NOTES
1374
larly desirable, as the spectra, which are often complex, weak and poorly-resolved, are difficult to analyze when accessory data cannot be gotten. In the present instance, the “chemical shift” for C13HC1,Fis about 11 p.p.m. on the high field side of that of C13C13F. Such a relative shift is certaiiily in harmony with the observations of Lauterbur,” according to which proton substitution in chloro- and ethoxy-substituted methanes produces a small upfield shift of the C13resonance. While the shielding value for CI3C1,F has not been reported upon the accepted scalei1 for CI3 spectra, it is here proposed that C13C13Fbe adopted as a secondary C13 standard for use in FfC13}decoupling studies. It is readily available and gives good signals, and ultimately could be used as an internal standard, though such mas not done in the present work. Even more important is the fact that fluorine shifts are increasingly being reported relative to CC13F; as shown in the Experimental section, it is necessary to correct the “apparent” C13 shifts for the large differences in fluorine shielding. Acknowledgment.-The author thanks Charles A. Brown and Emmett B. Aus for this careful n.m.r. spectral work. (11) P. C. Lauterbur, Ann. N . Y. Acad. Sei., 70, 841 (1958).
A SEMI-EMPIRICAL FORMULA FOR VISCOSITY OF A 12:6 LIQUID Faculty of Science, Department of Chemzstry, 17ncbersztl/ of Kolvom, West Bengal, Indza Recrzied J u l y 8 , 1962
I n the present note, an attempt has been made to calculate the viscosity of a liquid of molecules. which have a symmetrical field of force. For the purpose, we have taken the tunnel model of the liquid state as our starting point. On this model the molecules are imagined as moving in very long cells so narrow that the molecules in them move almost one-dimensionally. We imagine the volume V of the liquid divided into K hexagonal cylinders arranged in two-dimensional close packing, each of length I , and containing M molecules. The distance between the centers of neighboring cylinders being T , it follows that
where 1 is the space between the molecules in a given line and for our purpose we shall assume I = T . Barker’ has given the partition function for a single molecule in a liquid on this model as 1 V(0) exp(-F1/lcI’) exp - - 2 IcT)’~
(
where F , is the free energy per molecule of the one-dimensional system. The energy of the system when all the molecules are in their equilibrium positions is V(0) and for a 12 :6 fluid, V ( 0 )is given by
(F)’
- 5.2335
(F)4}
(1) J. A. Barker, Proc. Roy. Soe. (London), A289, 442 (1961).
where E is the minimum energy for equilibrium separation of the molecules and V o= Nu3, u being the collision diameter. The free-cross-sectional area is A* = r2S. The integral S is a tabulated function of lcT/e and V / V o a, table of which has been prepared by Barker, the required values of S being obtained by interpolation. The values of E/IC and cr for argon, nitrogen, and henzene have been taken from Hirschfelder2 and are given in Table I. TABLEI
@.I e l k OK.) E, (cal.) V,, n
(3)
Argon
Nitrogen
Benzene
3.465 116 2067.4 24.98 8.35
3.681 91.5 1660 29.31 8.35
5.270 440 11334 77 .OO 8.35
We have retained all the essentials of the above model of the liquid state, and following bLcLaughlin3 we assume further that holes in the liquid are possible, in addition to the normally occupied lattice sites, the existence of holes being a necessary requirement for the flow of mass and momentum. We nom use Barker’s partition function along with the rate theory equation4 in order to evaluate the additional Gibbs’ free energy of the activated state and following a procedure exactly analogous to hlclaughlin’s the coefficient of viscosity becomes
v=
BY DILIPKUXARMAJUVDAR
V ( 0 ) = N B j11.8875
Vol. 67
( 2 amk T) ”’ Ai*’’ exp(W’/lcT) exp(eo/liT) 2nua2
(4)
Calculation of &.--The hole in the liquid may be supposed to correspond to a p site while a molecule may be supposed to occupy an a site of the Lennard-Jones model of the liquid state. Since, however, the flow of a liquid involved transfer of molecules from cy t o p-site (holes), the interaction energy or rather the height of the potential barrier eo is determined entirely by the repulsive part of the intermolecular forces. It is therefore possible t o write6 eo =
wo
(;)4
= E
>(;”
Lennard-Jones has shown that wo is approximately equal to the potential energy a t the minimum of the potential energy curve for a pair of molecules. Work of Formation of Hole T’V.-EyringG has shown that the uiork W’required to form a hole of molecular size is a fraction of the average potential energy E, of the molecules in their equilibrium positions in the solid state. Further the energy W’ is itself a function of the volume. For a normal liquid, a t temperatures appreciably above the melting point, it is found that
The values of E, and n and the volume of the solid V , a t the melting points for argon, and C6H,are given in Table I. (2) J. Hirschfdder, C. F. Curtiss, a n d R. Bird, “The Molecular Theory of Gases a n d Liquids,” John Wiley and Sons, Inc., New York, N. Y., 1954. (3) E. McLaughlin, Trans. Faroday Soc., 65, 29 (1959). (4) H. Eyring, “The Theory of R a t e Processes,” McGraw-Hill Book Go., New York, N. Y., 1941. ( 5 ) J. Lennard-Jones, Proc. Rou. Soc. (London), A169, 317 (1939). (6) H. Eyring. J. Chem. Phys., 9, 393 (1941).
XOTES
June, 1963
TABLEI1 Molar volume, cni.3
Temp., O K .
Argon
28. 281° 28.70 33.09’3 33.51 34.61 89.403 90 51 91.67
84 2 87 3 69 1 71 4 77 3 298 2 508 2 318.2
Sitrogen
Benzene
-7
Expt.
X 108,poiseEq. 11
2 . 807 2.52 2 .318 2.09 1.58 6 .019 5.24 4.62
From experimental studies on viscosity, it appears that a hole of molecular size is not required to be pree it but a hole of much pared for a molecule to m o ~ into smaller size may be involved in viscous flow. So the actual work of formation ( W ) of a hole of size suitable for viscous flow is a fraction of 14”. Therefore, we may write
2.58 2.32 2.35 2.07 1.60 6.05 5.19 4.66
Fxyt.
3.17 2.75 2.01 1.79 1.40 6.13 5.30 4.60
450.4 471 .I
2438
TABLE I11 Temp.,
K.
W/L
eo/?%
W/eo
84.2 87.3 69.1 71.4 77.3 298.2 308.2 318.2
282.5 284.5 252.2 252.1 251 .7 1124 1138 1150
71.34 67.20 61.86 58.86 51.69 415.3 395.5 375.6
3.96 4.23 4.08 4.28 4.87 2.71 2.87 3.06
0
For argon, 126
=
1.663
+ 3.921(T/Tc)
For nitrogen, 120 = 2.826 4- 2.642(T/Tc) For benzene, 1 2 6
=
0.878
+ 3.737(T/Tc)
(8) (9) (10)
Substituting the values of eo and W into equation 4 one obtains
ivcr,.
732.68 726.00 628.92 592.12 580.38 3200.6 3184.6 3162.0
707.68 705.44 628.12 622.00 606.78 3078 6 3067 .O 3051.2
the energies of activation for viscous flow do not seem to agree well. It is seen from Table I11 that the ratio of the work of formation of a hole to the energy required by a molecule to move into the hole is between 3 and 5 which
Argon
The value of 0 has been empirically determined by equating known values of 7, A f , (r, etc., in equation 11 for nitrogen, argon, and benzene, a t different temperatures. It is found that the values of e range between 0.24 and 0.37 and increase with temperature. The plot of 128 against T/Tc where 2’, is the critical temperature for each of the compounds is linear and the best line through them is represented by
(ca1.)Eq. 11
-&tive
31cI..
Sitrogen
Benzene
is in good agreemjent with the observation made by Eyring.2 Since we are here comparing W and eo a t constant pressure and not a t constant volume, it is easy to understand the tendency of this ratio to slightly increase with temperature. Further it is seen that the activation energies for viscous flow as calculated from equation 11 are almost independent of temperature. -
RADIATION INDUCED REACTION OF NITRIC OXIDE WITH CYCLOHEXANE BY STANISLAW CIBOROWSKI Radrochemistry Department, Instrtute o f General Chemistry, Warsaw, Poland Reeezied October 29, 1068
The equakion may be compared with that of McLaughlin3which is
x is the coordination number and usually taken equal to
12, w is a fraction of the lattice energy and has been given an empirical estimate by NcLaughlin, 6fis the free volume per molecule. I n Table 11, the values of 7 calculated according to equations 11 and 12 and the energies of activation are compared with the experimental data. The coefficient of viscosity calculated according to equation 11 is in better agreement with the experimental values, while (7) Rudenko a n d Scbubnikow. Physzk. 2. Sowjet, 6 , 470 (1534). (8) J. Timmermans, “Pliyeieo-Chemical Constants of Pure Organic Compounds,” Elsevier, Amsterdam, 1950. ( 5 ) Bmer. Petroleum Inst. Project 44 (1948-1952). (IO) “International Critlcal Tables,” MoGraw-Hill Book Co., New York, N. Y., 1933.
Nitric oxide is an efficient radical scavenger and is expected to react with the cyclohexyl radicals produced in irradiated cyclohexane, to give nitrosocyclohexane. G(nitrosooye1ohexane) should be a measure of the number of cyclohexyl radicals formed in the radiolysis. It is however known that nitrosocyclohexane reacts with NO, the products being nitrocyclohexane, cyclohexyl nitrate, and cyclohexyl nitrjte. The formation of these products can best be explained by postulating the formation of an intermediate compound, N-nitroso-N-cyclohexylhydroxylamine It is therefore of interest to determine what is the net result of the two competitive reactions: (a) the radiation induced formation of nitrosocyclohexane and (b) its secondary reaction with nitric oxide. Recently Burrel14 has postulated that the reaction between nitrosocyclohexane and nitric oxide in irradi-. ated solutions proceeds rapidly to give the products ni-. trocyclohexane and cyclohexyl nitrate. On the other (1) J. F. Brown, J . Am. Chem. Soc., 79, 2480 (1557). ( 2 ) L. G. Donaruma a n d D. J. Carmody, J . Oro. Chem., aa, 635 (1957). (3) L. Batt and B. G. Goa-enlock, Trans. Faraday Sac., 66, 682 (1960). (4) E. J. Burrell, Jr., J . Phys. Chem., 66, 401 (1962).
