Uv SPECTRAOF MOLECULES OF GASEOUS Brz good correlation between AG* for the ion exchange and uZH- ulH. Thus, one can infer that there is a similarity bctwecn the energetics of the processes involved in promotion to the activated complcx and complete dissociation. For K, Rb, and Cs, the intramolecular ion migration apparently takes place entirely within thc solvcnt shell, as indicated by the following argument. The free encrgics of activation for thcse thrce systems are substantially less than thc free cnergics of dissociation givcn in Tablc 111, which would indicatc that thc transition statc cannot cntircly resemble scparated ions. Moreover, the calculated small negative entropies of activation indicate that the transition state is only slightly morc solvated than the contact ion pair and, accordingly, only slightly more ionic. For Na+DSQ. -, on the other hand, the entropy of activation is substantially morc negative, nearly one-half thc valuc for complctc dissociation. The free energy of activa-
1017 tion also approaches the free energy of dissociation, so the transition state for the ion exchange morc nearly resembles thc dissociated ions. The Li+-DSQ. - ion pair has not bcen observed to undergo this type of ion cxchange. Howcver, Gough and H i n d l ~ extrapolated ~~ their AG' data on the basis of the values for uzH - alH, to give an estimate of 14 kcal/mol as the free energy of activation for this exchange with the Li+ ion. This is substantially greater than any of our values for the free energy of dissociation. Thus, it scems likely that the trend toward increasingly ionic transition states should continue as the size of the cation decreases.
Acknowledgment. The authors wish to thank Professor R. J. Kurland for many helpful discussions and to acknowledge the support of this research by the Petroleum Research Fund, administered by the American Chemical Society.
Ultraviolet Spectra of Single and Double Molecules of Gaseous Bromine by Walter Y. Wen and Richard M. Noyes* Department of Chemistry, University of Oregon, Eugene, Oregon 97403
(Received October 16, 1971)
Publication costs assisted by the National Science Foundation
The absorption spectrum of bromine vapor between 220 and 290 nm has been measured at 30". Deviation from the Beer-Lambert law has been interpreted in terms of the formation of double molecules of Br2,and the relative contributions of single and double molecules of Brz t o t h e observed absorption have been assigned. At wavclcngths longer than 300 nm, light absorption by bromine vapor obeys Becr's law, and the spectrum has becn well characterized.' At shorter wavelcngths, a band ccntcrcd a t about 210 nm dcviatcs strongly from Bcer's law. Passchier, Christian, and Gregory' and also Ogryzlo and Sanctuary2 have attributcd some of this absorption to Br4 molecules. Reported absorbance data that recognizc Becr's law dcviations1~2 do not cover the region between 230 and 300 nm. In conncction with a kinctic study of the rcaction b e t w c n CI2 and HBr,3 we had occasion to measure the concentration dcperidencc of light absorption in this region. Mcasuroments were madc with a Bcckman DU spcctrophotometcr on a quartz cell with 9.8-cm optical path thcrmostatcd to 30" by a water jacltct. Mallinckrodt analytical grade bromine was dricd over P20, a t liquid nitrogen temperaturc and admitted to the cvacuatcd cell. Final pressure was measured to bctter than
1 mm with a Pacc Wiancko PIA-20 psia pressure transducer connected to a transducer indicator that had been calibrated against a mercury manometer. Conccntrations (in the range 0.002-0.009 M ) were computed by assuming the ideal gas law. Although the apparatus was designed primarily for kinetic measurement^,^ it was satisfactory for thc spectral measurements. Thc apparcnt extinction coefficients (defined as A/s1Br2lt, where A is the absorbance, s is the cell lcngth in centimeters, and [Br2Itis the total concentration of bromine in moles/litcr) are plotted against conccntration in Figure 1 and show thc deviations from Bcer's law at thc shorter wavelengths. If these dcviations are due to cquilibrium 1,then thc total absorbance can be describcd by eq 2, where e2 and e4 arc the molar (1) A . A . Passchier, J. D. Christian, and N. W. Gregory, J . P h y s . Chrm., 7 1 , 937 (1967), and references cited therein. (2) 13. A. Ogryelo and B. C. Sanctuary, i b i d , 69, 4422 (1965). (3) W. Y .Wen, Ph.D. Thesis, University of Oregon, 1971.
The Journal of Physical Chemistry, Vol. 76, N o . 7 , I972
WALTERY. WENAND RICHARD M. NOYES
1018
extinction coefficients of Brz and Br4 molecules, respecE tively, K , is the equilibrium constant for reaction 1 in reciprocal atmospheres, RT is in liter atmospheres per mole, and [Br2] is the true concentration of bromine molecules. If the extent of association is sufficiently small, no significant error is introduced by substituting [BrzIt for [Brz]in eq 2. The results of our measurements are presented in Tablc I and compared with previously reported values where possible. Values of e2 tend to be somewhat smaller than those reported by Aickin and B a y l i ~ s , ~ 1 2 3 4 5 6 even if allowance is made for their failure to recognize [ ~ r . ] ~IO'. x mole I-' B e d s law deviations, and the values of KPe4extend the Figure 1. Plots of the apparent extinction wavelength range reported by Passchier, Christian, coefficients against [Brz]t. and Greg0ry.I Table I : Calculated Extinction Coefficients for Brz and Br4 Wavnlength, nm
220 225 230 235 240 245 250 255 260 265 270 275 280 285 290
Kprc. I./(mol cm atm) Reported This work, 30°
2.84 f 0.13 2.93 f 0.09 2.66 f 0.05 2.80 Z!Z 0.06 2.22 -Ir 0.04 1.96 d= 0.04 1.59 f 0.04 1.00 f 0.04 0.92 i 0.05 0.54 f 0.04 0.28 zk 0.06 0.24 f 0.04 0.24 f 0.05 0.14 f 0.04 0.12 f 0.05
25.0' 21.0 f 0 . 1 14.3" 12.2 f 0.6 8.15" 7 . 6 =k 0 . 4 2.7 f 0 . 4 2.5 i 0 . 3 1.3 i 0 . 3 1.0 f 0.3 1.2 f 0.3 0.3 f 0.3 0.8 f 0.3 0.8 f 0.4 0.4 f 0.3
2.6" 3.33' 2.8" 3.23b 2.6" 3.30b 2. 2. 60' 2. lob 1.6gb 1 . 36' 1.08b 0 88' 0. 6jb 0. 4Sb 0.46' 0.35' 0 . 3gb I
0 . 1 1. 0 . 3 0 . 2 f 0.3
'
Room-temperature interpolated data of a 25" data of ref 1. ref 4, not corrected for concentration dependence of apparent extinction coefficients.
Any evaluation of e4 requires an independent evaluation of K,. Results of gas density measurements are ambiguous. Lasater, Colley, and Anderson6 interpreted deviations from the ideal gas law by mcans of van der Waals' equation without any assumptions
The Journal of Physical Chemistry, Vol. 76, No. 7 , 1979
6
9
about chemical equilibria, but Kokovina interpreted his data by cq 3. Such an interpretation implies G I "
log K , = ( 5 7 6 / T ) - 3.28 I./(mol cm) Reported This work, 30" tz,
7
(3)
= -2.6 kcal/mol for reaction 1, in good agreement with the temperature dependence of KPe4observed by Passchier, Christian, and Gregory' a t short wavelengths. However, such an evaluation of K , assumes that all deviations from ideal gas behavior arc due to association forming specific double molcculcs and that long-range intermolecular forces do not affect those deviations. Because there is considerable uncertainty in the value of any K , calculated by mcans of such assumptions, the data in Table I have bccri reported in terms of KPe4 without any attempt to evaluate e4. However, the K , of 0.043 atm-' a t 30" implied by the KokovinG data indicates that w e n saturated bromine vapor would have only about 1% Rr4 molecules and fully justifies the substitution of [Br2Itfor [Brz] in eq 2.
Acknowledgment. This research was supported a t different times by thc U. S. Army Research Office and by the National Science Foundation. (4) R. G. Aickin a n d N . S. Bayliss, T r a n s . Faraday SOC.,34, 1371 (1938). (5) J. A. Lasater, S. D. Colley, a n d It. C. Anderson, J . A m e r . Chem. Soc., 72, 1845 (1950). (6) G. A. Kokovin, Z h . Xeorg. K h i m . , 10, 287 (1965) ; Rzrss. J . Inorg. Chem., 10, 150 (1965).
