SIMPLE MOLECULAR SPECTRA EXPERIMENTS

Wmm there are many descriptions of laboratory exercises in atomic spectra suitable for physical chemis- try classes,' the choice is more restricted in molecular spectra; especially is this so if simplicity in equipment and interpretation are prerequisites. The two follow ing items, involving only the use of a visual spectro- meter giving wave-length readings to 1 a. or better, have been found very suitable in this laboratory. They illustrate many of the characteristic features in an absorption and an emission spectrum and they can be adequately described for preeent purposes in the form of an abbreviated instruction sheet. The emphasis throughout is on the determination of molecular factors of physicochemical interest.

THEORY

Simple molecules-and more particularly diatomic molecules such as I?, which are being considered here a b s o r b visible or ultraviolet radiation because quanta of that order excite their electronic structures, i. e., an electron is raised to anenergylevelhigherthan that found in the ordinary molecule. In both the normal and excited states the potential energy curves can be drawn repre- senting the conditions in each state for various inter-

MANSEL DAVIES The Edward Davies Chemical Laboratories, Aberystwyth, Great Britain

gies which the molecule can acquire are shown by the levels a t n = 0, n = 1, etc., where n is the vibrational quantum number. Most of the iodine molecules in the vapor at temperatures below 100°C. will be at the lowest vibrational level (n = 0) of the most stable elec- tronic state.? It is from this molecular condition having least energy that they will start in the absorp- tion process. If the atoms vere bound by a force obeying Hooke's law, i. e., by a perfectly elastic bond, their vibrations would be simple harmonic motions, the potential energy curve would be a parabola, and the successive vibrational energy levels would all be equally spaced. This is not found in practice as the restoring force decreases (slightly at first) on stretching the bond: consequently, the vibrational levels get closer together and with increasing values of r, U(r) reaches an upper limit corresponding to the completely separated atoms. Clearly Do is the energy required to dissociate the molecule from its normal ground state, and this is one of the most important factors to be determined from the spectra. In absorption the molecule is excited to the n' levels of the upper electronic state, the different values of n' giving the separate bands. These energy changes are shown by the vertical lines from n = 0 in Figure 1. The vibrational absorption bands get closer together in going toward the violet in the spec- trum owing to the convergence of the n' levels to a maximum energy value. Beyond the corresponding energy quantum L, there is a continuous (i. e., non- banded) absorption arising from the molecules dis- sociating into atoms with varying energies (i. e., veloci- ties) of separation.

In an emission spectrum, such as that of the Cz mole- cule below, transitions occur from the various excited vibrational levels n' to the different values of n for the stable electronic state. This gives rise to a more in- volved pattern of vibrational hands. Under high resolution the individual bands would be seen to be . .

riwre 1. Potential Energy Currea and Vibr.tiome1 Lavels composed of many h e lines, corresponding to the dif- ferent rotational energy changes accompanying a single

nuclear di~tances (r). These curves are of the formshown vibrational change. The present experiments are not in Figure 1. In these curvesthe different vibrational ener. concemd with this h e structure.

' E. g., H. W. THOMPSON, "A Course in Chemical Speetro- THE ABSORPTION SPECTRUM OF IODINE scopy," Oxford University Press, London, 1938. Far brief ac- counts of this field, in order of difficulty, the student is referred to: Experimental. A Point-0-lite lamp is set at 60 cm. (a) 0. K. RICE, "Electronic Structure and Chemical Bonding," or more from the slit of the spectrometer, whose col- Mc~raw- ill Book Co., New York 1940, Chap. IX. ( h ) S. limator, eyepiece, and cross wires are assumed in proper GLASSTONE, "Textbook of Physical Chemistry," D. Van Nostrand Co., New York, 1940, Chap. VIII. (c) A. E. RTJARK AND The population in the other vibrational levels becomes ap- H. C. UREY, "Atoms, Molecules and Quanta," McGraw-Hill preciable as the temperature is raised and gives rise to further Book Co., New York, 1930, Chap. XII. readily observed band sequences involvingn = 1 ,2 , ete.

474

SEPTEMBER, 1951 475

adjustment. An adequate opaque screen is conveni- ently arranged to reduce the illumination on the ob- server a t the eyepieco. An iodine absorption vessel is interposed, at the correct height, between the Point-o- lite and the slit: this can be a clean air-filled spherical bulb, or cylindrical cell with plane ends, giving an absorption path of 12 to 20 cm. Preferably, the cylm- drical cell is wound with a small (20-watt) heating coil, but otherwise the small amount of iodine vapor needed in the cell can be assured from the crystal or two placed in it by arranging the Point-o-lite rheo- stat at a suitable distance or by similarly adjusting a small Bunsen flame. The slits should be as narrow as is consistent with adequate background intensity, and the amount of iodine vapor controlled to give the clear- est definition of the hands being measured. A con- densing lens can greatly increase the illumination at the slit. Satisfactory conditions are very readily found in practice.

Careful measurements are made of the sharp band heads between 5432 A. and 5100 if.: the one near the former value corresponds to n' = 27, and the others must be numbered accordingly, i. e., n' = 28, 29, . . . 50, say.3 After converting from wave lengths to wave numbers (i. e., w in cm.? = 1O8/A in if.), and represent- ing the wave-number difference between successive bmd heads by Aw, the values of n', X (in if.), w (in cm.?), nud Au may be tabulated.

Evaluatzon of the Data. (a) The convergence limit. The energy (in cm.?) corresponding to L might be estimated in a number of ways. Thus the wave length (A,) where the bands are replaced by continuous ab- sorption might he directly observed, but this is not read~ly done satisfactorily. Again, aplot of w against n' shows the gradual approach to the limit w ~ . Much more satisfactory, however, is a plot of Aw for (n' + 1) - (n') for the different values of n', against (n' + '/z). The points so ohtained will show appreciable scatter about a straight line. Although they can be smoothed in various permissible ways, or the "best line" defined precisely by the method of least squares, it will suffice to draw the best straight line through them and extra- polate it to Aw = O.& The total area under this curve from some chosen value of (n' + '/2) to A 0 = 0 repre- sents the wave-number difference between the mean for the bands n' and (n' + I), and the required limit. The area must, of course, be expressed in the wave number units appropriate to the plot. Assuming that the line accurately represents the trend in the Au values, the student should satisfy himself that this procedure is correct. Thus both w, and n', are f ound.

(b) The vibrational frequency and the anharmonicitl~ constant. The vibrational levels in a molecule-and here we are referring to the electronically excited I*

a This numbering is arrived at from an accurate study of the baud sequences (e. g., ref. in footnote 5) and its correotness is ae- eepted in this experiment unless a much more detailed exemina- tion is made. ' The preciee form of this convergence has been examined by

W. G. BROWN, P h ~ s . Rev., 38,709 (1931).

molecule-have the following energy values in wave numbers :

En, = G + a'. (n' + - w ' ~ x ' ~ (n' + l/J2

of, is the vibrational wave number (i. e., the vibration frequency in units of em.?) of the I2 molecule for small vibrations in the excited state, and w', X 3 X 10'" the corresponding vibration frequency in set.-'; x'. is a small numerical factor, the anharmonicity constant, which measures the departures of the restoring force during the vibrations from Hooke's law. G is a con- stant referring the values to any appropriate point taken as the zero of the energy scale.

As the absorption starts from the normal 1% mole- cule with fixed energy value (n = 0: Figure 1) the measured wave numbers should follow the relation:

WV~,.. = woo + w ' ~ (n' + - w'. x'. (n' + '/s)' (1)

woo is the wave number constant corresponding to the transition n = 0 ton' = 0. The student should show in his notes that from this equation the slope of the Aw - (n' + plot is given by 2 wi,x'.. Thus, from the line in (a) the value of w1.x', is obtained in cm.? Using this value and substituting two reliable values of w,,., for n' values about 10 apart in equation (I), both woo and w', are calculated. From the latter and wl.x'., x', is ohtained. These constants define the vibrational energy levels in the excited state and a check on w~ is possible by calculating it from equation (1) with the value of n', found in (a).

(c) Dissociation energies and force constants. Clearly (wL - woo) is the dissociation energy D' for the excited molecules. Using the relation 1 cm.? per molecule = 2.858 cal. per g. mol., conversion to the thermal units is made. A significant estimate of the same important factor is possible on the basis of the relation deduced from the energy levels given by equation (1) above; namely, D1=w',/4x'.. Thisiscomparedwiththe previous value. Also, for the S. H. vibrator, o', X 3 X 10" =

(f'/p)"', where f' is the elastic force-constant 27 for the 1-1 bond in the excited state. If the masses in a diatomic molecule are A and B grams, p = reduce mass = AB/(A + B). This givesf' in dynes/cm.

Referring to Figure 1, it is seen that a t the conver- gence limit, observed as w ~ , the iodine molecule dis- sociates into one normal and one excited atom:

1% - I('PV,) + I* (PP~/ , )

Do is the dissociation energy of the I? molecule in its normal electronic state and is a factor of immediate significance to the chemist. I t is found from the energy relation w,, = Do + E,, where E,, is the excess energy of excitation of the I (2PljJ atom. Its value is Eo = 7598 cm.? and again Do is converted to cal./g. mol. It should be noticed that w,, the vibrational wave number in the ground state, is not observed in this spec- trum. The Raman spectrum of I2 gives it as 214.4 cm.-'; this value is used to calculate f, the force con-

476 JOURNAL OF CHEMICAL EDUCATION

- stant of the normal I* molecule. A summary of the re- having rotational fine structure not considered here) sults should include and these erouo themselves in the svectrum in se- - &

WOO = 15,590 cm.? or, = 20,040 em.-' n'z = (70) quences, each sequence having a given value of An = (n' - n) . Diagrammatically the form of the spec-

w ' s ' . = 0 . . 97 a'. = 131 cm.? tmm may be represented as in Figure 2. D' = 12.7 kg.- cel./g. mol. f' = 0.65 x 106 dyne/em. At least four sequences should be observed as broad Do = 35.58 kg.-cal./g. mol. f = 1.72 x lo6 dyne/cm. bands against a darker background-and, most likely,

the Nadoublet at 5893 A. Each of the sequences is The significant indications provided by the last four seen on careful examination to have a of bright factors and a comparison with those in other molecules edges; these are the features to be measured, as they are (see, for instance, below) should be discussed by the the individual band heads, The student can usefully student. Acceptable values5 are quoted above. reproduce Figure 2, indicating on it the number and in- THE SWAN BANDS AND THE CI MOLECULE tensity of the observed band heads. Three or four

wave-length readings of each head should he made and Hydrocarbons burning with a generous supply of the mean values taken for conversion to em.-' oxygen give a characteristic emission spectrum, known Eoaluation of the All the wave numbers are after its discoverer aa the Swan band system. This set into a table arranged emission is responsible for the blue-green color of the cone of the Bunsen burner. and it is well-established n o 1 2 3 4

that it arises from the Cz molecule.

Experimental. A Bunsen burner is supported a t least 40 em. from the spectrometer; its height and posi- tion and that of a large condensing lens are adjusted so that an image of the green inner cone is focused on the entrance slit. This luminous cone will be brightest with about three-fourths the maximum air supply; more air will turn it blue and greatly reduce the C2 band in- tensities. While the slit widths can he set say at 0.3 mm. during the preliminary observations, they should be reduced to give the sharpest definition of the fea- tures when measurements are being made. It is often helpful to be able to illuminate the cross wires in the eyepiece when wave-length settings on the weakest features are being made.

In this Cz emission spectrum the electronically ex- cited molecules are in different vibrational levels (n') and fall to different vibrational levels (n) in the ground state. Thus a large number of bands avvear (each

MECKE, R., Ann d. Physik, 71, 103 (1923); a d ref. in foot- nate4.

n'

0

1

2

3

4

It is noticed that the sequences form "diagonals" and that in any row thevaluesfall in goingfromleft to right; in a column, they increase on going from top to bottom. The student should account for these regularities in his notes.

The expressions for the vibrational energy levels in the excited (') and ground states in wave numbers are :

E' = Eo' + o'dn' + '1%) - w'.s'.(n' + '/dl E = En + (n + '/d - wa xs ( n + '/d2

where, again, the w,'s represent the vibrational wave numbers for zero amplitudes, and the x.'s are the an- harmonicity constants. For the transition n' = 0 -+ n = 0

EOO = E'o - EO + '/,(w'. - w.) - '/Xw.' xs' - w. xJ

This energy change corresponds to a wave number Eoo em.-', the origin of the band system. The other band wave numbers are given by (E' - E) for n' + n; Z. e., w .,,: urn.., = Eao + [n'w'. - ~ ' ~ w ' . ( n ' ~ + n')l - [no. -z.w.(n2 + n)1

= Em + [n'w'. - z'.w .n'a] - [no. - xa.nal - [n 'z ' .~ . - nxa-1

As w. and w', are of the same order, and both x, and XI. are within the accuracy of these observations the last term in brackets can be neglected. Thus for constant n' the above expression reduces to:

w,,. = Constant - [no. - zaene]

This relation must represent the wave numbers in any one row of the n'n array. Substituting in it the values from any row in which three or more entries occur, both w, and x, are calculated. The calculation can be

SEPTEMBER. 1951 471

repeated for any second row of three entries, and the mean values of these constants chosen. Using the re- lations previously quoted, the force constant f and the Morse value of the dissociation energy D for the ground state of the Ca molecule are calculated. Simi- larly, with constant n,

w,,, = Constant' + [n'w'. - z'd.n'']

This relation clearly applies to any column in the array. It is used with any three entries in one column to cal- culate f' and D' for the excited state of the molecule. All the results, including the products x,w,, and x'.w',, are summariaed in a table with the appropriate units indicated in each case. A significant discussion can he based on them in the light of the accepted electronic configuration of the Cz molecule (%) which represents a double bond. Precise data on this spectrum are readily a~ailable.~ A consideration of the data obtained and

E. g., A. G. GAYDOK, "The Dissociation Energies and Spectra of Diatomic Molecules," London, 1947; G. Henberg, "Molecular Spectra and Molecular Structure," Prentice-Hall, Ino., New York, 1939, Vol. I.

evaluated in this simple way leads to one important suggestion. The force constant, f, for the ground state of the Cz molecule is found to be 9.5 X lo5 dyne/ em., in satisfactory agreement with the interpretation of the 8u configuration as representing a double bond (compare, f = 9 to 10 units in simple ethylenic com- pounds). Hersberg' has argued in favor of a value for the dissociation energy of the ground state, D, equal to 83 kg.-cal./g. mol. (3.6 e. v.); Gaydon has tentatively used the same figure but recalls that the linear Birge- Sponer extrapolation leads to the much higher value of 160 kg.-cal./g. mol. The value obtained as above from the auharmonicity is 164 kg.-cal./g. mol. A figure of this order appears to conform far better to those in other diatomic molecules having double bonds than 83 kg.-cal./g. mol., which is more nearly characteristic of a normal single bond. Accordingly, in view of the value of the force constant and the well-known remarkable validity of the simple Morse potential function, the proposal is made that D really is in the region of 160 kc.-cal./c. mol. rather than half that value.

' Ibid., p. 472.