July, 1956
NUCLEAR SPIN CONTRIBUTION TO THERMODYNAMIC PROPERTIES OF Iz, Brz AND Clz
909
it is unreasonable t o say that heat conducted down TABLE I11 EFFECTOF TUBE DIAMETER ON CONSUMPTION RATEDURING the aluminum tube walls was able to heat the liquid TURBULEXT COMBUSTION OF THE SYSTEM 2-NITROPROPANE- to a sufficiently high temperature to produce the observed increase in consumption rate. Perhaps, 9570 " 0 s Inside diameter, mm.
~
89.4
Consumption Rate (cm./sec.) Pressure (atm.) 109.8 137
0.5" 1.24 2.74 1.2" 1.70 5.21 1.8" 3.71 8.53 2.5b 6.12 11.68 3.5b 6.22 12.87 4.0b 7.19 13.13 5.0b 8.48 14.91 6.0b 10.13 21.18 7.0b 11.66 24.79 8.0b 12.95 9.0b 19.66 Capillary tubing. * Standard tubing.
5.77 10.49 14.33 17.32 23.34
sumption rates than those obtained in Pyrex. During the time required to fill these tubes and carry out the combustion, a portion of the tube would dissolve in the mixture. Thus, data obtained in these tubes were not considered valid because essentially a different mix was being burned. As an example of high thermal conductivity material aluminum tubes were tried. Frequently the fuse wires would come in contact with the tube and short out prematurely; but some valid data were obtained from these tubes. The consumption rate in these tubes was two to three times higher than that obtained in Pyrex. This seemed quite reasonable since heat could be conducted down the tube wall and heat up the liquid. Therefore, the liquid would be burning a t an effectively higher ambient temperature. However, for this system this large increase in consumption rate would have to be due to the liquid burning a t an effective ambient temperature of something like 390". It has been shown that the surface temperature of this system is approximately 190°2; hence,
some of the aluminum was dissolved and the salts produced had a catalytic effect on the burning process. A search was made for tubes that would burn down as fast as the liquid was consumed. Many different combustible materials were tried but none seemed to work satisfactorily. For example, ballist.ite tubes, approximately the same dimensions as the Pyrex tubes, were prepared and an inhibitor was applied to the inside and outside surfaces of the tube, This prevented the liquid from being absorbed into the ballistite and prevented the ballistite from dissolving in the liquid to produce effects similar to those obtained with bakelite tubes. The rate obtained with ballistite tubes was an inteymediate between the ballistite burning rate alone and the rate of the liquid in Pyrex tubes. Since ballistite alone has a burning rate in the low pressure region greater,than that of the liquid this result was quite rea.sonable for the rate is a compromise on burning surface. The ballistite tube simply burns down ahead of the liquid, but the liquid flows over the edge of the ballistite tube and tends to increase its own burning surface and decrease the burning surface of the ballistite. I n the turbulent region where the liquid burns faster than the ballistite, results were similar t o those obtained in Pyrex tubes. To be successful, it would be necessary to use a solid whose burning rate is slightly less than that of the liquid a t all pressures and the pressure coefficient for the solid and the liquid would have to be very nearly the same, so that there would be no cross over in the burning rate curves of the two materials. From these studies, it appears that tubes of an inert substance will give the correct consumption rate but combustible tubes or tubes that react with the system being burned will very likely give spurious consumption rate values.
NUCLEAR SPIN CONTRIBUTION TO THE LOW TEMPERATURE THERMODYNAMIC PROPERTIES OF IODINE, BROMINE AND CHLORIKE BY H. W. DODGEN AND J. L. RAGLE Contributionfrom the Department of Chemistry, The State College of Washington, Pullman, Washington Received December 1.8, 1966
I t is pointed out that sufficient data exist for exact calculation of nuclear spin contributions to the thermodynamic properties of some substances. At low temperatures these contributions form the major part of such properties. Sample calculations have beer1 made from existing data for the cases of solid iodine, bromine and chlorine.
In 1924, two years before Uhlenbeck and Goudsmit postulated the existence of electron spin, Pauli suggested that the nucleus itself might possess a spin angular momentum. Following this, Gibson and Heitler' carried out a detailed statistical calculation, including possible nuclear spin effects, of the thermodynamic equilibrium constant for reactions typified by the dissociation of gaseous iodine. (1) G. E. Gibson and
W. Heitler, 2. P k y s i k ,
49, 465 (1928)
Giauque12in 1931, from consideration of existing heat capacity data for solid iodine, concluded that even a t temperatures slightly below 10°K. the populations of possible spin states had already reached the high temperature equilibrium distribution. This implied that the spacing of any such levels was much less than thermal energy a t this temperature in solid iodine. (2)
W. F. Siauqiie, J .
Am. Chem. Sur., SS, 507 (1931).
.
H. W. DODGEN AND J. L. RAGLE
910
I n the absence of external fields, the nuclear spin energy levels are 21 1 fold degenerate, where I is the nuclear spin. This degeneracy may be partially or completely removed by external electric or magnetic fields. Nuclei with spin greater than '/zmay possess an electric quadrupole moment and the electric field a t such a nucleus in a solid substance caused by valence electrons and/or the crystalline electric field may cause partial lifting of this degeneracy and hence splitting into several levels whose number and spacing depend on the magnitude of the nuclear spin, the magnitude of the nuclear quadrupole moment, and the gradient of the electric field a t the n u c l e ~ s . ~ ~ ~ Transitions between the levels thus produced were first observed about 5 years ago and have since been observed in several nuclear species and many different solid compounds. Those observed so far lie in the short-wave region of the radio frequency spectrum. It is the purpose of this paper to call attention to the fact that nuclear spin contributes to the equilibrium thermodynamic properties of many substances in an accessible temperature range. I n this respect, R. V. Pound has pointed out that significant nuclear alignment of should occur in IC1 a t accessible temperatures. I n the cdse of solid iodine ( I = 5/2) the electric field a t the nucleus causes splitting into three levels: m I = d=1/2, *33/2, *55/2, giving two absorption lines in accord with the selection rule A m 1 = f1. The pure nuclear quadrupole spectrum of iodine has been observed by both Dehmelt5 and Pound.6 At 4°K. Pound found lines a t 642.8 and 334.0 mcps., corresponding to the transitions r n ~= f5/2 ++ *3/2 and &3/2 ++ *1/2, respectively. Pure quadrupole spectra have also been observed in solid bromine' and chlorine.8 Both of these nuclei have spin 3/2, but natural samples contain two isotopic species, and therefore two lines are observed in each case. In bromine the observed frequencies
+
7' 2.0
I
M
1.5 I
3
8 1.0 -d 0.5 2 2
x
10-4
10-2 10-1 Temp., OK. Fig. 1.-A, C12; B,Brs; C, I*. 10-3
1
(3) W . Gordy, W. V. Smith and R. F. Trambsrulo, "Microwave Spectroscopy, ' John Wiley and Sons, Inc., New York, N. Y . , 1953, p. 289 ff. (4) C. H. Townes and B. P. Dailey, J . Cham. Phye., 20, 35 (1952). ( 5 ) H. G. Debmelt, Nohrzuias.. 11, 398 (1950). (6) R. V. Pound, Phys. Rsu., 82, 343 (1951). (7) H. G. Dehmelt, Z . Phusik. 130, 480 (1951). (8)R. Livingston, J . Chem. Phys., 19, 803 (1951).
Vol. 60
are 382.43 and 319.46 mcps. for Br79 and B P , while in chlorine, lines are observed a t 54.248 and 42.756 mcps. for C136and C137,respectively. It is known that the nuclei in these cases should approximate assemblies of independent localized systems quite well.9 Because of the small number of possible energy levels, the nuclear partition functions have simple forms, greatly facilitating numerical work. Straightforward calculations yield the following results for the nuclear contributions to the heat capacities of these substances Iodine:
Bromine:
cv
=
R
1
