A Gas Chromatography Experiment for Proving
the Application of QuantumSymmetry Restrictions in Homonuclear Diatomic Molecules M. Dosiere Universite de I'Etat a Mons. Facult6 des Sciences. Service de Chimie-Physique et Thermodynamique, Avenue Maistriau,21, B-7000 Mons, Belgium
Theoretical Background ( 1,2)
A homonuclear diatomic molecule is made up of two identical nuclei and one or several electrons. A wave function, $, solution of the Schrodinger equation that represents the state of a homonuclear diatomic molecule must be symmetrical or antisymmetrical in the exchange of the two nuclei if they are, respectively, hosons or fermions. The wave function must also he antisymmetricalin the exchange of any two electrons. The Hamiltonian H for one molecule is a t least approximately separable H=Htr+H,+Hvib+H.~+Hn
chromatographic assembly consists of a 1.5-m coiled glass column of 6-mm diameter filled with 20140-mesh activated alumina in series with a manometer-type flow meter and a Gow Mac thermal conductivity cell connected to a chart recorder (Fig. 1). All runs were made with the column immersed in liquid nitrogen and with the conductivity cell a t room temperature. Alumina was selected as a good diamagnetic absorbent which, a t 77 K, would not catalyze the orthopara conversion. Flow rates were in the range 150-300 em3/
(1)
and the wave function J. is *=*t.l..*rot.*,b.*d.h
(2)
(tr = translation; rot = rotation; vib = vibration; el = electronic; n = nuclear). In order to reach the range of temperatures where quantum effects would show up, very low temperatures are needed except for light molecules such as Hz and D2. For Hz, translation is classical, while the vibrational and electronic degrees of freedom are completely unexcited in the temperature range of interest (10-300 ti). As the hydrogen nucleus is a fermion, the wave function of the molecule Hz must be antisymmetrical in the nuclei. Parahydrogen and orthohydrogen molecules have, respectively, antisymmetrical and symmetrical nuclear wave functions. The ratio of the molar fractions of parahydrogen ( p H 2 ) and orthohydrogen (+Hz) is therefore N p . ~ -2 1 J=0.2,4 N o - ~ 23
Figure I . Experimental chromatographic assembly used fw separating the nuclear isomers of H,: (a) catharometer. (b) injector device, (c)chramatographic column. (dl liquidnitrogen. (e) Dewarflask.(f)dryingagent, (g)flow meter.
(W+ l)e-J~J+ll~rdT (3)
(25+ ~)~-JiJfl)BrdT
J=1,3,5
Orat is the characteristic rotation temperature (O,ot~H, = 87.2 K1 --,.
The equilihrium mixture approaches 100%p-Hz as T a p proaches 0 ti ( J = 0). The high temperature limit for N D J. ~ no.^% is 113, i.e., 25% p H 2 and 75% O-Hz.The equilihrium percentage of p-Hz in H Zgas can he easily computed from eqn. (3) as a function of temperature T. Thermodynamic functions for each species of hydrogen gas has been calculated by Giauque (3). Experimental
Orthohydrogen and parahydrogen can be separated by gas-adsorption chromatography (4-11). Activated alumina columns operated a t 77 K using neon as the carrier gas give separation of the nuclear spin isomers of Hz. The thermal conductivities of hydrogen, helium, and neon being, respectively, 0.1508, 0.0484, and 0.1868 W m-' ti-' a t 300 K, it is better to use neon rather than helium as the carrier gas. The
1
2
"
3
4
-
Time /minute
Figure 2. Gas chromatagrams: (a) hydraggn stocked at 295 K, (b) hydrogen equilibrated at 82 K on active charcoal for at least 2 hours. The injected volumes are in both cases around 0.4 om3..,
Volume 62
Number 10
October 1985
89 1
Gas Chromatoara~hlcAnalvser ol Hvdroaen pH2(%)
Temperature IK)
experimenlal
calculated
min; retention times were between 2 and 4 min. In our device, hydrogen was not converted to water over copper oxide prior to analysis in thermal conductivity cell as suggested by Moore (6). Partial deactivation with carbon dioxide restores ortho-para separation (7). Without catalyst, the half-time of interconversion between ortho and para states is very long compared with the time of an experiment. Active charcoal is found to be a catalyst for the ortho-parahydrogen conversion (12-14). Results
Chromatograms of hydrogen kept at 295 K and hydrogen equilibrated at 82 K on active charcoal for at least 2 h are shown by curves (a) and (b),respectively, in Figure 2. Since the peak area ratios represent mole ratios, the identification of each nuclear isomer is clearly demonstrated by the results
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Journal of Chemical Education
of analysis of two samples of hydrogen equilibrated at different temperatures. Experimental results are given in the table. Comparison with the theoretical, computed values shows good agreement, within 1 to 2%, which is due in part to estimation of error in the area under the peaks in the gas chromatogram. The temperature of 82 K was measured with a vapor-pressure thermometer filled with methane. The explanation of why O-Hzis preferentially retained in the alumina column during the chromatographic separation has been given by several authors (4,5,15,16). Literature CRed (1) Fowler. R., and E. A. Guggenheim. "Statistical Thermodynamifa; Cambridge University Press, 1965. (21 Hi1l.T. L.."An Introduction tostatistical Themodwarnin,"Addiwn-WesleyPublishing Co,lnc.,London. (31 Giauque. W. F.. and Johnston. H. L.. J. Amen Chem. Soc.. 50,3221(1928). I41 Sand1er.Y.L..J.Phys.Chem., 58.58(19541. 15) Sand1er.Y. L., J. Chem. Phys..29.97 (19581. 161 Moore, W. R., and Ward, H. R., J Amor Chem. Sm., 80.2909 (1958). (71 Evett,A. A., J. Chem. Phys,31,565(1959). (61 Smith H. A,. and Hunt. P. P.,J. Phys. Chem., 64.383 11960). (91 Van Hook, W. A., and Emmetf P.H., J. Phyr. Chom., 64,673 (1960). (101 Moare. W. R.,snd Wsrd,H.R., JPhys. Chem.,64,832 (19601. (Ill Hunt,P.P.,snd 5mith.H.A,, J Phyr. Chom., 65.87 (19611. (121 Bonhoeffer,K. F., and Harteek, P..Notunuisa., 17,182 (1929). (131 Bonhaeffer, K. F., and Harteck, P.,Siirbw.preuss. Ahad. Wiss.,103(1929). (141 Eueken,A.,andHiller.K.,Z Phydh. Cham..84,142(1929). (151 White,D.,andLssnet1re.E.N.. J. Chom.Phys.,32.72(1960). (161 Freeman, M. P.,and Hagyard, M. J., J. Chem. Phys, 49,4020 (1968).
