J. Leland Hollenberg University of Redlonds ~edlands,Colifornia
I
Pure Rotation Spectra of HCI and NH, A physical chemistry experiment
M a n y students of physical chemistry are now exposed to the concept of pure rotational energy levels of a molecule, the calculation of rotational partition functions, and the determination of their contribution to statistical thermodynamic quantities such as heat capacity and entropy. However, there are very few experiments which can be done a t the undergraduate level to give students a feeling of reality for rotational quantum levels. I t is true that vibration-rotation experiments (I) can give some of the same information as pure rotation spectra, but it is instructive t o show experimentally what results can be obtained when pure rotation spectra are observed. Unfortunately, most molecules which possess a permanent dipole moment and which therefore exhibit a pure rotation spectrum have such large moments of inertia that the transitions occur in the microwave region of the spectrum. Furthermore, very few undergraduate chemistry departments have microwave instruments available for student use. However, a few molecules, includin~HC1 and NHs, have small enough moments of inert; that some of the new broad-&nge, highresolution infrared spectrophotometersl can be used to observe a number of the higher-J rotational transitions. -~
For example, the Beekman IR-12 or the Perkin-Elmer 621 infrared spectrophotometer, both of which extend in range to 200 cm-'. 1
cm-' Figure 1. Part of Re pvre rotation infrored spectrum of path lrngth 10.0 cm, dii 2.5 cm-'. 700
Our junior year students in physical chemistry have obtained satisfactory results using the following procedure. A 10-em gas cell with polyethylene windows2 is filled on a vacuum line with about 700 mm of anhydrous HCI or about 100 mm of anhydrous NH,. The double-beam spectrum of each gas is run between about, 200 and 350 cnx-I, using two thicknesses of polyethylene identical to the cell windows in the reference beam to compensate for scattering and absorption losses. In Figures 1 and 2 are shown the portions of the rotation spectra of HC1 and NHa observable with this procedure. I t should be noted that interference from absorption by atmospheric water is a serious problem in this spectral region. After a preliminary run, the spectrum is spread out by means of higher chart-paper speed in order to facilitate greater precision of linear interpol* tion of frequencies. I n Tables 1 and 2 experimental frequencies and line spacings are presented which are typical of student results. The indexing of the absorption lines is in terms of the upper rotational state High-density polyethylene, 0.020 in. (obtainable from Csdillac Plastic and Chemical Co., 15111 Second Ave., Detroit, Mich.), is satisfactory for cell windows. Rigid metal frames may he used to bolt the windows against the approximately 38mm diameter glass cell body. A thin coating of high vacuum grease aids in sealing the polyethylene to the smoothly sawed ends of the cell. A ground joint and stopcock are necesutry for evacuating and filling the cell.
cm-I HCI.
Pressure
Figure 2. Port of the pvre rotation infrared spectrum of NHI. 1 00 mm, poR lenglh 10.0 cm, slit 2.5 cm-'.
Prenure
Volume 43, Number I , January 1966
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quantum number, J'. The value of J' for a particular transition is most conveniently determined by extrapolation of data given by McCubbin (9) for the lower wavenumber region. Table 1.
Pure Rotation Absorption Frequencies for HCI
J'
t' (cm-I)
10
206.2
Spacing (em-')
different portions of the spectrum. I n this experiment the internuclear distances in NH3 cannot be calculated because there are three moments of inertia (two of which are identical) and hence the data are insufficient. However, a procedure described under Non-rigid Rotor below suggests calculations which provide a basis for comparison. The Non-rigid Rotor
If a non-rigid rotor is assumed (5) one obtains for absorption: 5 =
Observed using a Beckman IR-12 spectrophotometer; no corrections to vacuum wavenumber were made. Table 2.
Pure Rotation Absorption Frequencies for NHa
J' 11
6"
(em-')
Spacing (om-')
215.6 1X 9
Observed using a Beckman IR-12 spectrophotometer; no corrections to vacuum wavenumber were made. The Rigid Rotor
If a rigid rotor model is assumed (5) the frequencies in cm-' of the absorption lines, P, are given by where the rotational constant B = h/8s21c (in units of cm-I), with h = Planck's constant, c = speed of light, I = moment of inertia, and J the initial value of the rotation quantum number for the transition. For absorption the selection rule AJ = +1 is to be used, and equation ( 1 ) reduces to Thus the spectrum should consist of a series of equidistant lines, with spacing 2 B. By selecting an average spacing between successive lines for HCl from Table 1, one obtains B = 10.0 cm-', so that I = 2.80 X g cm2. Since I = pr2 for a diatomic molecule like HCI where p = m,mz/(mr mr), with?, and n 2 ~the atomic masses, one calculates r = 1.31 A, which is somewhat larger than the value 1.29 A, based on data given by McCubbin (2) for J' = 1 , 2 , 3 , and 4. A result such as this is to be expected for application of the rigid rotor model to regions of the spectrum with such different values of J. Similarly, from Table 2 an average spacing between successive lines for KHs gives B = 9.20 cm-'. This g cm2, which is somegives a value of I of 3.05 X what greater than 2.83 X g cm2, calculated from n4cCubbinJs data for the first few values of J'. Again, just as for HC1, adiscrepancy of thissort is to be expected when the rigid rotor approximation is applied to quite
2 B(J
+ 1) - 4 D(J + 1)'
(3)
where in the cme of a diatomic molecule the centrifugal distortion constant b = 4 B 3 / 2 , with W = the vibrational frequency in cm-I. By rearrangement there results: 5/(J
+ 1) = 2 B - 4 D ( J + 1)'
(4)
This is the equation for a straight line! so that by plotting values of v / ( J 1) against (J f the intercept gives 2 B and the slope gives -4 D. When this is done for HC1 as in Figure 3, it is found that B = 10.42 + 0.02 cm-' which compares well with McCubbin's value of 10.40 cm-'. Using theoexperimental value of B, calculation of r gives 1.285 A. This may be compared to the effectiveinternuclear distance in the lowest vibrational level, ro = 1.2838 A, but should not agree as well with the equilibrium distance, r. = 1.2746 A, as given by Herzberg (4) since r, corresponds to the completely vibrationless state. The slope in Figure 3 is -2.0 X cm-l, which gives D = (5.0 =t0.5) X 10W4 cm-'. This may be compared to McCubbin's value of 4.0 X cm-'; or from the HC1 vibrational frequency, W = 2890 cm-I, one can calculate D = 5.4 X cm-l, which agrees with experiment within the limits of error. The correct treatment of the non-rigid symmetric top molecule, such as NH,, is much more involved, but according to Herzberg (5) if the pure rotation spectra are observed under low resolution the same formula which describes centrifugal distortion for diatomic molecules may be applied. However, the constant D
+
+
8
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Journol of Chernicol Education
20.4 0
50
IW
IS0
200
250'
Figure 3. Plot for HClto obtoin the rotational conston1 and thesentrifugal di$tetortion constant D. Ordinate 5/(J 11; abrcisso IJ 1P.
+
+
is now simply an approximate parameter used to fit the data. Application of equation (4) to the data for NHa gives Figure 4, whose slope yields B = 10.00 0.01 cm-'. This compares well with i\4cCubbinJs value
*
Even though B does not provide sufficient information to calculate the remaining moment of inertia about the figure axis and hence does not allow the geometry of the NH3 molecule to be determined, we have found the following procedure to be a rather challenging and satisfying conclusion to this experiment. From the experimentally determined value of B of 10.00 em-', I is found to he 2.799 X g cm2. From the known geometry of the NH3 molecule (6), our students calculate the two different moments of inertia. This requires careful application of theorems of mechanics studied in a previous physics course, but is not particularly difficult. Calculated values of I may he checked by comparison to Herzberg (5) in which the accepted value of 2.815 X loWM g cma is given. Students are then led to realize that this moment of inertia, which is computed about an axis of inertia perpendicular to the 3-fold axis of symmetry of NH3, involves rotation of the permanent dipole of the molecule, which is a necessary condition for interaction with light to produce a pure rotation spectrum. The agreement of calculated and observed I values is seen to be quite satisfactory. Literature Cited
\ 19 2
0
SO
IW
150
250
200
Figure 4. Plot for N K to obtain the rotationd constantiand thseontrifu1 I; abscissa IJ 119 gal distortion eonstant 6, Ordinate i / l J
+
+
of 9.990 cm-I. The value of b obtained from the slope cm-', which does not agree very is (7.7 + 0.2) X cn-I. well with McCubhiu's value of 4.44 X loW4
STAFFORD, F. E., HOLT,C. W., AND PAULSON, G. L., J. Chm. Educ., 40, 245 (1963); SHOEMAKER, D. P., AND GARLAND, C. W., ''Experiments in Physical Chemistry," MoGraw-Hill Book Co., New York, 1962, p. 309. T. K., J. Chem. Phus., 20,668 (1952). MCCUBBIN, B-ow, G. M., "Introduction to Molecular Spectroscopy," McGraw-Hill Book Co., New York, 1962, pp. 5P60. HERZBERG. G.. "S~ectraof Dhtomic Molecules." D. Van Nostrand cd., I";., Princeton, N. J., 1950, p. l i 4 . HERZRERG, G., "Infrared and Raman Spectra," D. Van Nostrand Co., Inc., Princeton, N . J., 1945, pp. 26-34. L. E., edilw, 'Tnteratomic Distances," The ChemiSUTTON, cslSociety, London, 1958.
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I, January 1966
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