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
NOTES
2056
tude greater than equilibrium in the reaction zone and decay toward equilibrium downstream. 1 Recently Fenimore and Jones2 studied the recombinations in the presence of SO2in low-pressure flames using mass spectroscopy and found that small quantities catalyzed the recombination of hydrogen atoms through the reaction sequence
-
+ sos + n/i H S O ~+ M H (or OH) + HSO2 +H2 (or H2O) + SO2 H
(3) (4)
with reactioli 3 being the rate-determining step. In this laboratory we have studied the catalytic recombination of H atoms in the presence of SO2 in flames a t atmospheric pressure by measuring the intensity of resonance radiation from sodium atoms by flame photometry. I n flames below 2000°K and in the absence of SOa, the sharp peak in intensity in the region of the reaction zone has been shown to be due to chemiluminescence, the sodium atoms being excited by H
+ H + ? J a + H 2 + Na*
H+OH+Na+HzO+Na* The decay of chemiluminescence under these conditions is such that l / f l is proportional to distance from the reaction zone. We have found that the addition of less than 0.5% of sulfur dioxide to flames containing sodium causes as much as a fivefold increase in the peak intensity of chemiluminescence from sodium atoms, although the rate of decay of intensity along the flame in the presence of SOz is greater. This extra excitation of the sodium is attributed to the reaction
and the more rapid decay is taken as evidence that H atom removal is faster in the presence of S02. In fact, separate experiments in which relative H atom concentrations were measured by observing the intensity of the CuH bands in emission when copper salts were added to the flames showed that as little as 0.1% of sulfur dioxide reduced the H atom concentration 1.0 cm from the reaction zone by a t least a factor of 10. If the catalyzed recombination is rapid compared with reactions 1 and 2 , the latter may be neglected when SO2 is present. The reaction scheme involving (3) and (4)then results in the following expression for the variation of [HI with time The Journal of Physical Chemistry
__
where Ka is the equilibrium constant of the rapidly balanced reaction H
+ HzO
OH
+ Hz
(6)
If ( 5 ) is the main reaction causing excitation of sodium atoms, the intensity I will be proportional to [HI so that a plot of log I vs. time (or distance from the reaction zone) should be linear and yield a value for k8 if [SOa],[MI, and Kg are known. I n the first instance we have calculated [SO21 from the original amount added assuming no conversion to H2S, and since water is likely to be the most efficient third body present in the flame gases,4we have put [M J = [HzO]. Kg was taken from the data quoted by Gaydon and W ~ l f h a r d . ~ Figure 1 shows a typical plot of log I us. distance from the reaction zone for a flat flame burning at atmospheric pressure on a nl&ker burner. For this flame [MI% 10'8 molecule ~ m and - ~ [SO2] 'u 1OI6 molecule ~ m - ~ , molecule-2 from which we calculate k3 = 6 X cm6sec-'. This is larger than the value kg 'v 2 X molecule-2 cm6 sec-I reported by Fenimore and Jones, but in their work they took [MJ as the total concentration of flame gases. When due allowance is made for this, the two values are almost identical.
0.61 0
1
0.5
1 1'0
1
1.5
1
DISTANCE FROM REACTION ZONE, m m
Figure 1. Decay of chemiluminescence from sodium lines in the presence of sulfur dioxide.
D
(1) E. M. Bulewicz, C. G. James, and T. hl. Sugden, Proc. Roy. SOC.
(London), A235, 89 (1956). (2) C. P. Fenimore and G. W. Jones, J . Phys. Chem., 69, 3593 (1965).
(3) P.J. Padley and T. M. Sugden, Proc. Roy.SOC.(London), A248, 248 (1958). (4) K.E.Russell and J. Simons, ibid., A217, 271 (1953). (5) A. G. Gaydon and H. G . Wolfhard, "Flames," Chapman and Hall, London, 1953, p 274.
