SIDNEY LV BENSON
3922
The pH Dependence of the Rate Catalyzed by Trypsin.-On a logarithmic scale the p H dependence of the trypsin-catalyzed reaction is extremely slight from pH 6 to 10, quite in contrast to the behavior of the other endopeptidases. However, on a linear scale a pH dependence much larger than the experimental uncertainty becomes evident (Fig. l b ) . Studies on benzoyl-L-arginine ethyl ester2"indicate a pKa for the enzyme-substrate complex of 6.25 arid no pk'h was evident up to pH 10. Various values for pKa were assumed and the p H dependence predicted. As can be seen in Fig. Ib, the observed pH dependence can be predicted below p H 9 assuming pk', = 6 . ( j . Below pH 9, then, the pH dependence of the rate is controlled by the (20) H. G u t f r e u n d , T ~ a n sF a v n d n y S o c . , 5 1 , 441 (1955)
[CONTRIBUTION FROM
THE
Vel. 80
charge state of the enzyme and is independent of the charge state of the substrate X variety of models in\-olving the charge state of the enzyme and the charge state and conformation of the polylysine were considered in an attempt to explain the pH behavior above pH 9 Several of these predicted a decrease in rate that was qualitatively correct None, however, stood out over the others However, the data must be extended to higher pH and the Alichaelis constants determined over the entire pH range before a meaningful interpretation can be given Acknowledgrnents.--\Z-e wish to thank A h - . James Monroe for assistance in analyzing some of the data and l l r . Richard Xntrim for the titration curve for polylysine.
DEPARTMENT O F THERMOCHEMISTRY A S D CHEMICBL KISETICS, MENLOPARK, CALIFORSIA]
STANFORD
RESEARCH IXSTITUTE,
On the Thermochemistry of Alkyl Polyoxides and Their Radicals' BY SIDNEY W. BENSON RECEIVED APRIL27, 1964 From data on heats of formation of oxides and peroxides, a new value for the partial molar heat of formation of the group O-(O): is selected. Its value is LHf(O-(O)?) = + I 9 i 4 kcal./mole. L-sing this and other more accurate data, it is possible to deduce AHr" for polyoxides R 0 , R ' with n = 2, 3, 4, etc., and R and R' = H, alkyl, etc. Together lvith data on LHr' for radicals, it is shown t h a t it is unlikely that tetroxides can be produced or isolated above 80 to 100°K. The trioxides on the other hand appear to have'reasonable thermal stability and recent observations by Czapski and BielskiZa on H:Oi production are in accord with these expectations. Free-radical methods will not produce very large amounts of these species. In the case of R 2 0 3 , where R is a tertiary radical, this is not the case and it is proposed that the recent production of a polyoxide by Milas and DjokicZhis very likely 2-BuOs-t-Bu rather than the claimed tetroxide.
Introduction In a recent paper3 it was estimated that the species H204 is thermodynamically unstable above SOOK. with respect to dissociation into 2HOz radicals. The lower homolog. Hz03, was estimated to be sufficiently stable to be isolable a t 200OK. Despite this, i t was shown on kinetic grounds that attempts which had been made to produce i t from gas-phase or gas-solid free-radical reactions were unlikely to succeed. Since then data have appeared? which further substantiated the kinetic conclusions on the unlikelihood of H 2 0 3or H 2 0 4preparation. However, some recent results on aqueous oxidation-reduction systems suggest the formation of H 2 0 3and HOs- viu alternate routes. In addition some experiments'b on the alkyl derivatives of peroxides have given direct support to the reality of the conipounds R z 0 3or R z 0 4 . In the light of these findings it was felt worthwhile reviewing the thermochemical data on the hydrogen polyoxides and extending the methods of analysis to the alkyl conipounds, their radicals, and derivatives. Thermodynamic Estimates.-The basis for the method of estimation of the heats of formation of the polyoxides derives from the principle of additivity of group properties as described by Benson and Buss5 in (1) This development was partly supported a t Stanford Research in^ s t i t u t e by a genei-al project o n "Reaction of Organic Compounds with Oxygen " ( 2 ) la) G Czapski and B H .I Birlski. J Piiys. C h r m . , 67, 2180 (1963), lilas and S 51 l l j o k i c , Chrm I u d . [ I n n d o n ) , 40.5 (1962) . Renson. J . Chrin. P h y s , 33, :306 (1900) (4) P. A G i g u h e , I C S L . R P , ~4 , 172 (1962). i.5) S W Benson and J. H Buss, J C h c m . P h > c , 2 9 , 316 (14.58). Follow-
conjunction with the less accurate principle of bond additivities. The former was found to give values of AHfoto within +1 kcal. in about 1000 cases, and the polyoxides should fit the scheme quite well. The problem is one of establishing the partial group value of AHfofor the group 0-(0)2, i.e., an oxygen atom bonded to two neighboring 0 atoms. In the preceding paper,:' this value was estimated from bond energies. Such estimates can be made from the values of A H f O ( H 2 0 ) and AH;3(H202) which would yield the value AHf'(0( 0 2 ) ) = +25 kcal. with a maximum expected error of + 6 kcal. based on a number of similar cases. If, however, the estimates are made from the data on AHr' (CH30CH3) and ~lHf'(CH300CH3),~ then we estimate A H f o ( O - ( 0 ) 2 ) = f 1 3 kcal. with similar error limits. The mean value of AHfo(O-(0)z) = +19 4 kcal. seems a reasonable compromise of both these estimates and is to be preferred on purely empirical grounds. This new group value of h H ~ o [ O - ( 0 )then z ] yields, together with the other appropriate group value^,^ the estimated heats of formation shown in Table I. To calculate bond dissociation energies for the compounds listed we use the AHrO for values the radicals shown in Table 11. Polyoxide Stability. Tetroxides.-The values listed for A H f o of H z 0 3and H204 are lower by about 2 and 4 kcal., respectively, than the ones suggested earlier, but ing t h e nomenclature adopted in this article l r H i o l O - f O ) ~ represents ) the partial molar group conti-ibution t o t h e total heat of foi-mation of a rni,lccule containing t h e g r o u p O-kOJ?, a n oxygen a t o m joined t o t w o neighhol-ing 0 atoms. As a n example. H202 contains only two identical groups O - ( H ) ( O J . while HzOi contains t h e s a m e t w o O-(H)(O) groups plus t h e O-fO)? grouii f D ) See compilation in S XV, Benson. i b i d . . 40, 1007 (1964)
THERMOCHEMISTRY OF ALKYLPOLYOXIDES AND THEIRRADICALS
Oct. 5 , 1964
TABLE I ESTIMATED HEATSO F FORMATION O F SOME IN THE GASPHASE Compound
AHfO, kcal /mole"
Hz0z Hz0i5 ~
~
0
POLYOXIDES
~
-32 -13 + 5 - 32 -13
5
CH30zCH3 CHZO~CH~~ CHZO~CH~~ CHiOzH CH303Hb CHzOrH' t-BuOz-t-Bu t-Bu03-t-B~~ t-Bu0a-t-B~~ t-BuOzH
5 5 f4 5 i 8
f4
+Sf8 - 32 -13 f 4
+ 6 i 8 - 85 -66 f 4 -47 8 - 59 -40 f 4
+
t-Bu03Hb
t-Bu04Hb -21 f 8 Values are taken from ref 6 except where error limits are Estimates made by the present method given a
AH{'
FOR SOME
Radical
TABLE I1 OXYGEN-CONTAINING RADICALS AH{', kcal./mole
0 HO HOz
59.6" 9 . 0 f 0.3b 5 . 0 f 2" 2 4 . 0 f 6' CHiO 2 i 26 CHOi 5 . 5 f 3f CH303 2 4 . 5 f 6d t-BuO -24 f '1 t-BuOz -21 5 i 2.5' t-BuOa - 2 5 5 6 ' P. Gray, Trans. Furaday Soc., 55, JAXAF Tables, 1962. 408 (1959). c Ref. 7 . From preceding member and A H f " ( 0 (0)2,e From pyrolysis of CH30CH3,S.W . Benson and K. H. Anderson [ J . Chem. Phys., 39, 1677 (1963)] give an estimate of D(CH30-H) := 102 kcal. and self-consistency of E,,, for dissociation of peroxides. f Assumption that D(R02-H) = D(HO2H ) = 89.5 kcal.; see ref. 7. g E,,, for pyrolysis of d t B P : L. Batt and S. W. Benson, J . Chem. P h y s . , 36, 895 (1962).
within the error limits previously cited. If we select a new value' of AHf'(H02) = f5.0 f 2 kcal./mole, which implies the bond dissociation energies D(H02-H) = 89.5 and D(H-02) = 47.0 kcal., we find that D (H02-OH) = 27.5 i 6 a n d D ( H O z - O z H ) = 4.5 f 12 kcal. These estimated stabilities of H203 and H204 are about 6 kcal. greater than our earlier estimates. H z 0 3is now expected to be stable below 25') but H204 is not expected to be stable a t temperatures much above 100°K. However, the uncertainty in bond energy is now so large as to make any very precise estimates of its region of stability of dubious value. Using the value of AHf'(CH30) = f 2 kcal./mole,6 we find AHf'(CH3O2) = 5.5 i 2 kcal./mole, D(CH302OCH,) = 20.5 f 6, D(CH302-02CH3)= 5 12, D(CH302-OH) = 26.5 + 6, and D(CH30-02H) = 20.5 f 6 kcal. with similar values to be expected for the t-Bu oxides8 or for alkyl oxides in general, since the RO-OR bond energies seem to be very close to each other.6 I&7esee that the thermodynamic stability of the alkyl and hydrogen polyoxides are very similar; that is, the
*
(7) S. S . Foner and R . L. Hudson, J . ('hem. P h y s . , 36, 2681 (1962). (8)For t h e 1-Bu series, using t h e corrected value for AHr'(t-BuO) = -24.0 kcal./mole, AHro(I-BuOi) = -21 5 2 kcal./mole and D(1-BuOi0-1-Bu) = 20.5 k 6 , D(L-BuOFO~-I-BU)= 4 i 12, D ( t - B u O r O H ) = 27.5 k 6 . T I ! ! liu0-0rHj = 21 i 6, and D ( t - B u 0 ~ 0 ~ H = ) 4.5 + 12 kcal.
+
3923
compounds K 0 3 R and R03H are expected to be stable below 250'K., while RO4R and ROIH would be stable below 100'K. It should be emphasized that we use the term stability here in a kinetic sense to indicate that the dissociation into radicals would have a half-life in excess of 1 hr., assuming that the first-order rate constant for the dissociation has an Arrhenius .4 factor of 1015 sec.-1.9 This criterion further assumes that once formed in a dissociation step, the radicals would then react to produce final products by very rapid disproportionation steps. We omit from consideration for the moment the very real prospect that they would set up chains by attack on the parent compounds. This would lower even further the temperature for kinetic stability. While the alkyl tetroxides are not very stable towards dissociation into two peroxy radicals, their chief mode of decomposition would appear to be the concerted, exothermic reaction to produce two alkoxy radicals and 0 2 . ROaR +RO
+ + OR 0 2
(1)
This reaction is about 2 f 10 kcal. exothermic and almost independent of the group R . Even if we take the extreme limits of uncertainty and consider the reaction endothermic by 8 kcal., i t would yield a stability temperature of 100'K. This makes somewhat dubious the claims of Milas and DjokicZbto have isolated the tetraoxide of t-Bu radicals a t temperatures below 240'K. The compound R04H has D(ROz-OzH) = 4.5 f 13 kcal. which would give i t the same stability temperature as R04R. The dissociation into RO f OH 4- 02 is, however, endothermic by 5 f 10 kcal. and so again represents a lower energy path for decomposition than the peroxy radical formation. This limits the existence of RO4H to temperatures below 60 or 180°K. if we accept the largest value for the expected error in estimated endothermicity. In contrast to R 0 4 R , H 0 4 H is stable with respect to the formation of 2 0 H f 02, the endothermicity of the reaction being 12.5 i 8 kcal. This is therefore a less favorable dissociation than the direct split into 2 H 0 2 radicals. This also helps explain the observation that the gas phase pyrolysis of H202is not a chain reaction,I0l1 while R 0 2 H does undergo chain reaction by the relatively fast, nonterminating, exothermic step6 2R02
+2 R 0
+
0 2
(2)
+20H
+
0 2
(3)
The similar reaction 2H02
is endothermic by 8
f
4 kcal. and thus is expected t o
(9) We are extending t o polyoxides t h e empirical result t h a t radicalradical reactions in t h e gas phase and in n o n - H ~ b o n d i n gsolvents appear t o have zero activation energy. On this basis t h e activation energies f o r dissociation may be taken to be equal to t h e bond dissociation energies. I n t h e same way, we are also assuming t h a t t h e high frequency factors (10'5 to I O L 6 sec. -') characteristic of first-order peroxide decompositions A lower limit of 1 0 1 4 , 3 are also applicable t o t h e hydrogen polyoxides sec -1 for such A factors is indicated from very conservative transition-state models. An error of +1 power of 10 would introduce a corresponding error of k570in t h e absolute values of t h e ceiling temperatui-es (10) P. A Giguere and I D Liu, C a n J . C h r m , 35, 283 ( 1 9 5 7 ) ; W Forst ibid.,36, 1308 (1958); R R . Baldwin and D. B r a t t e n , Eighth International Symposium o n Combustion, Pasadena, Calif , 1960, Williams and Wilkens C o . , Baltimore, M d . , 1962, p. 110 (11) D . E . Hoare, J B Protheroe, and A D Walsh, Tvans. F a i a d a y Soc , 66, 548 (1959).
SIDNEY W. BENSON
3924
be of negligible importance relative to the rapid disproportionation reaction12,13 2H02
--f
HnO?
+ Oa
(4)
Polyoxide Stability. Trioxides.-The bond dissociation energies for the trioxides, for their lowest energy paths, are all similar and all close to 20 f 6 kcal. In accordance with our earlier conclusions, this would suggest the trioxides as the most reasonable candidates for low temperature isolability. The principal problem would be the method of preparation. In our previous discussion of H ~ O Zit, was ~ pointed out t h a t the addition of H atoms to O3was a very unlikely source because of the great exothermicity of the reaction H
+ 03 --+
HO
+ O2 + 77 kcal.
(5)
It is very unlikely that any H03 will survive the addition of H to 03. Even if a small amount of excited HO3 were thermalized in a solid matrix, we see (Table 11) that i t is unstable with respect to the dissociation into HO O2 by 13 f 6 kcal. and again unlikely to survive for participation in any further radical reactions. These conclusions are very much in accord with the experiences of Giguere and Chin,I4who found t h a t cold, gaseous 0 3 exploded when exposed to H atoms, while solid films gave only HzO2 H20. The alternative radical route to H203 from the crossaddition of HO HOa can be shown to be very unlikely relative to the completing reactions of disproportionation which are known to be very rapid. l 3 However, in the experiments of Czapski and Bielski,’” these arguments must be moderated since they claimed to observe only very small amounts of Hz03,which would in fact be in the range to be expected from the steady-state calculations. They generated H 0 2 in a flow system by exposing 02-saturated H 2 0 to an intense electron beam. Titrating downstream a t various times after irradiation with Fe +?, they observed an oxidizing intermediate
+
+
+
(12) J . H . K n o x a n d C. H. J Wells, Tvans. F a r a d a y Soc , 59, 2786 (19631, have suggested t h a t ( 3 ) can still be i m p o r t a n t in t h e gas-phase oxidation of hydrocarbons a t 360’ if it occurs oto a brief formation of excited HzOa which t h e n goes o n t o decompose v i a reaction 3 with a large frequency factor. Their conclusion is, however, based on false reasoning since t h e rate-limiting process is t h e r a t e of formation of HnOi with t h e necessary 5 kcal. of activation energy. I t does n o t m a t t e r how rapidly t h e excited Hz04 then decomposes. Using values of 10:O I /mole-sec f o r t h e A factors for HzOr formation a n d reaction 4 , t h e l a t t e r will be favored by about 100-fold a t 6,50°K. because of t h e energy requirement for ( 3 ) . We are again assuming t h a t radical-radical reactions in t h e gas phase have zero activation energy 8 This is in a p p a r e n t “not real” contradiction t o t h e observation (ref 19) t h a t in 0.8 S HI SO^ t h e disproportionation of 2H02 has about a 6 ~ k c a l . activation energy I n H-bonded liquids, t h e strength of H bonding is sufficiently great so t h a t a n y change in t h e relative number of H bonds going f r o m solvated species t o transition s t a t e could contribute something I n t h e gas s t a t e or in of t h i s order of magnitude to t h e activation energy nonpolar salt-ents, one would expect such activation energies to vanish. (13) B €I J . Bielski a n d E . S a i t o , J . P h y s C h ~ m, 6 6 , 2266 (1962), reported a r a t e c o n s t a n t 2 . 4 X 106 I.;mole-sec f r o m e s . r . techniques a n d confirmed this ( r e f . 2a) using a titration technique. (1.1) P. A . Giguere a n d U. Chin, J . C h e m . P h y s . , 31, 1685 (1950).
VOl. 86
which decayed by a first-order rate law (at all pH values) to a nonoxidizing species. I t s half-life was a maximum of -2 sec. a t p H 1 to 2 and some 23-fold smaller a t p H 0 or p H 3 . The maximum observed lifetime is compatible with any of the expected limits on D(HO*-OH). The lower limit of 21.5 kcal. would give a lifetime a t 25’ of about 10 sec. In fact, their maximum observed lifetime of 2 sec. puts a lower limit on D(HO2-OH) in solution of about 20 kcal. if indeed this is their species. This estimate is quite independent of the observation that the “observed” H203disappears by an acid-catalyzed mechanism. It simply means that any homolytic process is slower than this observed catalyzed decomposition. In the case of the alkyl trioxides, the energetics of radical addition to 0 3 are equally unfavorable. KO3 is unstable with respect to cleavage into RO O2 by 22 f 8 kcal. and thus a very unlikely intermediate. The radical addition of RO to RO2 is, however, more favorable than in the case of HO HOz since there is only one competing disproportionation for primary or secondary radicals.
+
+
R’zCHO
+ R’zCHO? +R’2CHOzH + K’zCO
(6)
For tertiary radicals, R’$2O and R3C02,however, no fast disproportionation is possible and R203 formation should be favored. From this point of view it seems most likely that the white solid isolated by Milas and Djokic” was more likely t-Bu203than the t-Ru204 which they reported. Their identification was somewhat tenuous in that they reported no data on analysis or stoichiometry, only a descriptive statement concerning the evolution of 02 and t-Bu202 from the solid. However, from their method of production, which involved the formation of large’initial yields of f-Ru202 and 0 2 , it is clear that they must have had large amounts of fBuO radicals as well as L-BUOP~ and i t is very unlikely that with t-Bu202as the major product that the favored t-Bu203will not be formed in considerable excess of any t-BU204. One final comment seems appropriate in reference to the polyoxides, and this concerns their use as rocket fuels. It can be seen from Table I that H203 is not as energetic an oxidizer as O3 or 02. In a similar vein, the more stable CH303CH3is a less energetic oxidizer than O3 or O2 and only slightly more energetic than appropriate O2 C2H6mixtures. Even in the radical series (Table 11) we note that HO3 is a less energetic oxidizer than 03,while HOz is only slightly more energetic than 0 2 . Acknowledgments.-The author wishes to express his appreciation to Dr. David Golden for many interesting discussions on the above subjects.
+
