COMMUNICATION TO THE EDITOR
July, 1956
This entropy breakdown may be summarized as Obsd. integral adsorbate entropy, e.u. Configurational entropy, e.u. 1.0 Rotational entropy, e.u. 8.4 Entropy of vibration perpendicular to 2-.. 6 adsorbent surface, e.u. Total Residual entropy assigned to motion in plane of adsorbent surface, e.u.
29.3
statistical mechanics, the following expression for the translation entropy ST =
R [In
2nmkTa
hP +
12.0 17.3
The residual 17.3 e.u., assigned to motion in the plane of the surface, determines the separation required for isolation of sites. Since the bond is weak and predominantly electrostatic, an adsorbed water molecule will have very considerable mobility, over the site. This suggests, as a useful approximation, that the motion in the plane parallel to the adsorbent surface be treated as translation instead of vibration. If the adsorbed molecule is assumed to move a t random within a circle of which the site is the center, the radius of this circle may be calculated from the residual entropy. The partition function for isolated translation in two dimensions gives, by the usual methods of QT =
1023
2nmkTa ___ ha
R m k
T
= gas constant = mass of one molecule = Boltzmann constant = absolute temp.
ll
a = area covered by the
oscillation of an adsorbed molecule h = Planck’s constant
Solution for a ($Tom an entropy of 17.3 e.u.) gives a value of 120 A.2 for the area of freedom of an adsoorbate molecule. The corresponding radius is 6.2 A. , indicating a Qecessary separation between sites of roughly 12 A. It is apparent from this result that the hydrophilic sites on Graphon are much more widely separated than the minimum necessary t o prevent interaction between adsorbed molecules. The area normally occupied by an adsorbed water molecule is about 10.8 A.2.* Essentially complete isolation of sites should thus be possible, if the area of the first water monolayer is less than about one-eleventh of the total surface area of the adsorbent and if the sites are not grouped in clusters. (8) H. K. Livingston, J . Colloid Sci., 4, 447 (1949).
COMMUNICATION TO THE EDITOR SECOND EXPLOSION LIMITS OF CARBON MONOXIDE-OXYGEN MIXTURES
Sir: I n a criticism’ of our recent paper on this subject2, points were raised which do not clearly reflect the content of our paper. It was claimed that since our results were influenced by surface, no mechanism could be deduced from ‘ the experimental results. There is no logical reason for the above criticism if the effect of surface is taken into account. We have reasons from both experimental and theoretical evidence for the various elementary reactions in our mechanism, We have also discussed and rejected key reactions in previously postulated mechanisms. Where our mechanism might be questioned upon theoretical grounds, we have given detailed justification. Contrary to the statement of Roth, von Elbe and Lewis,‘ the mechanism which we have postulated easily accounts for the effects of composition, surface to volume ratio, and inerts. In addition, this mechanism is consistent with our spectral studies of the CO-O2 explosion. Roth, von Elbe, and Lewis‘ claim that they have developed a procedure which effectively suppresses (1) W. Rotli,
G.von Elbe and E. Lewis, THE JOURNAL, 60, 512
(1956). (2) A. S. Gordon and R. H. Knipe, %bid., 59, llG0 (1955). (3) R . 13. Knipe and A. S. Gordon, J. Chem. Pliys., 28, 2097 (1955).
the surface chain branching reaction “over a wide range of mixture composition and temperature.” However, their published data and curves4 show that this lack of surface dependence exists only at one mixture composition, namely, 1CO :202. Compositions on either side, 4CO:lOz and 1C0:402 show a large surface effect. Von Elbe, Lewis and Roth claim that they lose surface dependence when they heat their vessels for two hours under vacuum at 800-900” (using a 1CO:202 mix). Using the same mixture, we have previously reported that this treatment did not lessen the effect of surface. The heating is claimed to remove a strongly adsorbed film of COZ which they believe is responsible for the surface effects. We have grave doubts that COz plays such a role because, as discussed above, their loss of surface dependence is for only one composition. Also, both voii Elbe, Lewis and Roth, and ourselves report a slow reaction prior to ,the explosion. Thus, even if the walls were clean at the start they should be covered with COz by the time that the explosion temperature is achieved. Von Elbe, Lewis and Roth derive Eq. 2 in their paper4 from the following postulated reactions (using their notation) O+01+M = 0 3 O+CO+M=CO
+ M
+ni
(1)
(11)
(4) G. yon Elbe, B. Lewis and ?V. Rotli, ”Fifth S y ~ n p o s i u n io n Combustion,” Reinhuld Publisliinp Corp., New York, 1965, p. 610.
COMMUNICATION TO THE EDITOR
1024 CO:
co: + 02 = coz + 20 + + M = COz + 02 + M 0 2
(VI (VI)
Employing the usual technique of setting the rate of chain break reactions equal to the rate of chain branch reactions for the critical situation a t the chain branch explosion limit, the following equation is readily derived 1
[MI. =
k6 -
Vol. GO
- --hfo, k2fCO
hfoz
kSl+w
Unfortunately, the authors have confused the sign of the numerator and denominator in their derivation and their published Eq. 2 reads
This is not a typographical error, since the authors make the point that their equation predicts an infinite pressure limit a t a critical value of mixture composition which is consistent with their data. The correctly derived equation predicts a zero pressure limit a t this critical value of the mixture composition. It should be noted that equation 2 is the crux of their discussion. CHEMISTRY DIVISION ALVINS. GORDON U. S. NAVAL ORDNANCE TESTSTATION R. H. KNIPE CHINALAKE,CALIFORNIA RECEIVED APRIL30, 1956
I
b
