HOMOGENEOUB DWOMPORITION
May, 1957
JDENTIFICATION OF
Soap from stearic acid sample
OF
HYDROGEN PEROXIDE VAPOR
537
TABLE VI1 HYDRATION STATE OF CALCIUM STEARATTI FROM X-RAYDIFFRACTION PATTERNS Feasibility of detection of hydration state from diffraction pattern
Ref.
I 5R3 5R3.3 11, 111, 5
Readily Possible, but some variations from standard pattern Only after a considerable aging period Not possible with these leas pure fatty acids
13 14 15 13, 15
Form prepant a t room temp. after thermal treatment Sample
5R3AH 5133
Ref.
Phase
14 33
VI-N Hydrate
Prior treatment
Qwnched from cetane-water systems Quenched from cetane-water systems
Ease of rehydration of various forma under different conditions SRmple
I I I 5R3AI-I 5R3AI-I 5R3AH
Ref.
Phase
13 13 13 14 14
VI-A VI- A VI-N VI-N VI-A
14
VI-A
Thermal treatment
......
Ease of rehydratlon
No hydrate after 36 hr. in water at 80"
...... Hydrate present after 1 hr. in water a t 100" Quenched from 165" Reverted readily to hydrate at room temp. Quenched Rehydrated partially after 1 mo. a t room temp. ...... No hydrate formation on exposure to laboratory air at room temp. ...... Hydrated completely a t room temp. on sealing in a tube with water
propertics of greases.83 Although water can form a rnonohydrate with calcium stearate,13 after equilibration of systems a t 155", which is above the decomposition temperature, hydrate can be present only if it reforms during quenching or on standing a t room temperature. There is some difficulty in identification by X-ray diffraction techniques since the pattern obtained is strongly dependent on the presence or absence of traces of adsorbed salts,ln the available evidence as to change of pattern wit8h hydration state and ease of hydration of the dry soa,p being summarized in Table VII. Undor the conditions of the present experiments even in the water-containing systems the soap must have been present a t room temperature predominantly in the anhydrous VI-N form in all cases with possible traces of VI-A and monohydrate. I n the case of stearic acid the X-ray evidence (Fig, 5) indicates the formattion of a molecular compound with cal-
cium stearate under some conditions." However, if the effect of the additive were due solely to formation of an addition compound with the soap it would be expected that the ultimate liquid loss and initial rate of loss would be minimum a t a composition ratio of additive t o soap corresponding to complete formation of the complex, and that this would occur at low integral molal ratios. Study of Figs. 3 and 4 shows that the molal ratio of additive to soap is usually non-integral a t the minima, is different a t the compositions of minimum rate of loss of liquid and of minimum ultimate loss, and again different a t the composition of maximum yield value of the gel.28*34I n view of the variability of these ratios and their failure to accord with the compositions of any plausible addition compound it seems unlikely that compound formation can be adduced as the mechanism of stabilization by these additives.
(33) D. H. Birdsall and R . B. Farrington, THIE JOWRNAL. 5a, 1416 (1 948).
(34) H. F. Coffer, Ph.D. Dissertation, Univeraity of Southern California Library, 1951.
HOMOGENEOUS DECOMPOSITION OF HYDROGEN PEROXIDE VAPOR BY CHARLES N. SATTERFIELD AND THEODORE W. STEIN Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Mass. Received Xsplembsr IO, 1866
Studies of the thermal decomposition of hydrogen peroxide vapor under flow conditions in a relatively inert glass reactor show a transition from heterogeneous to homogeneous reaction in the temperature range of 400 to 450°, a t a artial pressure of 0.02 atmosphere. The homogeneous reaction was of 3/2 order and had an activation energy of 55,000 cap. The decomposition mechanism appears to involve very long straight chains.
Numerous studies have been made of the thermal study by McLane2 were experimental conditions decomposition of hydrogen peroxide vapor ,(these such that at least a portion of the reaction seemed have been summarized' recently) but only in the to be occurring homogeneously. The present study shows quite clearly the conditions under which a (1) W. C. Sohumb, C. N. Satterfield and R. L. Wentworth, "Hydrofrom heterogeneous to homogeneous degen Peroxide," A. C,. 8. Monograph No. 128. Reinhold Publ. Corp., New York, N. Y., 1966, pp. 447-468.
(2) C. K. McLane. J . Chem. Phys., 17, 379 (1939).
, CHARLES N. SATTERFIELD AND THEODORE W. STEIN
538
T E M P E R A T U R E OC.
500 4 5 0 IOO.0
50.0
400
2 tIn
0 TUBE NO. 100 0 TUBE NO. 103 TUBES NO.IOO,IOJ,
20.0
4
W -I
0
3 0
10.0
VOLUME = 300 cc. SURFACE A R E A - 5 9 0 ~
c)
X W
5.0
l-
a
a
z
0 c
2.0
0
n
z
1.0
0
u
w 0
0.5
02 0.I
13
1.4
1.5
1.6 10001T
1.7
1.8
1.9
(1) the sharp increase in the temperature coefficient of the decomposition rate and (2) the fact that different tubes showed different decomposition rates in the lower (heterogeneous) temperature region but the same results in the higher temperature region. The data in the heterogeneous range were obtained at average hydrogen peroxide partial pressures of 0.025 to 0.038 atmosphere, those in the homogeneous range from 0.006 to 0.029 atmosphere. To put the results on a comparable basis, the rates of decomposition were recalculated for a hydrogen peroxide partial pressure of 0.02atmosphere, assuming that in the homogeneous range the rate is proportional to the 312 power of the hydrogen peroxide concentration, and in the heterogeneous range that the concentration effect is the same as that found at lower temperatures3-slightly greater than first order. The homogeneous reaction is so rapid under these conditions that a large fraction of the hydrogen peroxide entering the Pyrex tube decomposed therein, so that it must be treated as an "integral reactor." To determine the correct manner in which to average inlet and exit hydrogen peroxide concentrations, data obtained at a common temperature of 460" and several concentrations were plotted as on Fig. 2. The slope corresponds to a 3 / 2 order reaction
- dn&o* -__ V d8
20
(OK:'),
Fig. I.-Effect of temperature on the decomposition rate of hydrogen peroxide vapor ( P H ~ O=, 0.02 atm.).
composition may be observed and provides some information on the kinetics of the homogeneous reaction. A mixture of hydrogen peroxide and water vapor at one atmosphere total pressure was produced a t a constant rate and composition by boiling an aqueous solution of hydrogen peroxide of appropriate composition. The vapor was passed continuously through a Pyrex tube held in a constant temperature bath. The amount of decompositionoccurring in the tube was determined by continuous removal of vapor samples before and after the tube, with quick quenching, followed by analysis of the condensate with standardized permanganate in the usual fashion. The appamtus is described in more detail elsewhereea In a series of studies at temperatures up to 250", and hydrogen peroxide concentrations up to 0.20 atmosphere the rate per unit of surface area was found to be independent of the surface-volume ratio, for the most inert surfaces studied3 showing, in agreement with previous investigators, that the homogeneous reaction cannot be detected at these temperatures. The temperature range from 215 to 490" was then investigated in three Pyrex tubes, each of which previously had been treated with 4 N phosphoric acid to provide a highly inert surface. Each tube had a surface area of 590 cm.2 and a volume of 300 cma8 The results are shown on Fig. 1. Two facts show quite clearly that a transition from heterogeneous to homogeneous decomposition occurred in the temperature range of 400 to 450"; (3) C. N. Satterfield and T. W. Stein,I n d . Eng. Chem., in prens.
Vol. 61
P
kPa,o,"/r
pR,"s =
p p o u t
+ 2
6
(1)
c
where the average value of PH,o,is given by '1s
t
]
918
(2)
Homogeneous rate data obtained at blightly different average partial pressures were recalculated to a common basis of a hydrogen peroxide partial resdure of 0.02, yielding the curve in Fig. 1 for the Romogeneous reaction: The dope of this curve corresponds to an activation energy of about 55 kcal./g. mole. The temperatures reported are an average of the bath temperature and that of the vapor entering bhe reactor. This is a satisfactory measure of reaction temperature when reaction takes place exclusively on the tube wall. However in the homogeneous range the exothermicity of the reaction may cause the vapor to be appreciably hotter than the tube wall. To estimate this factor, the ternperature variation of the vapor as a function of tube length was calculated for the various H202 concentrations studied, assuming the heat transfer coefficient t80be 3.5 ATU/(hr.)("F.)(ft.2), the latter being based on the Reynolds number with allowance for entering turbulence. It was concluded that for only one set of runs (those at an average hydrogen peroxide partial pressure of about 0.03 atm.) was this factor an appreciable source of error and that here the vapor temperature was about 10" higher than the wall temperature. For plotting on Fig. 2 this one set of observed values were therefore corrected using the Arrhenius equation with an activation energy of 55 kcal. Further evidence for a 3/2 order reaction comes from the data of Miss Huang4 which were obtained (4) Y. A I . Huang, S.M. thesis in Chemical Engineering, M.I.T., August, 1965.
*
. r
HOMOGENEOUS DECOMPOSITION OF HYDROGEN PEROXIDE VAPOR
May, 1957
539
in the same type of apparatus, differing principally in that the reaction temperature was determined from five thermocouple wells placed equidistantly along the reaction tube. A group of nine runs a t temperatures between 466 and 489" and a t average hydrogen peroxide partial pressures of from 0.001 G to 0.035 atmosphere were available for evaluation. x 2 lTer rate data were adjusted to the common tern- 2 j 0 I Iicrature of 475" using the Arrhenius equation and an activation energy of 55,000 kcal. Although the C f - 1 data scatter slightly, the results, shown on Fig. 3, ,? ":: , clearly correspond to a 3/2 order expression rather, z 2' t,han to a first or a second order. The data of Miss E, G IIuang when recalculated to 475" and 0.02 partial pressure of hydrogen peroxide and allowing for the ua0, differcnce in reactor volumes correspond to a rate n of homogeneous reaction about 30% less than that shown in Fig. 1. McLane2 obtained data in boric acid-coated Pyrex a t average concentrations of 0.002 atmosphere pressure of hydrogen peroxide and below 0.0 I 0.02 0.03 0.04 0,05 arid at temperatures of 470-540". His rate reportP o r t i a 1 P r e s s u r e O f H y d r o gen Peroxide, rtclly followed a first-order expression and in the Atm. lowest surface-volume ratio vessel studied (S/V = of concentration on tho homogeneou~odecom3 cm. - I ) he reported an activation energy of 50,000 Fig.2.-Effect position rate of hydrogen peroxide, T = 460 cal. Therr! axe several important differences between his experimental conditions and those in the present study. The hydrogen peroxide concentrations here were one to two orders of magnitude greater; the surface--voliime ratio of the present vessel was about 2 cm. - I , compared to 3 cm.-l of McLane, and the flow pattern here approximated slug flow whereas that of McLane appeared to be close to that of a completely mixed reactor. The present rate data are about, twice those reported by McLane if the rate is tnkon to be proportional to the 3/2 power, or aboiit ten times those of McLane if the reaction were assumed to follow a first-order expression. This most probably reflects an increase in chain length of the reaction as the surface-volume ratio is lowered and the HzOz concentration is raised. The most probable initiating step in the reaction is II?Oz $- h i
--+ 2 0 H
(3)
The energy required for this reaction is about 52.6 kcal./g. mole whereas about 90 kcal./g. mole would be needed for the only alternate initiating step, formation of H and OOH. Chain propagation i s most probably by OH + HzOz ---+ OOH + H20 (4) and OOH
--
+ HJ)~
rIzo
+ o2+ OH
(5)
both of which are exothermic whereas all chain branching steps are endotherniic. Chain breaking can occur by adsorption of radicals on the walls or by 3-body combination reactions of OH or OOH, thus
+ +
20H M ---+ HzOz OH HOo M +Oa -I- HzOz 2H02 M +HzOz Oa
+
+
+
(Gal (6b)
(6c)
If the rates of reactions 3 , 4 , 5 and 6a are formulated in terms of the appropriate rate constants and
1
0.2t
0.I
0.001 0.002 0.005 0.01 0.02
Partial Pressure
0.05 0.1
Of H y d r o g e n P e r o x i d e ,
Atm. Fig. 3.-Effect of concentration on the homogeneous decoypositionrate of hydrogen peroxide (from Huang), T = 475 .
reactant concentrations, and the rate of production and destruction of each of the free radicals is equated, one can derive the expression
A 3/2 order expression is also obtained if one of the other free radical combination reactions is chosen instead of 6a. However, if 3-body free radical combination reactions are regarded as negligible and chain stopping is assumed instead to occur by
J. Y.TONGAND P.E. YANKWICH
540
adsorption on walls, the mathematical formulation leads to a second-order expression. The fnat that the decomposition rate in fact followed a 3/2-order expression suggests that the 3-body free radical recombinations were the chain stopping mechanism here and not wall reactions. It is interesting to compare the observed decomposition rate with the number of collisions of hydrogen peroxide molecules in which the energy is greater than 55,000 cal./g. mole. The measured decomposition rate at 460” and hydrogen peroxide partial pressure of 0.02 atmosphere corresponds to about 1.9 X 10’’ molecules decomposing per cc. per second. Assuming that the fraction of collisions having activation ener ies greater than 55,000 cal./g. mole equals e - E ET, the number of such
9
Vol. 61
activated collisions involving a hydrogen peroxide molecule is about 1.8 X 1Olo collisions per CC. per second. There are, of course, considerable sources of error in calculating the number of “effective collisions,” such as the uncertainty as to the value of the activation energy and, as to the collision crosssections, and aIso the possibility that the activation energy may be shared between more than two 1 I square terms,” and therefore that the fraction of effective collisions may be somewhat greater than e-E/RT. Nevertheless, the enormous difference between the two numbers clearly indicates that long chains are involved here. Acknowledgment.-The authors wish to wknowledge the financial aupport of the Office of Naval Research, under Contract Nonr-1841 (11).
A
*
0
CALCULATION OF EXPERIMENTAL ISOTOPE EFFECTS FOR PSEUDO FIRST-ORDER IRREVERSIBLE REACTIONS BY JAMES YING-PEH TONUAND PETEJR E.YANKWICH Contribulion from the Noyes Chemical Laboratory, Unweraily of Illinois, Urbana, Illinois Recdvsd Septsmbsr 8.4, 1068
Foiir exact equations are derived for the calculation of experimental ieotope effects of Bysteme of pseudo Bret-order irra versible reactions. The input data are either measured isotope ratios alone, or a combination of isotope ratioa with the meaanred reaction coordinate. The advantagee and disadvantages of these equatione over those of the zero-time approximsr tion method are diecussed.
Introduction In this paper, we are concerned with a system of pserido first-order irreversible reactions A‘ pP qQ -+ B’ + uU VV (1) A“ pP -I-qQ --+B” uU VV (2) where one atom of the element Z is transferred from a molecule of A to one of B during one stoichiometric unit of reaction. The symbols A‘ and B’ stand for the compounds A and B containing the lighter isotope Z’, and the symbols A” and R ” stand for the compounds A and B containing the heavier isotope Z”. The rate equations are assumed to be
+ + +
+ + +
-d(A’)/dt = k‘(A‘)F -d(A”)/dt = k”(A”)F
(3) (4)
where F is a function of the concentrations of reactants, catalysts and products, other than A and B. Conventionally, the isotope e.#‘ect is defined as the deviation from unity of the ratio of isotopic rate constants r ; Le. (.
- 1) = ( k ‘ / k ” ) - 1
(5)
An approximate method‘ which has been employed in several studies2J involves the determination of the isotope ratios R b t and Rho, (or Rae), the corrected isotope ratios (B”)/(B’) of product accumulated to times t and infinity; collection of the sample with which the former measurement is to be made is stopped at a value of the reaction coordinate, f, so small that the time t may be (1) J. Bigeleisen, Science. 110, 14 (1949). (2) J. Bigeleisen, J . Chem. Phya., 17, 425 (1949). (3) P. E. Yankwich, R. L. Belford and G. Fraenkel, J . Am. Chem.
am..76,832 (1953).
t
considered equal to zero. The isotope effect, then is computed from the relation (r
- 1)
3 .
(Rbm/Rbt)t*
-1
(6)
Several other worker^'^ have published the results of studies baaed on other approximation methods which employ iaotope ratios determined on product material accumulated up t o large values of the reaction coordinate f; in all of these, the approximation has been the application of an equation valid only when one isotope is present at the trace level. I n a system of two simultaneous irreversible reactions involving isotopically different reactants and products, one can meamre three isotope ratioa and the reaction coardinate; the isotope effect can be computed from any grouping of three of these quantities. In this paper we shall examine four esmt equations applicable t o systems of any original isotopic constitution and each of which employs a different grouping of the input data. For each of these equations and equation 6 we shall calculate and compare the errors in r arising from typical imprecisions in the input data. Derivations The four measurable quantities are: the isoto e ratio of the starting material, Rao (which is thpe same as that of the accumulated product at complete reaction, R b - ) ; the isotope ratio of the residual reactant at time t, Rat; the isotope ratio of (4) A. A. Bothner-By and J. Bigeleisen, J . Cham. Phvs., 10, 755 (1951). (5) J. A. Sohmitt, A. L. Myeraon and F. Daniels, T H i s JOURNAL, 86, 917 (1952). (6) A. M. Downea, Aurlralion J . Sei. Rssearch, AB, 521 (1962).
i
*
r’
