1640
Communications to the Editor
COMMUNICATIONS TO THE EDITOR
infrared Spectra of Strong Acids and Bases’
WMLENGTH 1.92
Publication costs assisted by the Office of Naval Research
Sir: In an earlier paper on this subject2 we reported the results of a study of the reflectance spectra of aqueous solutions of strong acids and bases; from measured values of spectral reflectance R(v) we used a Kramers-Kronig analysis to obtain the real n(v) and imaginary h(u) parts of the complex index of refraction fi = n(v) ik(u) in the spectral region 400-5000 cm-’. With regard to major absorption bands, our results were in general agreement with those obtained in the earlier absorption study of Falk and G i g ~ e r e , ~ and we adopted their assignment of certain bands in the spectrum of HC1 solutions to the ion H30+. I t has been brought to our attention that our results and this assignment are in disagreement with those obtained by Ackermann,* who has made a quantitative study of the transmission spectra of strong acids and bases in the range 1100-4000 cm-l. Ackermann reported that the absorption spectra of acids and bases are essentially similar and can be interpreted as mere radical modifications of the spectrum of water. In particular, he raised questions as to the assignment of bands to the H30+ ion. In order to check our earlier results we have remeasured the reflection spectrum of HBr at two concentrations and are including our results for spectral reflectance R(u), n(v), and k(v) in Figures 1’-7’ (supplementary material; see paragraph at end of text regarding supplementary material). In order to determine the differences between the solution spectra and the spectrum of water, we have also prepared curves showing the differences between the absorption indices h(so1ution) and k(water) as a function of wave number; the curve for a 48% solution of HBr is shown in Figure 1. In spectral regions where k(so1ution) - k(water) is negative, the solution is more transparent than water; one such region occurs near 3400 cm-’ and is probably associated with a shift of the strong valence-vibration band of water; a second such region occurs near 700 cm-l and is probably associated with a shift in the librational band of water.5 Three strong maxima occur near 2800, 1750, and 1100 cm-1 in the curve shown in Figure 1. Each of these maxima is in close proximity to a band reported for the H30+ ion in crystal hydrates.6-s This agreement between the frequencies of bands observed in solution and in hydrated crystals is our major reason for attributing the solution bands to the H30+ ion. Since the H30+ ion is isoelectronic with NH3 and is probably pyramidal, the observed bands appear in the anticipated spectral regions.2 The value h(so1ution) - h(water) in Figure 1 is positive throughout the entire spectral region between 3200 and 900 cm-l; this indicates that the HBr solution is more strongly absorbing than water. Similar strong general absorption was noted for solutions of HC1, NaOH, and KOH in our
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The Journal of Physical Chemistry, Vol. 80. No. 14, 1976
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WAVE NUMBER
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Figure 1. Difference between the spectral absorption index of a 48% aqueous solution of HBr and the corresponding index of water ( T = 25 ‘C).
earlier study.’ With respect to this generally increased absorption for both acids and bases as compared with w Iter, our results agree with those of Ackermann. However, the .shapes of the absorption curves for acids and bases are quite different. No strong absorption maxima near 1750 and 1100 cm-l appear in the hydroxide spectra. Although a region of strong absorption occurs near 2800 cm-l in the hydroxide spectra, the shape of the hydroxide absorption curve in this region is quite different from the shape of the acid absorption curve. We conclude by noting that our results agree with the experimental results of Ackermann with regard to generally increased absorption of acid and hydroxide solutions throughout most of the near infrared but disagree with his results with regard to the shapes of the absorption curves. Our interpretation of the peaks shown in Figure 1 in terms of the H30+ ion is in sharp disagreement with Ackermann’s conclusions. Supplementary Material Available: Spectral reflectance a t near-normal incidence, refractive index, and absorption index for 24 and 48% HBr solutions (Figures 1’-7’,7 pages). Ordering information is available on any current masthead page.
References and Notes (1) Supported in pari by the Office of Naval Research. (2) P. Rhine, D. Williams, G. M. Hale, and M. R. Querry, J. Pbys. Chern.. 78, 1405 (1974). (3) M. Falk and P. A. Giguere, Can. J. Chem., 35, 1195 (1957). (4) T. Ackermann, 2. Phys. Chem. (frankfurtam Main), 27, 253 (1961). (5)D. A. Draegert and D. Williams, J. Chern. Pbys., 48, 401 (1968). (6) D. E. Bethell and N. J. Sheppard, J. Chim. Pbys., 50, C72 (1953). (7) C. C. Ferriso and D. F. Hornig. J. Am. Chern. SOC.,7 5 , 41 13 (1953). (8) C. C. Ferriso and D. F. Hornig; J. Chem. Pbys., 23, 1464 (1959).
1641
Communications to the Editor Editor's note: Professor Ackermann4 has communicated to us his agreement with the assignment of the solution bands to H30+, based on these new data obtained with an improved experimental technique. He further indicates his conclusion that "there are two different types of characteristic changes in the infrared spectra of strong acids: (i) The appearance of characteristic absorption bands, which can be attributed to the H30+ ion: (ii) A generally increased absorpfion, which can be observed in the infrared spectra of bases as well as acids."
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Depart~entof Physics Kansas State University Manhattan, Kansas 66506
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Harry D. Downlng Dudley Wllllams"
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ReceivedFebruary 13, 1976
INTERNUCLEAR DISTANCE
On the Cross Section of 0- Formation in e-02 Collisions between 9 and 17 eV
Flgure 1. Hypothetical potential curves for the ground state of a diatomic molecule X2 and a repulsive state of negative ion Xp- with a outgoing oscillatory wave function. Vertical lines (solid and broken) are drawn at the center of the distribution and at the classical turning points of X p . These delimit the Franck-Condon region.
Sir: Negative ion production in oxygen has been d e t e ~ t e d l - ~ Let us relate this to the energy of the incoming electrons. a t electron beam energies between 9 and 17 eV, in addition to Consider the energy of the incoming electrons to be increased the well-known direct dissociative attachment peak at 6.7 from zero onward. At about 4 eV the value of the cross section eV3-l0 produced by the reaction u begins to increase. In addition when the energy of the electrons is about 7 eV, u is maximum. For energies greater than 7 eV the value of u decreases and becomes very small for E However, in some work, for example, Hagstrum: no 0- ions 9 eV. Since the value of RkO is small but nonzero (because of were found in this energy range. There have been some reports some net overlap after cancellation) (r is predicted to be small on the study of the dependence of the 0- formation cross but nonzero a t energies above 9 eV. As the energy is.further section on p r e ~ s u r e , ~ Jand ~ J ~some suggested interpretaincreased u stays nonzero but small, with very sharp variations.11J2 tions. For energies of the incoming electrons 220 eV the The purpose of this work was to determine what an elephenomena of ion-pair formation becomes the dominant mentary theory predicts for the cross section for 0- formation process. in the energy range 9-17 eV, and to compare this theory with Small peaks in this intermediate region (9 to 17 eV) can be the available data. explained simply in terms of the values of RkO. Since the The Franck-Condon principle13 applies to the optical cancellation of the overlap is not the same for all values of k transition probabilities between states belonging to different (i.e., k 2 12 A-1) the values of RkO are different, and so are the electronic levels. According to this principle, the intensity in values of transition probabilities. Therefore, in this region of absorption from the level u" = 0 is proportional to energy, small peaks occur because of different overlap of the wave functions for different k values. To see if this qualitative description holds quantitatively, where calculation of the overlap integrals was carried out using an IBM 370 computer. The Schrodinger equation with a repulsive potential curve of the form and V ( x ) = A exp(-x/L) (2) Rko = .f $k$O dr is the overlap integral, $k and $0 are the wave functions for the upper unbound level designated by k ( k = m l h ) ,and the lower bound vibrational level with qdantum number u" = 0, respectively. For a transition from the ground state with u" = 0 to some upper state k on the energy scale, the value of R k O is a maximum when the broad maximum of the oscillating outgoing wave function of the unbound state lies approximately above the bell-shaped wave function of the ground state, as shown in Figure 1. One may hypothesize that the Franck-Condon principle might be applicable to electron-molecule collisions. With this assumption, the square of the overlap integral R k o 2 is proportional to the cross section, and will be a maximum for some value of k , e.g., 6 A-1. For large k , the value of Rho2 becomes very small but not zero.
was transformed14 to
y2F" t yF' t ( p 2 - y 2 ) = 0
(3)
where
p = 2Lk and Y = p exp(x/2L)
The standard solutions15 were used to solve eq 3 in terms of the Bessel's function with real arguments and pure imaginary large orders designated here by y and p , respectively. The repulsive potential curve of 0 2 - used was taken from Rapp and Briglia16and was corrected to take into account the survival probability6 with A = 477.76 eV and L = 0.2625 h; defined in eq 2. The Journal of PhysicalChemistry, Vol. 80, No. 14, 1976
