NOTEB
Sept., 1963 state but molecular oxygen is consumed by reactions such as 0 2
+ 2 N 0 +2 5 0 2
(3)
+ R +ROz
(4)
and On
KO*. The addition of nitrogen dioxide does increase the rate of production of oxygen. Some additional oxygen is formed, of course, by the photolysis of the nitrogen dioxide itself. However, a t low concentrations of added nitrogen dioxide (0.05 mm.) this correction to the rate of formation of oxygen is relatively small, cc. (STP)/min. Thus, after this about 1.5 X correction is made, the rate of formation of oxygen with added nitrogen dioxide is 3.8 x 10-3 cc. (STP)/min., which is the ,same as the rate of formation of ethyl nitrite a t very low conversions. The formation of ethyl nitrite and oxygen atoms by the photolysis of ethyl nitrate is not too surprising. The equivalence of process V is reported to occur in the photolysis of inorganic nitrate in the solid phase and in solution^.^ It is also reported to occur in the yradiolysis of inorganic nitrates. The evidence presented would seem to indicate that it also occurs for the gas-phase photolysis of organic nitrates. Evidence for process IV is the large increase in the rate of formation of acetaldehyde and ethyl nitrite in the presence of small amounts of nitric oxide. A large addition of nitric oxide brings about a reduction in the rate of formatiion of both products. The increase can be accounted for by the reactions 1and 5.
+ KO +CHDCHO + HNO
(5)
A rough estimate of the ratio kl/ks can be obtained from the ratio of ethyl nitrite to acetaldehyde forrned in the presence of iiitric oxide and corrected for the amount of both substances formed a t very low conversions. This gives h / k s = 3.3, which is a reasonable estimate in view of McMillan’s6 value of k 6 / k , = 6.6 at 26’ for the reactions (CH3)zCHO
+ NO
+ (CHJzCHONO
+ (CH3)ZCO
It is also in agreement with the estimate of 2 to 3 for the ratio k l / k s made in the photolysis of nitroethane.’ The formation of small amounts of niethyl nitrite can be accounted for by process IV followed by the reactions CzHsO +CH3
Thus, the rate of oxygen formation decreases. There is the possibility that oxygen may be iorined by the secondary photolysis of the product NOz. However, a t low conversions (below O.l%, which is equivalent to an experiment of about 12-min. duration), it can be estimated from blank experiments that less than 25% of the oxygen could be formed in this may. Moreover, a t higher conversions, where presumably more KO2 is present, less oxygen is formed. I n agreement with this, Gray and Style12who carried out experiments in which the conversion was 4%, did not report any oxygen while KO,was the predominant oxide of nitrogen present. It is also difficult to reconcile the small change in oxygen production reported in Table I for a lchange in NO2 pressure from 0.05 to 0.25 mm., if oxygen is formed only from the photolysis of
C2H60
1925
(6)
+ HNO (7)
(3) G. K.Rollefson and M. Burton, “Photochemistry and the Mechanism of Chemical Reactions,” Prentice-Hall, Inc., New York, N. Y., pp. 140, 375. (4) T.-H. Chen and E. R. Johnson, J . Phys. Chem., 66, 2249 (1962). ( 5 ) G. R. RiIcMillaz., J . Am. C h e n . Soe., 88, 3018 (1961).
CH3
+ CHzO
+ KO2 +CH3ONO
(8)
(9) The formation of acetaldehyde as a major product a t low conversions and the fact that acetaldehyde is not appreciably reduced in the presence of an excess of ethylene are evidence in favor of process 111. A rough calculation of the relative importance of each process and of the quantum yield associated with each process can be made if we assume that the rate of formation of ethyl nitrite a t zero time is due to process V, that the rate of formation of acetaldehyde a t zero time is due to process 111, and that the additional ethyl nitrite and a,cetaldehyde formed in the presence of S O , plus the methyl nitrite formed under the same conditions is due to process IV. Thus, we have a111 = 0.094, @pv = 0.139, and @IV = 0.240. The quantum yield of processes I11 and V may be slightly high. However, the quaiitum yield of process I V probably is low since the back reaction C2H60
+ KOz +CzH60N02
(10) This makes the total
must take place to some extent. quantum yield -0.5. I n the liquid phase, ethyl nitrite is produced but no oxygen is found. It is difficult to decide whether process V occurs but the oxygen atom is somehow consumed, or if process V does not occur and ethyl nitrite is formed in some other manner. The very small quantity of methyl nitrite indicates that reaction 8 does not occur to any large extent in the liquid phase. This is to be expected in the liquid phase where the excess energy of the ethoxy radical is collisionally deactivated. Process I11 and IV both seem t o occur, but it is difficult to estimate the contribution of each. Acknowledgment.-The author wishes to thank Dr. Peter Ausloos for suggesting this problem and for his many helpful suggestions. We wish to acknowledge financial support of this research by a grant from the United States Public Health Service, Department of Health, Education and Welfare.
-
COMPLICATING FACTORS IN THE GAS PHAS.E PHOTOLYSIS OF AZOMETHANE BYR. E. REBBBXTAND P. J. AUSLOOS National Bureau of Standards, Washington 86,D . C. Ileceined ;March 18, 196s
I n a recent publication on the gas phase photolysis of azomethaiie, Toby and Weiss’ suggested a new ethaneproducing reaction 2CH3Nz * CzHa
+ 2N2
(1) On the other side, Rebbert and Ausloos2 presented evidence for the foriniation of ethane by a unimolecular elimination from azomethane
CH3NzCH3
+ h~ +CzHe + Nz
(1) S. Toby and B. H. Weiss, J . Phya. Cham., 66, 2682 (1962). (2) R. E. Rebbert and P. Ausloos, ibid., 66, 2253 (1962).
(I)
1926
NOTES
The present study was undertaken in order to determine if the pressure trends observed by Toby and Weiss could not at least be partly accounted for by the occurrence of primary process I. It was thought that an answer to this question, as well as to other related problems, could be most readily obtained by photolyzing equimolar mixtures of CH3KzCH3-CD3KzCD3. Experimental The experimental procedure was identical with that described before.2 CDsN2CD3, C H Z N ~ C Hand ~ , CD3COCDa were obtained from Merck, Sharp and Dohme of Canada. Mass spectrometric analysis showed 4.8% CD3N2CDgH in the azomethane-da and 3.8% CDaCOCDzH in the acetone-&. No other chemical impurities could be observed. All materials were rigorously purified by vacuum distillation. All experiments were carried out a t 150’ because it is a t this temperature that the effect of pressure shows up most clearly.’
Vol. 67
Nzin the gas phase photolysis of azomethane-1,4cyclohexadiene mixtures. It is, thus, obvious that rate determinations of the methyl radical reactions should not be based on the yield of CzD6 or CzH6but rather on the rate of formation of CH3CD3. It may be reasonably assumed that CH3CD3 is formed exclusively jn reaction 7 . The following rate expressions can be deduced from the proposed reaction mechanism
Results The following reaction scheme mill be tentatively considered
+ hv Nz+ CzHs (Ia) CH3KzCH3+ hv +Nz+ 2CH3 (IIa) CDJzCD3 + hv Nn + CnD6 (Ib) CDJYzCD3 + h~ S z 4- 2CD3 (IIb) CD3 + CHdXzCH3 --+ CD3H + CHzN2GH3 (2) CD3 + CD3SzCD3 + CD4 + CDzY2CD3 (3) CH3 + CHaYzCH3 +CH, + CHzXzCH3 (4) CH3 + C&?JZCD3 +CH3D + CD,NzCD3 ( 5 ) CH3YzCHa
--+
+
---*
CH3 $- CH3 --+ CnHs CH3 CD3
(6)
+ CD3 +CH3CD3
(7)
+
(8)
CD3 + CzD6
The occurrence of primary processes I a and I b is demonstrated by considering the variations of the isotopic distribution of the ethanes C2H6, CZD6, and CH3CD3 with pressure and intensity. If one assumes that the rate constants of reactions 6, 7, and 8 are identical, one would expect CH3CD3 C2H,j”’. C2D6”2
-
A lower value will be obtainad if processes Ia and I b contribute to the formation of ethanes. The results indicate that, except in the very high intensity experiment (number 3, Table I), the values of the ratio CH3CD3/C2H6’/zX C2D6‘/*are always smaller than two. As may be expected if process I is of importance, a n increase in pressure or decrease in intensity lowers the value of the above ratio, because under those conditions, the contribution of reactions 6 to 8 to the total ethane yield becomes of relatively lesser importance. Taking (aNz = 1, one can calculate (experiments 10 and 11) a quantum yield of atout 0.009 for process I in good agreement with the values recently obtained in the photolysis of azon~etbane-02 mixtures a t 25’ as well as with the value of 0.015 reported by Herk, Feld, and Szwarc3 for the ratio C2&/ (3) L. Herk, &I. Feld, and3I. Szwaro, J . Am. Chem. Soc., 88, 2988 (1961).
These equations are correct only if the methanes are exclusively produced by thermal hydrogen atom abstraction reactions between a methyl radical and azomethane. Because, as indicated by isotopic distrjbution of the methanes, k z 3 ~ :IC4 and (CH3)N (CD3),the square root of eq. B, except for the omission of the contribution of “molecular” ethane, is comparable to the expression RCHr/RC2ns1/e [A] used in earlier activation energy determinations. As one may expect if the methanes are formed by CHa and CD3 radical reactions, the values for C’/$and D1I2, given in Table I, are, within experimental error, identical under all experimental conditions. Effect of Conversion.-There is a definite increase of the four rate expressions with increase in conversion (compare experiment 4 with experiment 8 as we41 as 10 and 11). It may also be noted that the ratio CH3CD8/C2D,’/’ X CnH61/2 diminishes with an increase in conversion. Both effects can be accounted for if one assumes that, in the course of the photolysis, some product is being produced with which the methyl radicals react faster than with azomethane. Effect of Intensity.-The ratios CD3H/CD4 (given in Table I) and CH4/CDH3 decrease with increase in absorbed intensity (for instance, compare experiments 3 and 4 or experiments 8 and 10). It may be pointed out that only a t the lowest intensities (experiments 10 and 11) does the ratio CD,H/CD, approach the expected value of 5.8, clearly indicating4 that there is an additional source for the formation of methane. In this connection, it may be pointed out that the values of the ratio CD,H/CD4 observed in the liquid phase photolysis of CH8KzCH3-CD3NzCD3 were also considerably lower than prediched. There are at least two passible explanations which may account for this effect. (a) Hot mkhyl radicals are produced which abstract from both CH3K2CH3and CD3N2CD3 with roughly equal probability. It may indeed be expected that, at high intensities where a large number of thermal methyl radicals ~7ill undergo recombination reactions, the methane formed by a hot radical effect will show up
w.
+(S) This value isbased on the expceaaion ku/I%D = exp(1500/RT)’ Jackson, J. R.MoNesby, and B. deB. Darwent, J . Chem. PfWs., 87, 1610 (1962).
KOTES
Sept., 1963
1927
more prominently. Hot methyl radical reactions have been proposed before in order to account for the formation of methane in the flash photolysis of azomethane.6 The hot radical effect is, to some extent, supported by experiments carried out in the presence of KO (not given in Table I) in which the yield of CD, was found to be equal to that of CDaH. However, the quantum yield of CD, formation was only 5 X which is too small to account for the observed intensity effect. (b) The intensity effect could also be accounted for by a disproportionation reaction between the methyl radical and another radical produced in the system. It is obvious that, no matter what the correct interpretation is, an increase in intensity will lead to a n augmentation of the values A , B, C , and D given in Table I. The fact that the increase is more pronounced for A l l 2 and least pronounced for B112indicates that the additional methane-producing reaction shows a smaller isotope effect than the normal thermal abstraction process. Effect of Pressure.-In view of the effect of conversion and intensity, it is rather difficult to draw any definitive conclusions about the effect of pressure on the ratios of the rates of formation given in Table I. Most of the following remarks will be based on expression I3 because this expression should be least affected by a variation in intensity. If one compares experiments 1 and 6 carried out at approximately the same conversion, it can be not,iced that there is a considerable decrease in B1Ipwith increase in pressure from 15.5 to 49 mm. A similar pressure effect has been observed by Toby and Weiss.' These authors ascribed it to a third body requirement in the formation of ethane. That this interpretation is indeed a correct one is demonstrated by the fact that acetone-d6, which may be expected to be a good deactivator, considerably reduces B'/%a t 15.5 mm. but has no apparent effect at 49 mm. The results of experiments carried out above 15.5 mm. do not show any appreciable reduction of B'/% with an increase in pressure. For instance, experiments 6 and 11, which were performed a t approximately the same conversion, show the same value of B'12 while there is only a 10 to 20% reduction of B'/%from experiments 4 or 6 to experiment 9 which were carried out at about the same incident intensity. Pressure effects of this order of magnitude have also been observed in the photolysis of acetone a t pressures above 40 mm.687 and may perhaps be ascribed to residual third body effects as well as tlo effects related to the geometry (of the light beam and/or reaction cell. It is obvious that a more pronounced pressure effect similar to the one reported by Toby and Weiss would be observed if the total methane and ethane yields were used in the rate expression. It thus may be concluded that reaction 1, which has been proposed by these authors to account for t>heobserved pressure effect, has not been clearly established. It should be noted that the effect of primary process I will also be appreciable on earlier rate determinations which were carried out under conditions in which ethane is only a few per cent of the yield of nitrogen. The 9 3 m
c:
mdim
wt-
m a 0 3 3 3
( 5 ) W. C . Sleppy and J. G . Calvert, J . A m . Chem. Sue., 81,769 (1959). (6) A. F. Trotman-Diekenson and E. W. R. Steaeie, J . Chem. Phys., 18,
1897 (1950). (7) R.H.Linnen and W. A. Noyes, Jr., J . Am. Chem. Soe., 7 8 , 3986 (1951).
KOTES
1928
observed intensity and conversion effects should be considered as additional complications. Acknowledgment.-This research was supported by a grant from the United States Public Health Service, Department of Health, Education, and Welfare. CLUSTER INTEGRAL EXPASSIONS IS INHOMOGENEOUS FLUIDS’ BYHARTLAND H. SCHMIDT D e p a i t m e n t of Chemzstry, Unzuerszty of Calzfornra, Rzzerszde, Calrfornsa Recezved Mamh 16. 19557
It is the purpose of this note to show how the cluster integral expansion methods employed by Bellemans*s3 to separate surface contributions to the therniodynarnic and distribution functions of a fluid from bulk contributions may be generalized to express the effect upon the fluid of an externally applied force field. The relationships between the resulting expansions and those in a recent paper by Stillinger and Buff4 are pointed out, and it is shown that the present expansions, being much more direct functions of the external potential, may be more useful in the treatment of some problems. Consider a potential U(r) superimposed upon the intermolecular potential energy Zz1 u(rtl) of a bounded fluid where u(rt,) has been assumed to represent pairwise additive central forcesa5 Without loss of generality we may consider U(r) to be positive infinite outside the surface Q of the fluid and to have a reference value Uo,taken to be zero, for a homogeneous fluid a t the same activity 01 as the system. When U is shortrange compared to the size of the system, the reference state may be identified with the state of the system far from the boundary. The grand partition function and local density can be expressed in the usual cluster integral formalism
m
where the cluster integral sum blU(rl)is given by
101. ti/
It should be noted that the difference between eq. 3 and the usual homogeneous fluid expression is the presence of one factor exp[-pU(rk)] with each drk, and a final factor exp [ -l?Lr(r,)]. h 1 y of the diagram reductions corresponding to rearrangements of the integral in (3) used by Bellemans2,3may be performed by retaining the appropriate factor exp[-PU(rdI = d r J in the integrand with each dr,. Thus it may be shown readily by methods analogous to those used in ref. 3 that the diagrams representing eq. 3 may be factored into ordinary Mayer irreducible cluster integral diagrams to be integrated over all space with U(r) = 0, and “inhomogeneity diagram” factors which are the sole contributors to the inhomogenous effects. The algebraic result of this diagram reduction is
2knk
=
1- 1
Zknk = 1
-m
m
>1
Here the ,& are homogeneous irreducible cluster iutegrals of k 1 vertices, and m!bUnmis the sum of all “inhomogeneity cluster diagrams” of m vertices of the same form as Bellemsiis’ ”superficial” diagrams. These diagrams contain all possible combinations of connected black and white squares to total m squares such that all terminal subparts’ of the diagrams are black squares except the terminal subpart containing “1”; all other vertices including any terminal subpart containing “1” are white squares. The integrations which each of these diagrams represents are (a) with each link associate a factor fs3; (b) with each terminal subpart associate a factor (n:[g(rk) - l ] ) ,X being the number of black squares and U(r,) being infinite outside Q ; (c) associate with each white square a factor g(rk); (d) integrate over the coordinates of the black squares over all space and over the coordinates of the white squares except “1”in the volume within Q. A typical diagram and the integral it represents in the m = 4 set would be 3 1 2 4
+
drz dr,. .drl (3) fi,
= exp[-Pu(r,,)
1-1
the summation being over all connected cluster diagrams of l vertices.6 Also we have (4) (1) Thin work was supported in part b y Air Force Office of Scientific Research Contract AF49(638)-284. (2) A. Bellemans, Physiea, 28, 493 (1962). (3) A. Bellemana, ibid., 28, 617 (1962). (4) F. H. Stillinger and F. P. Buff, J. C h e m . Phys., 37, 1 (1962). ( 5 ) This assumption could easily be eliminated in the surface region in the formal development by using u(r2,ri). The integrals of eq. 5 , 6, a n d 7, etc., then would become more complex. See ref. 2, eq. 9.6 and 9.11. (6) T. L. Hill, “Statistical Mechanics,” bIcGraw-Hill Book Go., Inc., New York, N. Y., 1956, Chapter 5.
The advantage in the above transformations is that the integrations which actually must be performed are limited to those necessary to obtain the properties in the inhomogeneous region, the integrations yielding the bulk properties being clearly separated into factors which can be related to the homogeneous region density taken as a i l independent variable. The steps involved in incorporatiiig the homogeneous region density n into eq. 5 ansl2_la_placPaf the activity (7) A “terminal subpart” IS defined as a set of vertices which 18 attached to the rest of the connected dlagram by only one vertex and ahlch w i t h the point of connection constitutes a RIayer irreduclble diagram. The point of connection is not Considered a pait of the terminal subpart.
