057
Communications to t h e Editor
TABLE I: Parameters for Sorption in 5A (Linde) Zeolitea Kr
CH,
should be exchanged for the following treatment. Expand Ar
02
A
3.44 3.5 3.6 3.8 16.3 16.0 l O Z 5 c y , cm3 molecule-' 25 26 1 71 froi(at 298°K) 1 72 K O , molecule cavity-' 1.26 X 1.9 X 1.04 x 1.48 X 10-6 10-6 Torrmi 10-6 10-6 3.36 3.30 q o , kcal mol-' 4.24 4.54 1.24 K p o i y I K m o n o (at 298°K) 2.56 22 15 f(at 2 98"K) The Henry constant is given by K = KOexp(qo/RT). Values of K Oand q o for CH4, Ai-, and Kr are taken from the thesis of Derrah.2 0,
n=O
where H , is the Hermite polynomina12 of order n obeying
H,," - 2zHn'
+
2nHn = 0
(33a)
LmHn(z)Hm(z) exp(-z2) dz = 2"n!GS,,
(33b)
Hfl'(z) = 2nHn-i(z)
(33c)
2zHn(z) = H,+~(z)+ 212Hn-,(z)
(334
and
Q
The values for 0 2 are from unpublished data obtained in this laboratory. Values of u and a are from Hirschfelder et al.3
The conservation of total material gives = -ac,(t) -
4-20 a-q(t) pz3
and, from eq 3 and 4,the ratio of the Henry constants will be given by fltrans mono
(5)
Kmono
Since the ratio of translational partition functions is simply the ratio of molecular weights raised to the three-halves power:
where
=AO = z,c/aii, a = Aexc/A1
Inserting (32) and (34) into (28) and utilizing (33a-d) one finds
(1) E. Cohen de Lara and Y. Delaval, J. Phys. Chem., 78, 2180 (1974). (2) R. I. Derrah, Ph.D. Thesis, University of New Brunswick, Fredericton. New Brunswick, Canada, 1973. (3) J. 0. Hirschfelder, C. F. Curtiss, and R. B. Bird, "Molecular Theory of Gases and Liquids", Wiley, New York, N.Y., 1954.
Department of Chemical Engineering University of New Brunswick Federicton, New Brunswick, Canada
D. M. Ruthven
Received January 8, 1975
A Correction and Improvement of "On the Kinetics of Step-Wise Micelle Association" by E. A. G. Aniansson and S. N. Wall' Sir: The part of ref 1 from eq 31b up to and including eq 37
(374
and
1
+
k - =k - a ( 1 + c,) o2 n3 The time dependence of the higher c,s' can be found similarly and will contain successively smaller time constants given by - ='T
l/Tn
References and Notes
(35)
has been used and we have introduced
= C,(O) Comparative data for the sorption of CH4/Kr and On/Ar in 5A (CaA) zeolite are given in Table I. For these pairs of molecules the conditions of equal size (as measured by the Lennard-Jones U ) and polarizability are very nearly fulfilled and the limiting heats of sorption (40) for the species of each pair are almost the same, as is to be expected if the configuration integrals are similar. The rotational partition functions for the adsorbed molecules, estimated according to eq 6, are 15 for CH4 and 22 for 0 2 . These values, which may be compared with values of 71-72 for the freely rotating gaseous molecules, suggest that although rotation is somewhat restricted in the adsorbed state an appreciable degree of rotational freedom is retained, in accordance with the spectroscopic evidence.
(34)
= nk-/a2
(374 In relaxation experiments the quantity measured is & ( t )or its equivalent so that until new experimental methods sensitive to the finer details of the micellar size distributions are developed only co and c1 are needed. Under the present assumptions, then, only one relaxation time constant governs the fast rearrangement process even at very large deviations from equilibrium. At small deviations from equilibrium c o
