., London, 1963. (5) B. M. Mitzner, J. Opt. Soc. Am., 45, 997 (1955).
NOTES
in which T = 293”K, and we might interpret (C’V CLv)T as a measure of conversion of translational and rotational motions of the vapor into intermolecular motions in the liquid. (Classically, each degree of freedom so converted will add ’lzR to CLv, compared with C’V). To locate the energy of the ground electronic state for the vapor of Figure 1 or 2 we should then add (CLv - CvV)T to the observed energy of vaporization of the substance. The calculation from experimental quantities can be illustrated for benzene. The energy of vaporization of benzene is known to be 7.49 kcal/mole.6 Heat capacities at constant pressure are available, namely CLp = 31.5 cal/mole deg’ and Cvp = 19.5 cal/mole deg.6 For each phase we may find CV from the relation CP - CV = T V p z / ~in which T is the absolute temperature as before, V is the molar volume at T, 0 is the coefficient of volume expansion at T, and K is the isothermal compressibility at T. For vapors, it is well known that Cp - Cv reduces to 2.0 cal/mole deg. For liquid benzene, measured values of V , 0,and K~ give CP - CV = 10.1 cal/mole deg. These figures give CLv - Cvv = 4 cal/deg mole. On adding 4 T to 7.5 kcal/mole we obtain 8.7 kcal/mole as the “solvent shift” for the ground electronic state. Figure 1 shows how the “solvent shift” for the excited electronic state follows by addition of the observed transition energy for vapor and liquid, respectively. For benzene the several peaks exhibited by the liquid5 are quite similar in appearance to those of a low-resolution spectrum of the vapor.4 Each liquid peak lies about 460 cm-l to lower frequencies than a corresponding vapor peak. Thus it seems safe to assume that 460 cm-I or 1.32 kcal/mole represents the effect of change of phase on the unobserved electronic origin of the band system. (The magnitude is typical of solvent shifts of weak a*-a transitions.) In summary, the shift of the excited state is found to be 1.3 kcal/mole greater than for the ground state, an increase of about 15%.9 For acetone, the absorption exhibits only a broad maximum, regardless of phase. Therefore, the excited states cannot be fixed accurately on the same scale as the ground states. Nevertheless the shifts again may be determined separately. It is only necessary to assume that the close similarity of the intensity envelope of the band system of the vapor with that of the liquid is sufficient evidence that the difference in observed maxima (Amax) measures the effect of the phase change on the separation of electronic states. The numbers 2800 A4 and XLm,, 2750 A.5 The “blue-shift” are ,,A,’ of 650 cm-l or 1.86 kcal/mole is typical of solvent shifts for a*-n transitions.
2055
The construction of the electronic energy level diagram (Figure 2) proceeds as for benzene. We have used, in addition to the transition energies, an energy of vaporization at room temperature, 7.00 kcal/mole,’ and a difference of heat capacities CLp - C’P = 10.8 cal/mole deg.’ As for benzene, it is found that CLv CV ’ = 4 cal/deg mole. The ground-state solvent shift is therefore 8.2 kcal/mole while that of the excited state is 6.3 kcal/mole. The decrease is almost 25%. It is striking that the solvent shifts of the ground states of benzene and acetone are so nearly equal. Evidently, in theoretical descriptions of the acetone shift, it will not be easy to distinguish polar effects from dispersion force contributions.
Acknowledgment. This work was supported by the National Science Foundation through Grant GP-5126. (6) F. D. Rossini, et al., “Selected Values of Physical and Thermo,; dynamic Properties of Hydrocarbons and Related Compounds, Carnegie Press, Pittsburgh, Pa., 1953. (7) “International Critical Tables,” McGraw-Hill Book Co., Inc., New York, N. Y . , 1929. (8) “American Institute of Physics Handbook,” McGraw-Hill Book Co., Inc., New York, N. Y., 1957. (9) The spectrum of solid benzene has been studied intensively. (See, for example, the review by H. C. Wolf, Solid State Phys., 9, 29 (1959).) It is interesting that the gross shift compared to the vapor is nearly the same as for the liquid and vapor. This can be understood in terms of shifts for ground and excited states separately as follows. The energy of sublimation is greater than that for vaporization by 0.4 kcal/mole, but the factor (C’V - CVv)Tis smaller than (CLv - CVv)T so that the net separation of ground states of solid and vapor is about 0.2 kcal/mole smaller than for liquid and vapor. Therefore, we may expect that, if we based an analog of Figure 1 on an arbitrary zero energy for the solid a t , say, Oo, the energies of Figure 1 would be correct for solid and vapor to within a few tenths of a kilocalorie.
Reactions of Sulfur Dioxide in Hydrogen Flames
by A. S. Kallend Central Electricity Research Laboratories, Leatherhead, Surrey, England (Received December 23, 1966)
In the reaction zone of fuel-rich hydrogen-oxygen flames, H and OH radicals are formed in branchedchain reactions and are removed by recombination in the presence of a third body by the reactions
+ OH + M +HzO + R I H + H + M +Hz + M
H
(1) (2)
Because (1) and (2) are relatively slow compared with the bimolecular reactions forming the radicals, the concentrations of H and OH are often orders of magniVolume 70,Number 6 June 1966
