1742
NOTES
after both sides of (23) are multiplied by Fi-om (21) we have
-l / c ~ - / ~ + . . -I_
Also, inequality 22, the redwidwit condition for gravitational stability at t = 0, becomes
+ H2Kz+ > - (.\/a-/a+) (H1K1- +
HlI 0
(33)
It is apparent that (33) will be satisfied if (31) and
Inequalities 24 and 25 together imply
(32) are satisfied. Furthermore, gravitational instability, or convection, will occur a t some time HIKI’ f U21 - (HIK1- -/- HzKz-) (26) t or some position x if condition 31 is not satisfied, because inequality 20 (and hence inequality 31) is which is identical with inequality 22. Thus, if a necessary condition for a positive density gradiinequality 16 is valid, then conditions 20 and 21 ent (inequality 2 ) . Thus, if we had been unaware for gravitational stability a t t > 0 also imply of condition 31, we might have prepared solutions condition 22 for gravitational stability a t t = 0. for a diffusion experiment so that AC2 < 0 and AC, Therefore conditions 20 and 21 are sufficient to > - 1.4861ACz, under the erroneous impression ensure gravitational stability for all times t 3 0 that condition 33 for gravitational stability a t t = during the free diffusion process and a t all posi- 0 also would ensure gravitational stability a t all tions a > z > - 0 0 in the diffusing boundary. later times and a t all positions. For the special case of a ternary systcm for which The magnitude of the negative density gradient produced a t some time during a diffusion experi(D12)v = ( W V = 0 (27) ment because condition 20 was not satisfied may be small as to cause no observable disturbance where the faster diffusing solute is designated by the of so the diffusing boundary. Also, it should be subscript 2, so that emphasized that condition 21 was proved to be suficient but not necessary for gravitational sta(022)v > ( I 1 l l ) V (28) bility; therefore, if this condition is not satisfied, then conditious 20 and 21, respcctively, reduce to a negative density gradient will not necessarily be produced. But to be absolutely certain that NzACz 0 (2% no convective mixing will occur during a diffusion experiment, conditions 20 and 21 both should be aiid satisfied for all studies of free diffusion in threecomponent systems. Acknowledgments.-The author wishes to thank Appiication.-From equations 20 and 21 the Professor L. J. Costing for his helpful discussions of relative values of ACl and AC, which will give a this research. This work was supported, in part, gravitationally stable free diffusion experiment can by research grants from the National Sciencr: be calculated, provided that values are available Foundation (G-7401) and the n’ational Institute for H I , H z , and the four diffusion coefficients. If of Arthritis and hfetabolic Diseases (U.S.P.H.S.) no estimates of values of the (D,,)v are available, (A-5177), and from the Research Committee of two or more preliminary experiments which seem the University of Wisconsin Graduate School very likely to be gravitationally stable may be from funds supplied by the Wisconsin Alumni performed; the resulting preliminary data for the Research Foundation. H , and the (Dl,)v then ran be used to calculate whether other desired relative values of AC1 and ACs may be safely used. DECOMPOSITION OF n-PROPAh’E AND A simple illustration of the application of the criteria for gravitational stability is obtained by n-BUTANE ON CLEAN RHODIUAI FILJIS cxaminiiig data for the system H?O-glycine-KCI BYRICHARD W. ROBERTS which mas studied recently by Voolf, Miller, and O E i i t d Electric RPsearch Laboratory, Schenerfadv,.‘\I Y. Gosti1ig.1~ For this system a t C1 = 0.3 and Cz = Recezved March 5’1, 1988 0.5 mole/l., where the subscripts 1 and 2 dcsigiiatc The surface decomposition of saturated hydroglycine and ICCI, respectively, ralucs obtained were (Dll)v = 0.!&2 X lo-& cm.2/sec., (&)v = carbons has been investigated by a number of -0.00~7 X 10-5 cm.2/sec., (DL1)v = - 0 . 0 1 ~ X workerslS2 on a variety of metal surfaces. In cm.2/sec., ( D s z ) ~= 1.7446X 10-j cm.2/sec., general, they concluded that carbon-carbon bond H1 = 0.03014 kg./mole, and H z = 0.04479 k%./ cleavage (cracking) did not occur a t temperamole. At this composition both cross-term dif- tures below about 140’. The vacuum conditions fusion coefficieiits are very small; if they are con- (-loF5 torr.) used in their experiments suggest sidered to be zero, conditions 29 and 30 then bcrome that the metal surfaces mere contaminated by adsorbed gases. AC, 3 0 (31) Recently, it has been demonstrated that adsorbed gases have a pronounced effect on hydrocarbon and
>
AC1 f 1.11G2AC2 > 0
(1) I
