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J. A. DAVIES AND P. P. MANNING
Vol. 79
but we have no information as to the exact states of our palladium catalysts. Variations in hydrogen absorpiion may be responsible for some of the variations in exchange patterns. On the whole, however, variations in exchange patterns were minor. Relative Rates of Exchange.-The rate of production of exchanged hydrocarbon molecules of all degrees of :exchange is equal to the rate of adsorption of hydrocarbon. The relative rates of exchange listed in Table I provide some information as to the nature of the transition state in this process.
more rapidly than the primary ones.17 The tertiary hydrogen atom in isobutane exchanges rapidly. l7 The sequence cycloheptane > cyclopentane > cyclohexane suggests that the transition state provides some relief from the strain occasioned by eclipsed hydrogen atoms. l5 Bonding of monoadsorbed alkane by multiple partial bonds as in interstitial carbides could account for this. A possible transition state is shown in Fig. 5 in which the separated hydrogen atom initially proceeds to below the surface.1s Alternatively the hydrogen atom might move sidewise with a geometry somewhat resembling that of an S N i reaction. The larger number of partial bonds in the eclipsed than in the staggered vic-diadsorbed alkane would stabilize the eclipsed conformation. We have postponed until this place a possible objection to an eclipsed vic-diadsorbed species. 2,3Dimethylbutane exhibits an isotopic exchange pattern little different from that of hexane or 3-methylhexane. For exchange beyond seven hydrogen atoms in one adsorption step with 2,3-dimethylbutane, one requires 2,3-diadsorbed-2,3-dimethylbutane which involves two sets of eclipsed methyl groups. Perhaps, however, the enthalpy of adFig. 5.-Possible transition state separating alkane (v) sorption a t two tertiary positions compensates for the additional eclipsing strain. and monoadsorbed alkane. Acknowledgment.-This research was supported I n part, high reactivity seems to be correlated by the Office of Naval Research. We are inwith low bond dissociation energies.’? Hydrocar- debted to Dr. K. W. Greenlee, American Petrobons with only primary hydrogen atoms react leum Institute, Project 45, a t the Ohio State Unislowly: methane and ethane, l5 neopentane.a,lB versity for the sample of 1,l-dimethylcyclopentane. Secondary hydrogen atoms in propane exchange (17) C. Kemball, Proc. Roy. SOL.(London), 2 2 5 8 , 377 (1954). (14) A. F. Trotman-Dickenson, “Gas Kinetics,” Butterworth Scientific Publications, London, 1955, p. 15. (15) K. Morikawa, S. R. Trenner and H. S. Taylor, THISJOURNAL, 69, 1103 (1937). (16) C. Kernball, Trans. Faraday SOL.,SO, 1344 (1954).
[CONTRIBUTION FROM THE
(18) H C. Brown, R. S. Fletcher and R. B. Johannesen, T H I s JOUR‘IS, 212 (1951). (19) A similar proposal has been made for hydrogen chemisorption. M E Winfield, Rev. Piire A p p l . Chcm., 6 , 217 (1955). NAL,
EVASSTON,ILLIKOIS
DEPARTMENT O F PHYSICAL CHEMISTRY, USIVERSITY OF LEEDS]
Photochemical Technique BY J. A. D A V I E AND S ~ ~P. P. MANNING’~ RECEIVED FEBRUARY 20, 1957 The range of concentration and wave length over which a photochemical reaction can be studied usefully may be increased if a mirror is used to reflect transmitted light back into the reaction system. This makes the intensity distribution much more uniform and so allows a reaction not directly proportional t o intensity to be studied a t higher concentration than would ofherwise be possible. The necessary theory and a n experimental method for determining the reflectivity of the mirror is given.
1. Introduction The range of concentration, or of wave length, over which a photochemical reaction can be studied is often quite severely limited by the optical properties of the light-absorbing species. At one limit absorption may be strong enough to cause a very non-uniform distribution of intensity, a most undesirable feature when the reaction rate is not directly proportional t o intensity. At the (1) (a) Atomic Energy of Canada L t d , Chalk River, Ontario, CRnada (b) Plast~cqDivision, Imperial Chemical Industries, Ltd , Il’riwja i;drdeu City, He&, England.
other limit absorption may be so weak that i t is difficult t o obtain satisfactory rates with convenient intensities, or it may be necessary to decompose a significant proportion of the reactants if products are to be obtained in measurable quantities. The main object of this paper is t o show how the useful range of study may be extended by using a mirror to reflect transmitted light back into the reaction medium, This gives a gain of intensity a t low absorptions, but also has the more important effect of greatly increasing the uniformity when the
Oct. 5, 1957
PHOTOCHEMICAL TECHNIQUE
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absorption is quite large, so permitting work a t oxalate actinometer recently developed by Parker higher extinction coefficients than would other- is suitable for this purpose. wise be possible. The reflectivity of the mirror (b) I n many photochemical reactions i t is difficannot be calculated satisfactorily and a method cult t o obtain a high enough absorbed intensity for determining this experimentally using an acti- while still retaining satisfactory optical conditions. nometer in which only part of the light is absorbed is This sometimes can be overcome by surrounding a given. At low concentrations it is necessary to cylindrical source with a coaxial annular vessel, correct for slight decomposition of the actino- end-effects being minimized by using a source longer than the cell and silvering the ends of the latter. metric species. 2. Reflection Corrections.-If a gas reaction is If the diameter of the source is small compared being studied, or if a mirror is used, the reflection with the inner diameter of the cell the light flux is of transmitted light cannot be neglected and i t is radial. necessary to know the ratio of absorbed to incident Suppose the radii of the inner faces of the cell intensity as a function of the optical density of are x1 and x , ( X I < x 2 ) , that the corresponding rethe reactants and the reflection coefficients of the flection coefficients are rl and r t , and that r is now interfaces. The latter can be calculated from that fraction of light incident on the inner wall of Fresnel's law or, for a mirror, measured experi- the cell in the direction of decreasing x which is mentally by the method described later. The transmitted by this face and is incident on the opformulas for two optical arrangements are given posite side of the cell after passing through the in this section source. (r1 r ) is the effective reflection coeffi(a) For a cell with two parallel plane faces, d cm. cient for the inner surface. apart, in a beam of parallel monochromatic light The intensity of the primary beam decreases in incident normally on one face. If E is the molar the positive x direction due t o absorption and the extinction coefficient of the light-absorbing species increasing surface area giving and c the concentration, the fraction of light ab-' I= - '+I - 'IbA A = 2 ~ x (2.04) sorbed in a single passage through the cell contents ax ax aAax is (1 - 5') where Solving this equation, and that for the reverse direcS = e-pc fi = 2.303cd (2.01) tion, and summing corrections as in the previous Suppose that the intensity entering the cell con- example the absorbed intensity is found t o be tents directly from the source is IO,this being the quantity measured by a total absorption actinometer, that fractions rl and rl incident on the insides of the faces nearer and farther away from the provided all intensities are reduced to the area of source are reflected back into the cell, and that a the inner surface of the cell, this being the area over fraction r of the light incident on the inside of the which a total absorption actinometer would measface farther from the cell is transmitted. r l , yr and ure IO.For an opaque source T is zero and (2.05) r may be composite quantities including reflections reduces to (2.02). For a transparent source r can from surfaces parallel to the faces of the cell, for approach unity and if rt is made large by silvering example windows in a thermostat. the outside of the cell I, is nearly independent of The intensity absorbed from the primary beam S. Under these conditions most of the light is is 10(l- S ) , leaving IOS incident on the second photochemically effective even though the cell face of the cell to give a reflected beam of initial contents may only absorb weakly. intensity Ior,S. From the latter an intensity The greater uniformity achieved by using a mirIorS(1 - S ) is absorbed. Proceeding in this way ror can be simply demonstrated for case (a). and summing the resulting series the total ab- Taking 11 to be zero the change of intensity across sorbed intensity is found t o be the cell as a percentage of that a t the face nearest the source is
+
(2.02)
and the transmitted intensity (2.03)
When r l and r , are equal (2.02) and (2.03) reduce to the formulas obtained by Hunt and Hi1L2 When 71 and rl are known (2.03) generally can be applied because I , can be measured a t most wave lengths by actinometry while S easily is calculated or measured on a spectrophotometer. When a mirror is used r2 cannot be calculated from Fresnel's law for normal incidence, but can be determined experimentally by fitting (2.02) t o a series of values of I, and S for the actinometric solution if an accurate value is required. The potassium ferri(2) Hunt and Hill, J . Cbrm. Phyr.. 15, 111 (1947).
Figure 1 shows A as a function of S for rt equal to 0.90 and zero, corresponding t o using the cell with and without a mirror. The improvement is marked and little affected by ri in the range 0.85 to 0.95. At 40% absorption the non-uniformity is only 10% when a mirror is used. The remaining discussion in this paper applies t o the optical arrangement (a). An almost identical treatment can be given for (b). 3. Corrections for Finite Decomposition.-I, has been obtained as a function of S and the constants of the optical system. Since S changes during an experiment I, also changes and it may be necessary to correct for this, the correction often being quite appreciable because many reactions have (31 Packer. Proc. Roy. SOC.(London), Aa20, 104 (1953).
J. A . DAVIESAND P.P. MANNING
5150
1701.
tions in Iowhen (4.02) is integrated.
IOC
Io(t) = 10
90
+ &(t)
lo
=
f
$9
Writing Io(t) dt (4.03)
8 0
F(S) = F(S)
70
+ f ( S ) , F ( S ) = $ JOT
F(S)dt
(4.02) becomes a. bo
(4.04)
50
Generally the integral in (4.04) can be neglected but this should be verified by calculating an upper limit to the error so introduced directly from the experimental data. Using Schwartz's inequality
4 0
30
I
I /
'
20 IO
0
but IO
20
40
30
50
60
70
80
90
100
100 (1 - S) = % Absorption. Fig. 1.
JOT f Z ( t ) dt
to be taken to lOy0 decomposition or more to obtain measurable quantities of the products. The rate of change of the concentration of the light-absorbing species depends on I a and hence is some function of S , say dc - .~ = G(s) dt
(3.01)
which can be combined with (2.01) to give
