pression on the solution rather thaii on the uiimixed components. If we substituted Vm” = Vn0 = pmO - BE into eq. 28 and 29 we obtain
notion that SVEshould be zero is possibly more nearly valid. We now turn to the general process I11
l’rocess IIB
l’rocees 111 .xcC(T,r”’,
Equations 30 and 31 are actually even simpler than eq. 8 aud 10, but the necessary data are generally less available for the solution than for the pure components. The differclnces betn een the I I B and IIA functions usually are trivial because of the small size of PE, ;.o that the distinction between the two usually caii be ignored. Thus, for be_nzene ethylene chloride (Table 111), A”[IBVE - A I I A ’ ~ = 0.2 cal., ~ = -0.03 cal. Intheworst while T ( . T I J B-~.!TIIA\EE) of our sevcii cases, n-hex%iie n-perfluorohexane (Tcble IXI,-A”IIB~’~ - A1raXE = 12 cal., while T(S1lBvE - JIIA” =~ 42) cal. ; this last correction is small compared with the differences between Prscesses I and 11, and is of uncertain significance. T S I I Bbecomes ~~ -17 cal.. closer to zero than the value for proce.. 11. This improvement may result from th(3 fact that when the volume change is poiitive, process I I B takes place in u smaller voliinie, :it higher density, where thc intuitive
+
+
-
p ( T > p l l )= -
1
X( T’PO),”
(\-!’/ -
Fmu,2 +
Presunia_bly TCI should select T’’ as the smallest of the set VIo, V20, Vmo,in which case negative pressures are avoided. This we designat’e as process IIIB. The differences between the I I I B agd IIIh_fuiictioiis are more important’ because Vmo - V’” is sizable in most mses. For example, for benzene ethylene chloride_, if we choose @”’ = Vgo = 79.2 ml., we obtain A I I I B ~ A~ ” I I I ~ ,=~ ~17 e$. and T ( S I I I B-~S~I I I . A=~~ 7) cal. ; this makes A 1 l l B C E = - 15 cal. and T S I I I B “ = ~ 11 cal. These are still significaiitly different from those for process 11. but their difference from the values for process IIIA is a measure of t’he unreality _of t’he-constant molecular density process for large VIo - V2”.
+
THE I i E . x n o s OF HYDROGEX ATOMS WITH SOLID PKOYEXE AT LOW TEMPERATURES’ BY R . ~ P IKI L E I Nh, ~h ~i ~ o xD. SCHEEI~ .im JOHN G. I\.ILLEB?~ iVutLoriul Rureuu of Standards, Kushznyton, D.C. Received Febi uarg 1.5, 1860
The rcwtioii of liytlrogei~ittoin5 tvit)h solid films of propene hcts been studied beloiv 100°K. Tlic hydrogel1 xtmis diffuse through and r c w t with thp propene films to forni propane and PJ-dimethylbut,ane. A one dinimsional tiiffusion cqu:tt,ion containing a chemical r e a d o n t,erm is uwd to describe the kinet,ics of this process. A value of 5 x 10’ rc./niolc P P C . is obtained for t’he specific rat,c constant a t i i ” K . for the reaction 1% CH2-CH=CH2 + CX-CH-CH,. The ratio of pro palie to 2,3-diniet’hylbutaneis aliout 9 arid does not change as t h e conccmtration of propcrir ih varivd over two ortlerz of magnitude. Thc propane as w l l :IS the 2,3-dirnc?t,h?ll)tititrle must t,hcrcfore I-xformcd 1)y :iproccva 11hich is eec.ond order \Tit11 respect, to the isopropyl radical conceritrat,ion.
+
Introduction The observatioii that hydrogen atoriis react ivit’li d i d olefins at lon temperatures, aiid the technique used for following these reactioiis, provide a quantitati\.e approach to kinetic studies in the low temperat>ure region. Simplificatioii occurs through t8heabsence of high act’ivation energy reactions, but’ diffusion processes could in some iiistmalices be rate rontrolliiig. (1) This research was performed under tlie National Bureau of Standards Free Radiials l ~ e s r a r c l r P r o g r a i n , aiil)porrpd by the Department of t h ? Army. ( 2 ) ( a ) ( i u e s t Scientist. R l e l i ~ i t i ,I I N i b ) G u e s t Scientist, British O X ~ - E CResearch II and D e r e i o ~ ~ r r i e nLtd. t,
111 the approach descarihed pre\-iously, j thc i t nctioii between hydrogen atoms aiid solid olefiiis followed h y iiotiiig deposited on a - 1%’ nail the pressure dcciease 111 the rf3l(’tl~Jilvessel (wiitaining the hydrogen gas. The atoms were generated thermally on a tungsten ribbon. Observations also have been made using an electrodeless discharge as the atom source with similar results. Direct information on the course of the reaction may be obtained by examining the olefin film during reartioil by spectroscopic methods Spm iemi:iiitae nicasureii1ciit5 are i i 4 to r i t a1)lisli
~
ko)
13 l\Iein r i d A1 U h t l m 1 , l’!!!s J U L I I ~ A L 62, 101 I (14;8)
124s
Vol. 61
an upper limit on the iiuniber of free spins in the solid. Certain features of a reaction system in which gas phase species irnpringe on, diffuse into, and react’ with a solid can be described in a general way. The propene-hydrogen atom system has been chosen for st,udy.
Experimental Results The reacticc was studied in a system described p r e ~ i o u s l y . ~I’roducts were alialysed after wmiup with gas-iiquid chromatography and mass spectroscopy. In the hydrogen at,om addition to solid propene, only propane and a six carbon alkane are formed. Methane, a product of atomic cracking reactions, never has been obseryed. The hexane products for the gas phase reaction have been shon-ii to be pi*eclornii~ant,ly2,3-diniethylbutaiit!,4n*bwith a small amount of 2-methylpentane. The hydrogen atom addition to s d i d propene also results in 2,3-dimethylbutane, the dimer of isopropyl. At most about S Y , of the CB fraction is 2-methylpentane. This is indicated in Table I where pertinent mass spect,ral peaks are compared with those for standard samples of 3methylpen tane and 2,3-dimethylbu tane. The ratio of propane to 2,3-dimethylbutaiie iu t’heproducts is of considerable importance for estahlishing t,he niechaiiism of the hydrogen atom addition reactioii to solid propene. Analysis was made with gas chromatography on a two meter dimethylsulfolane on Chromosorb column at. 50”. Table I1 gives the propane-Ca ratios for various film thicknesses, temperatures, propene concentrations, conversions, and gas phase concentration of hydrogen atoms. The concentration of propcne was coiitrolled by admixtiire with butane anti the H a t m i concentration was fixed by the tungsten ribhon t,emperat’ure. l’he results givcii in Table I1 show that t’he propaiie-C~ ratio is rernarkahly Constant, Init, considerahly higher than the ~ - a l u eof atmiit 0.5 fcrintl for t,lw gas ph:ise reaction in the pressure region \vlicw atoniic cr:ic,l;iiig is rni~iiniized.~~~
T A B L E 11 I’ROPANE/C~ RATIOUNDER VARIEDEXFERIXESTAL CONDI-
TIOh-s Ri*!aii\e
film thichnass
1 3 10
:.‘ilm t:nlli.,
‘Iii tan;. p , i l i d proiicnc -rate of reaction has been re-investigated. Ten to 16.0 16.0 &i one butane to propene mixtures were coiidensed 100.0 iI 101) ii 1:io, 0 iii films whose thickness was varied from 6 X 5.(1 :i. 0 ;i ) 2:; ! 10 -fi t o 3 x lo-* em. Figure 1 shons the change 3.1 6.2 57 42.5 in the initial rate of hydrogen pickup with film 4.2 5.2 50 lfi.!) thickness. It is clear that for films above a certaiii 33.4 32.0 55 L‘i .u thickness (in this case about 2 x em.), the The distribution of deuterium in the products rate is independent of thichess. Below this value of the tleuteriuni atom addition to solid propene is a linear relationship holds. For films of pure of interest. The isot,ope experiments, reported propene a similar behavior must apply but the briefly in reference 1, have been extended to in- m e a r region mould occur a t much smaller film clude the analysis of both propene and propane. thicknesses. The observations reported previThese were separated on a tsvo meter silica gel ously3n w e made only in the thick film region. Diffusion in the Solid.-Hydrogen atonis proc ~ l u m nand , each fraction was analyzed septtrat,ely duced in the gas phase impinge 011 the deposited Wall, J . Clrein. 1’7, 1325 (1!140); (1) IV. .I. ?,Ioor.e nnii L olefin film and diffuse through and react with it. (t,) 1’. , I _ Do,li1y nud .I. c. I b. l’roc. E o # . d o c . (Loiidoi.), 249, 518 The layer of propene is taken as a slab of uni( 19S!)) . I
(ti)
,
J’h~j.~..
REACTION OF HYDROGEN ATOMSWITH SOLIDPROPENE
Sept., 1960
1240
form thickness, I (Fig. 2). At X = 1 the hydrogen atom concentration is designated as Ho. The appropriate one dimensional steady-state diffusion equation with chemical reaction is
where D is the diffusion coefficient and K = kl(Pr), kl being the specific rate constant for the hydrogen atom addition to propene, Pr. The boundary conditions are H = HoatX= 0 bH bX=OatX=l I
I
The latter arises because the surface on which the olefin is deposited is assumed neither to adsorb nor cause recombination of hydrogen atoms. The solution of (1) is H
=
H O [cosh
4;
X - tanh
4; dE 1 sinh
0
2
1
3
4
fllm IhiCknCII. ! X I04cm
Fig. 1.-The
variation of the initial rate of hydrogen pickup with film thickness.
X] (2)
I n terms of the observed rate
1/mHo tanh $ 1
(3)
where A is the area of the film. Two limiting cases for the rate are those in which (a) the hyperbolic tangent is approximately equal to its argument and (b) the hyperbolic tangent is approximately equal to one. Case (a) is equivalent to a film in which the hydrogen atom concentration is constant throughout and equal to Ho.
-a(%)
initial
=KHul
(4)
It is evident that the rate should be directly proportional to the film thickness and the propene concentration in this region. If the boundary condition H = 0 at X = 1 obtained, the hydrogen atom concentration profile for thin films and low propene concentrations would be linear in X . This requires a dependence of rate proportional to the second power of the film thickness. The experimental results clearly show a linear relationship, and hence the boundary condition dH/dX = 0 a t X = 1 is most probably correct. For case (b) Here the rate is independent of film thickness but proportional to the square root of propene concentration. As the film thickness is increased, the expected departure from linearity occurs as seen in Fig. 1. The entire curve closely approximates that of a hyperbolic tangent as required by the model. This indicates that the assumptions made are reasonably correct. Calculation of the pertinent constants can now be made. It is assumed that the concentration of H atoms on either side of X = 0 is approximately the same. The value of Ha,the concentration of hydrogen atoms a t the surface of the film, is computed from the tungsten ribbon temperature,
Fig. 2.-Schematic
model for the interaction of hydrogen atoms with propene films.
2000°K. in these experiments, and the hydrogen pressure in the vessel, 30 p . The assumption is made that atom recombination does not occur in the gas and the rate of dissociation at the filament is rapid compared to recombination at the wall. This leads to a value of Ho equal to 5 X moles/cc. The slope of the linear region of Fig. 1 gives a value for KHo of 25 X lob6 mole/cc. mole/cc., the resec. With (Pr) = 1 X action rate constant for the addition of hydrogen atoms to propene at 77°K. is calculated to be k = 5 X 10' cc./moles sec. This is a lower limit for k since the hydrogen atom concentration used in the calculation represents an upper limit value. It is interesting to note that, without taking account of the change from solid to gas, a value of 1.5 kcal. for the activation energy of this reaction leads to a value of k = 10" a t 300°K. the same as that determined by Melville and Robb.K The diffusion coefficient D for H atoms in butane at 77°K. may be derived from the data of Fig. 1 and equation 6. m
K HO = 2.5 X 10-0
D = 5 X 10-4cm.2/sec. (6) Chemical Mechanism.-Chemical evidence shows that reactions ( l ) , (2) and (3) occur in the hydrogen-atom-solid propene system a t low temperatures
+
H CHa-CH=CHZ +CHs-CH-CHa C&-CH--CH, CH3-CH-CH3 ---f CHa-CHZ-CHa 4 CHa-CH=CHz ( 5 ) H.
+
W. Melville and J. C. Robb, ibid., Al96, 494 (1949).
[I J [ 2]
1250
Yol. 64
HAROLD KwsnT
is further demonstrated by the deuterium distribution in the products of D CH3--CH=CH2 shown in Table 111. The extensive deuteration of the propene and the formation of deuterated propanes other than propane-d2 is most readily accounted for by the occurrence of reaction 2 rather than 4. The high propane to 2,3-dimethylbutane ratio might be interpreted to support the hypothesis of persistence of excess energy in the radical since the addition of a hydrogen atom to propene is exothermic to the extent of 43 kcal. 'mole. In the gas phase, in the region of 300°1(., a ratio of 0.5 is obtained under conditions where the radicals are thermalised..lbs6 It has been observed that this ratio increases at lower pressures, an indication that disproportionation is favored over dimeriaatioii for "hot" It must be pointed out, hoxver-er, that the high value of the propane to Cs ratio obtained in this work at 77°K. in comparisoii with the ratio for temperatures in the vicinity of 300°K. obtained by other investigators"' may well be explained by an activation energy difference of only 0.3 kcal. between the disproportioiiatioii arid recombiriation reactions.
+
CHI-CH-CHB
[8]
The hydrogen atom addition to the radical has H
+ CH8-CH-
CH3 ----f CH3-CH2--CH3
[AI
been postulated p r e ~ i o u s l y ,but ~ it is doubtful whether this reaction does take place in the system under study. It may be noted that Boddy and R ~ b observed b ~ ~ 4-methylpentene-1, isopentane, and eight other fractions upon subjecting the products of the gas phase hydrogen-atom reaction with propene to chromatographic analysis. This is in contrast to the atom reaction with solid propene at -195" where only propane and a c6 are ever observed. The latter, as previously noted, ronsiste of at least 927, 2,3-dimethylbutane. Further, methane never has been detected either mass qpectronietrically or with g.1.c. There is no doubt that reactions referred to as "atomic cracking" do not occur. Equations 1 , 2 and 3, if they occur exclusively, explain product formation as well as the invariance of the propane-Ce ratio. The C6 must be formed by isopropyl dimerization and hence propane formation is also required to be second order with respect to the radical. Therefore the inclusion of reaction 4 in the mechanism is precluded. The importance of isopropyl disproportionation
SOME ASPECTS OF THE BOTATISG SECTOR DETER311SA1TIOSOl' THE ABSOLUTE €LATE COXSTAXTS Iiv RADICAL POLY3IERIZXTIOS REACTIOXS' BY HAROLD KIT-ART~ Converse Memorial Laboratory of Hurvwrd Cnzcerszty and the Department Del.
0.f
Chemzstry
OJ'
Ihe 1 *nilersztu of Delaware, A-ewarh,
Received February 18, 19fi0
Some of the possible sources of error in the rotating sector determination are examined. A method of coniputing the absolute rate constants in radical photopolymerization reaction has been devised which takes account of dark reaction rates in both the dark and light periods of the measurement. A basis is presented for estiniat,ing the magnitudes of dark reaction rates which can be neglected in such calculations. Consideration also is given to the effect of a non-uniform distribution of radical centers due to such factors as non-uniform absorption of the incident beam.
The average lifetime of radicals in a chain reaction is most readily determined by means of the rotating sect'ion method. The theory of this experiment was delineated originally by Briars, Chapman and Walters3and subsequently discussed by D i ~ k i n s o nSwain ,~ and Bartlett5 and by Burnett and All these a ~ t h o r s ~ haye - ~ developed
somewhat different approaches to computing radical lifetimes in homopolymerization reactions from data obtained by rotating sector nieasuremeiits in photoinitiated reactions. Similar developments have been published with certain extensions to take consideration of a steady dark rate accompanying the intermittent photoreaction. Gee and Bateman' have presented a method of computation ( 1 ) This n-ork was supported b y t h e Office of Kava1 R c s e n i c h , Project S o . KR-056-095; Principal Invehtigator, Profebsor 1'. n. in cases of radical chain oxidation processes where Hartlett. P a r t of the material in this article was presented in s teclithe thermal dark rate is very appreciable. Mathenical regort t o t h e O.K.R., h-o. 35-ori-76, J u n e 1, 1949. son, h e r , Revilacqua and HartS have shown that ( 2 ) Department of Chemistry, Unirersity of llela\vare, S c w a r 6 , this situation also occurs in many photopolymeri1)rlarnare. (:i)F. Briars, D. L. Chapman a n d E. Walters, J . Chem. Soc., Sti2 ( 1926).
( 4 ) See
\V. .4.S o y e s , J r . , and P. A . Zeighton, "The Photochemistry
u f Gases," Reinhuld Pnhl. Corp., ?iew York, h-. Y.. 1911, 1'. 202, e t aep.
(,5) C . C:. Swain and P. I). Bartlett, J . A m . C i i < ~ mSoc., . 68, 2381 (1946).
(6) C, 31 Burnett and 1% TT- \Ielxille, Pior R o y Roc ( L o n d o n ) Al89, 156 (1947). (7) G. G e e and I. Bateiiisn P r o c R o y . So< i L i i r d o i i ) , 8 1 9 5 , 3 i i
(1948) (8) ill S Matheson E I; 4uer F. B B e \ i l a r J. A m Chem. S o c , 71, 497 (1949).
IIIA
and F J. Hair,
