Enhancement of the Rotation-Vibration Bands of HCI W. 0. George, I. W. Griffiths, B. Minty, and Rh. ~ewis'
School of Applied Sciences, University of Glamorgan, Pontypridd, Wales. U.K This paper focusses upon a less well-known source of deviation from the Beer-Lambert law whereby nonabsorbing components ('buffer gases') intensify the observed spectrum of an infrared absorber, an effect that we describe as 'spectral enhancement' and that the molar absorptivity of the absorber appears to increase with the polarity and partial pressure of the buffer gas. A dramatic of this effect, provided by J. Corbett, is shown in Figure 1, where the transmittance of 0.13 torrof CO is monitored as a function of gas pressure in a 40-m cell using a spectrometer resolution of 1em-'. As the buffer gas pressure increases, the rotation-vibration lines become more intense causing the CO spectrum to "grow" apparently out of the spectrometer noise. Direct observations of line-broadening for gaseous systems require the use of spectrometers that are capable of resolving the doppler line widths, but (as this paper demonstrates) considerable semi-quantitative information may be obtained using analytical spectrometers that operate at lower resolution where spectral lines are distorted by the spectrometer. The investigations are expanded readily into a student physical chemistry project. In this paper, student measurements of the enhancement of HCl(g) at low resolution by several foreign gases are reported and the enhancement rationalized in terms of rotational-translational (R-T) energy transfer between HCl and the molecules of added gas. Familiarity with the origin of infrared spectra (1)and with intermolecular forces is assumed. Finally, the practical consequences of spectral enhancement to analytical measurements are briefly discussed. '~uthorto whom correspondence should be addressed
Tars1 pressures (N2): (tori)
A 8 C
--
-
-
0.13
0
29
E
83
F = 760
Experimental Infrared spectra were recorded over 64 scans at 2 cm-' resolution at ambient temperature using a Digilab FTS-50 (TGS detector, dry air purge) with triangular apodisation. Peak areas were evaluated using the Digilab Quant 32 routine. Samples were contained in a 10-cm glass cell with KBr windows. HC1 (BDH Ltd) was used without purification. Liquids were degassed before use. Deuterated benzene and acetone were used to minimize the overlappingof bands between the buffer gas and HC1. The Enhancement of HCI Bands Figure 2 shows the spectrum obtained after subtraction of the spectrum of 50 torr HCl(g)from that of a mixture of 50 torr HCl and 710 tom argon. It is evident that all the bands are enhanced by the argon, with preferential enhancement occurring for the PI and R, bands. These bands are produced by the following transitions: u"= O S ' = l + u ' =
1J'= 0
[Pll
that is, the enhancement shows a J"-dependence. This may be contrasted with the spectnnn of pure HCl(g)where the PQband (corresponding to the maximum rotational population a t u = 0 J = 3) is the most intense. The percentage increase in absorbance (by peak heights and peak areas) for the P-bands is listed in Table 1. Previous studies of HC1 at high resolution (2)have shown that self-broadening is most pronounced in the Pg band; whereas, added gases cause the greatest broadeningin the PI and R, lines for both Hg5C1and Hg7C1.The similaritv of such results to those contained in Tahlc 1 confirms that at low resolution the broadenina of' lines bv colliwms ~ " ~ r e s sure-broadening")mainfests rtself as band enhancement, Different groups of students may be asked to carry out the measurements at different resolutions. Our measurements have confirmed that the percentage increase in ahsorbance is independent of resolution within the range 2-8 ern-', the range in which most commercial spectrometers operate. Similar experiments may be conducted by replacing the argon gas with different gases and vapors (Table 2), with
117
322
Figure 1. Spectra of the 2143 cm" band of a constant partial pressure (0.13torr) of CO in N.,
Figure 2. Subtraction spectrum (50 torr HCI) + (710 torr Ar) - (50torr HCI: resolution = 2 cm-'. Volume 71 Number 7 July 1994
626
Table 1. Peak Absorbances and Enhancement of HCI Bands
Peak height band
PI
wavenumber /cm? 2865
50r HCI
50r HC1+71or
% increme in the area of the PI band
6 0
%increasein absorbance Peak height
Peak area
121
118
Ar
0.0471
0.1040
" 0
20
60
40
80
100
partial pressure of ethene I torr Figure 3. Variation of the enhancement of HCi with the partial pressure of ethane. Table 2. Comparison of the Enhancement Gradients for the PI Band of HCI at 50 torr Pressure by Added Gases
Gas
% increase in PI area per torr
Argon Ethene
0.41
r=- h
2nAv
Carbon monoxide Carbon dioxide
0.58
Tetrachloromethane Ethyne ds-benzene
0.83
Trichloromethane Sulphur dioxide Fluorobenzene ds-acetone Hydrogen cyanide
2.04
Ethanai
2.22
Acryionitrile
2.26
The average percentage standard deviation of the gradients was t 1 %
measurements being restricted to the P1 hand for which enhancement is greatest. The variation of the percentage increase in absorbance for the P1 band for HCKg) at 50 torr pressure with the partial pressure of added gas was generally linear below 100torr and the slope ('enhancement gradient') was taken as a measure of the enhancement properties of the added gas. For example, the ethenemC1 mixture yielded Figure 3 with an enhancement gradient of 0.51% per unit torr of ethene. Discussion
A qualitative explanation of the J-dependence of enhancement is obtained by considering the collision between the molecules of buffer gas and a rotating HC1 molecule in the upper (v = 1) vibrational state. Classically, the collision is more effective in slowing down the rotating HCl molecule if the HC1 enters the collision in a lower rotational state. Alternatively, enhancement may he pictured as a quenching process. The effect of a collision is to reduce the lifetime of the vibrational-rotation state produced by 622
the absorption of a photon from the spectrometer beam, with a resultant increase in the uncertainty of the absorption freauencv causing a broadenine of the s~ectralline. s rklated to the The full iine &dth at Llf-height ( ~ u y ithen lifetime (TIof the excited state by the expression:
Journal of Chemical Education
(1)
where h is the Planck constant (3). The collision rate, Z, between a molecule A and molecules of B is given by the equation: z = 3.349 x 10" dm2 (mr)-0.5pB (2) where P g is the pressure of gas B (in atm), T the temperature of the system (K),dm the average collision diameter (in hgstroms), and m the reduced mass of the collision pair in amu (4).When A = B the collision rate is reduced by half. Use of this equation in conjunction with eq 1,and assuming that every collision is effective in quenching the excited state, gives a self-broadened line width for HCl of 8.5 x lo4 em-'. This calculation predicts the same line width regardless of the nature ofthe quenching molecules, and it also assumes that every collision transfen energy with equal probability (no J-dependence). Nevertheless, the generated line widths are of the same order as ohsewed experimentally (2). This model may be adapted successllly to explain the obsewed J-dependence of HCl enhancement by buffer gases by followinn the ideas of Crane-Robinson and Thomps& (5). ~ e c a u s ethe energy gaps hetween successiverotational encrm levels in HCI hecome laraeras J (the rotational quantumnumher) increases, energy transfer between a rotationally excited (v=l, J')HC1 molecule and the buffer gas becomes less probable as J' increases. Since the time of the CraneRobinson paper, the field of molecular dynamics and energy transfer has expanded greatly, and the relaxation of the HC1 excited state by collision is now attributed to rotation-translation ( S T )energy transfer (6). What evidence is there for this mechanism? First, studies of relaxation in gases have demonstrated that V-T transfer, although much faster than V-V transfer, is much slower than R-T transfer (6). This confirms that the relaxation of the vibrational state may be neglected over the time scale that rotational energy transfer occurs. Second, this model of line broadening also requires that R-T energy transfer is itself J-dependent, and this pattern has been confirmed bvindenendent molecular dvnamical studien of the relaxaGon uf'11~1 gas itself. The ionRlifetime of vibrationally excited HCI r = 2.8 x 10-' s, for the fundamen~
~~~~~
tal transition (7)makes direct observation of infrared fluorescence complicated because of collisions with vessel walls, but Polanyi and Woodall (8)have studied rotationally resolved emission from vibrationally excited HCI produced by the reaction: H t C1, = HC1 W J ) + C1 in which a considerable fraction of the reaction exoergicity goes into the rotational excitation. Their data is consistent with a selection rule of M = 1and a simple energy gap law in which the probability (PIof R-T transfer decreases as the amount of energy (a) transferred increases. Studies of rotational energy transfer are unable to directly distinguish between R-T and R-R (rotation-rotation) transfer, but since addition of buffer gas (which favors R-T transfer) slows down the overall depletion of a rotational state (6)it is believed that R-R transfer is the faster process. The expectation that the self-relaxation of pure gases proceeds predominantly by R-R transfer (single auantum transitions between molecules that Dossess resonant energy levels) explains why the corresponding J-dependence of self-broadeningfollows the Boltzmann distribution of ground rotational states. Are the s ~ e c t r aof other infrared absorbers enhanced in a similar way to HCI? A suitable case to study is CO. Although the spectra of CO is enhanced by buffer gases, the PI and % bands are not selectively intensified to the same degree as HC1. This may be explained by considering the rotational energy levels in the molecule. CO has a smaller rotational constant than HCI so that the rotational states are closer; the R-T relaxation rates of different rotational states would then be expected to be similar. Because R-T transfer can only occur once a collision has taken place, it is reasonable to expect the probability of enerw transfer to increase as the intermolecular force betweGthe buffer gas and HCl molecules increase. This rationalizes the different demees of enhancement caused bv different buffer gases. lnt&nolecular forces may be tak& to be the sum of di~oledi~ole. di~oleand . . di~ole-induced . dispersive contributions, and students may estimate the totul inwrmolecular using standard ex~ressions19). Such calculations show that &pole-dipole f&ces are the most important contribution to the intermolecular interaction for polar molecules. Figure 4 shows a plot of enhancement gradient versus the dipole moment of the buffer gas molecules. Asimilar correlation originally was noted by Kortum and Verleger (10). This explains why line-broadening has been used as a probe of intermolecular forces (11). Concluding Remarks
the HC1 infrared The bands (PI, P2, % . . maldng fundamental may be regarded as separate spectra produced by many different 'molecules' corresponding to HCI in different ground rotational states. To put the enhancemerit effect into context, we need only to consider one of these 'molecules', such as the H3'C1 monomer in the v = 0 J = 1level that rise to the p1(H35C1)line centered at 2865 cn-'. The measured absorbance of a s a m ~ l of e HCl at a fixed pathlength at 2865 ~ m - depends l three "ariables. The fmst, the concentration of H3'Cl (v = 0 J = I), is a consequence of the primary requirement that absorption only occurs when binary collisions take place between the absorber and photons of specified frequency. The concentration of absorber will be proportional to the total pressure of HC1 at that temperature. The second contribution, self-enhancement, is a consequence of collisions between H3'C1 (U = 0 J = 1)molecules. This is also proportional to
upon
,,
Enhancement oradientl % inr; per torr
2 - - ~ - ~ ~ -- ~ ~
1.5.~
~
~
.-
-
-
.
.~~
1
o
t
2
3
4
Dipole moment / D Figure 4. Correlation of enhancement with dipole moment of added gas. the total HC1 pressure (eq 2) and cannot be distinguished from the first contribution except under sub-Doppler resolution. The third contribution, enhancement by buffer gases as modified by the fmite resolution ofthe spectrometer, is pmportional to the pressure of the foreign gas. All of the foreign gases listed in Table 2 form identifiable hydrogen-bonded complexes with HCl(I2, 13).This phenomenon is best regarded as quite separate from the enhancement of spectral bands. Whereas, the degree of enhancement is roughly pmportional to the polarity of the added gas, the strength of hydrogen bonds is a complex function of several parameters. For example, amines generally are observed to form stronger hydrogen bonds than the correspondingnitriles (14);whereas, the amines (being more polar) are expected to show the greater enhancement effect. The presence of enhancement effects in spectra has potentially serious implications for (say)the analytical determination of samples containing HCl and other gases using calibrations based upon pure HCI. The simple additive rule of spectroscopy, whereby an absorbance at a particular frequency is assumed to be the sum of the absorbances of the pure components at that frequency, is rendered inapplicable by enhancement in the same way that the rule fails when components react chemically. One practical solution frequently adopted with mixtures of trace gases is to swamp all other enhancement effects by pressurizing the gas sample to a set pressure with excess diluent (e.g., air). Only at low total pressures will enhancement effects cease to be important. Such pressures often are present in stellar clouds and in the upper atmosphere, andin these cases the ~~~~l~~line widths Literature Cited
I. B ~ ~ . u , c . N . ~ ~ ~ ~ ~ . ~ I ~ ~ M o I ~ ~ I I I s ~198S,Chap PPLLL~~M~G~~w ter 3.
2. B a b w H.:Amem,G. Benesch, W.J C h m . P h w 1360,33(1),16150. 3. Shtiver, D. F; A t h a . P.W. W a r d , C . H.Inogonie Chemistry: M G o r d Universjty fie- ~~ s s-a"&R -~~ ~ ~- , 4. Yardley,J. T. Intmdudion LoMdoculor h e w k w f w ; Academic Press, 1980, pp
1wzo. 5. C.ane-~obinm, c.:momp-, H . w P-. ~ o sot y A. 1m,272,45346. ~ S . ~ e s1988, . 1,121-127. 6. ~lygare,W. H . A ~ U ~ them. 7. & ~ 4 P, 68.
8. Polanyi, J. C.; Waadall, K B. J. Chem. Phys. 1972,56,1561. pphysiml Orfmd Univrrsity 1990, 6 5 4 4 2 . 10. ~ ~ r tc.;verleger u ~ , H.P-. phye S ~ C (. h d m ) . 1 8 t ~ ) 63.4~69. , 11. Val'ou8 contribufor~,F a d y Discvss. Chem. Sot. 1888.86.3146. 12. George. W 0.;Lewls,Rh. Hussain, G. RRB,G. J. Mol. Strud. 1988,189,211-226. 13, Geoqe, W,O,; hwis, Rh Chem,,m ress. 14. M U ~ IJ.. N . C ~ ~ ~ 1889,107-110. . B ~ ; ~ .
,,,,,
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