NOTES pairs containing hydrogen only in the asymmetric positions, e.g., CHFClCHFCl. Inversion Products in Condensed Phases. The yields of meso-2,3-DCB-t from the reactions of T * with the dl parent are definitely higher in the condensed phases than in the gas phase, even though still small. The most probable explanation for these increased yields is that some dl-2,3-DCB-t molecules, ini tially formed by T-for-H substitution, are sufficiently excited to decompose by C-C1 bond rupture. The residual C ~ H T TC1 radical can then undergo either (a) immediate recombination with the C1 atom, retaining the original stereochemistry; or (b) racemization to a mixture of radicals of both “dl” and “meso” form, and then recombination with the C1 atom, providing additional yields of both labeled isomeric forms. These recombination processes can be facilitated in the condensed phase by the surrounding solvent or crystal cage, capable of retaining atom and radical in close proximity to one another. Studies of 38Clreactions with 2,3-DCB in the condensed phases show large yields of both labeled isomers, in both liquid and solid. The presence of both labeled forms in nonequilibrium amounts in the 38Cl experiments has been attributed in close competition between the time scales for racemization of newlyformed CH3CHC1CHCHa radicals and combination of these radicals with others in the cage. With W 1 in the liquid phase a t room temperature, about 30% of the reformed molecules have the “opposite” configuration from that of the parent.14 Such cage recombinations, however, play only a small percentage role in the tritium experiments. Assuming similar competitive rates for racemization and recombination, the contribution of cage reactions to the total parent yield is no more than 8% in recoil tritium reactions with 2,3-dichlorobut ane. An alternate hypothesis seems much less likely, but cannot be eliminated by present data. If a substitution-with-inversion mechanism is postulated to require the simultaneous deposition of very large amounts of excitation energy,I5 the fraction of such molecules surviving in the gas phase could be substantially smaller than for labeled molecules formed by substitutionwith-retention, in agreement with the observations of Table I. Such a postulate is not wildly unreasonable when inversion would be accompanied by motion of CH,, C1, and CHClCH3 groups. I n any event, the total yield corresponding to stabilized “inversion” product, as measured in condensed phases, is very much smaller than that of the “retention”product, and the heavily predominant mechanism of T-for-H substitution must still be identified as the retention mode. (14) F. 8. Rowlmd, C. M. Wai, C. T. Ting, and G. Miller, “Chemical Effects on Nuclear Transformations,” Vol. I, IAEA, Vienna, 1965, p 333.
(15) See E. K. C. Lee and F. S. Rowland, J , Amer. Chem. Sac,, 85, 897 (1963).
677
A Multilayer Isotherm with Sensible Spreading Pressure Limits
by C. M. Greenlief and G. D. Halsey Department of Chemistry, University of Washington, Seattle, Washington 98106 (Received July $8, 19f30)
Isotherm equations that cover the entire range of adsorption have exhibited one of two types of thermodynamic difficulties: either the lack of a Henry’s law region at low coverage, or in the case of the BET equation a spreading pressure that approaches infinity as the pressure tends toward the saturation vapor pressure, Po.’ One of us has proposed an equation that has the virtue of having the correct limiting behavior at both low and high coverage.2 It is the purpose of this note to explore this equation further. The isotherm is a linear combination of a virial expansion at low coverage and a term at high coverage due to the decay of surface energy with the third power of the distance. Specifically
P = bn exp[(c/b)n]
+ POexp[-a(~/v,)-~]
(1)
where c is negative and a and b are positive. n is the amount of gas adsorbed, v is the volume of gas adsorbed, and urn is the volume of a monolayer of gas; a is a measure of the adsorption potential. For low coverages, eq 1 becomes P = b n + c n 2 + ..,
(2)
These constants can be expressed in terms of gas-solid (b = KT/BAs and C = k T C A A B / virial ~oefficients,~ PAS). The expansion is valid only if c is negative, but this is to be expected in the temperature range below the critical temperature of the adsorbate, in the region where a multilayer isotherm becomes appropriate.4 At high coverages eq 1approaches the limit In (P/Po) = -aa/03
(3)
where e = v/vrn, the surface coverage in monolayers. Typical isotherms of eq 1 are shown in Figure 1. The isotherm as proposed has no empirical parameters, and its only arbitrary feature is the choice of a simple exponential blending function. I n Figure 2, experimental data of Prenzlow and Halsey5 for the adsorption of argon on one layer of xenon preadsorbed on graphitized carbon black are fitted to eq 1. The constants have been adjusted to the Cassel, J , Phys, Chem., 48, 195 (1944), (2) G. D. Halsey, “The Solid-Gas Interface,” E. A. Flood, Ed., Marcel Dekker, New York, N. Y., 1967. (3) W. A. Steele, Advan. CoZZoidInterfac.Sei., 1 , 3 (1967). (4) G . D. Halsey, J . Chem. Phys., 36,1688 (1962). (5) C. F. Prenzlow and G . D. Halsey, J . Phys. Chem., 61, 1158 (1957). (1)
Volume 74, Number d February 6, 1970
678
NOTES k=co
1.5-
1.0-
e 0.5-
0
'I
I
0
I
I
I
0.75
0.50
0.25
1.00
PIP,
Figure 1. Adsorption isotherms for the equation
P / P ~=
ee-ke
+ e-110'.
behavior is encountered in the k = 0.5 isotherm of this figure. Because of the nature of this loop, it is not possible to find two phases of equal spreading pressure. Indeed, a calculation of spreading pressure, shown in Figure 3, indicates that the spreading pressure, although it follows the ideal gas law at low coverages, may ultimately pass through zero and become negative. The thick film cannot be in equilibrium with the thin film; this situation corresponds to a liquid not wetting a surface. At saturation the surface would be covered with a rarified film, given by the lowest intersection of the isotherm with the saturation line. We are indebted to Dr. J. P. Hobson, who sent us a preprint that contains an isotherm of xenon on silver quite similar t o the upper part of the IC = 1.4 isotherm in Figure 1. However, there is a strongly held first layer and a resultant knee in the isotherm that our equation in its simple form cannot fit.
Radiation-Induced Chain Decomposition of Hexachloroethane in Cyclohexane Solutions. Reactions of the Pentachloroethyl Radical
by A. Horowitz and L. A. Rajbenbach 0.25
0.50
Soreq Nuclear Research Centre, Yavne, Israel (Received March 9, 1969)
0.75
P/P,
Figure 2. Adsorption isotherms of argon on xenon and eq 1 in the form PIP0 = (1.0) Oe-2.16 e
+
Investigation of the kinetics of chlorine atom elimination from chloro-substituted alkyl radicals CJ&n+1-,C1,
CnHzn+l-mClm-1
+ C1
(1)
has been so far limited to several studies in the gas phase.1-6 Such reactions can appropriately be studied in the gas phase since they require relatively high temperatures, mainly because the activation energy of the forward step of reaction 1 is quite high2J (-20 kcal mol-') while that of the reverse step is negligible.6 The purpose of this study was to investigate the kinetics of the chlorine elimination reaction from ,
1
-
2
4
,
6
r
a
I
10
Figure 3. Spreading pressure curves based on the isotherm
P / P ~=
ee-ke
+ e-"".
initial slope and ultimate cube-law regions. The agreement in the intermediate region is reasonable. It is clear from the shape of the examples of the isotherm that unstable regions are a possibility. Aside from the obvious two-dimensional phase change in the IC = 2.1, 1.4 isotherms in Figure 1, another type of The Journal of Physical Chemistry
(1) (a) P.B.Ayscough, A. J. Cocker, and F. S. Dainton, Trans. Faraday SOC.,58, 1128 (1962); (b) P. B. Ayscough, A. J. Cocker, F. S. Dainton, and S. Hirst, ibid., 58,295 (1962); (c) ibid., 58, 318 (1962); (d) F. S. Dainton, D. A. Lomax, and M. Weston, ibid., 58, 308 (1962). (2) (a) S. Dusoleil, P. Goldfinger, A. M. Van der Auwera, G. Martens, and D. Van der Auwera, ibid., 57, 2917 (1961); (b) P. Goldfinger, G. Huybrechts, and G. Martens, ibzd., 57, 2200 (1961); (c) P.Goldfinger and G. Martens, ibid., 57,2210(1961). (3) 6. Huybrechts, L. Meyers, and G. Verbeke, ibad., 58, 1128 (1962). (4) J. H. Knox and J. Riddiok, ibid., 6 2 , 1190 (1986). (6) P.B.Ayscough, F. S. Dainton, and B. E. Fleischfreser, ibid., 62, 1838 (1966). (6) C. Cillien, P. Goldfinger, G. Huybrechts, and G. Martens, ibid., 63, 1631 (1967).
