RICHARD K. WOLFORD
632 and since En(2xa) is of order In 2xa H ( x ) = O ( x In xa)
F,(b)
+ const.
(A71 Since J1(x) has a coefficient of order x 2 , we see that the error in h ( c ) resulting from the replacement of J1(x) by Jl(0) is of order x 3 In %a c3/2 In c and hence permissible within our desired order of approximation. Finally, we consider the asymptotic expansion of the function F ( b ) which appears in (61); it may be written
-
F ( b ) = 2/b
+ (b/4)Fp(b) - MFn(b) - AFp(b) (A8)
where F2(b) is the bracketed quantity in (62))Fn(b) and Fp(b)are the bracketed quantities in (57) and (B),and M and A are given by (22), (24), (30))and (32). Since TI b2e-b/2 and T z b2eb/2,it is easy to see that Fz(b) approaches unity for large values of b. The coefficient M also approaches unity. I n F,(b), the function j,(b) asymptotically behaves like e-b/b and hence becomes negligible compared to In b; hence
-
Vol. 67
-
N
l/b - 1
+ r / 2 + (In b)/2
(A9)
The last term of (A8) is most readily estimated by carrying the e-b of TI inside; ( 1 - T1)in the denominator can safely be approximated by unity for large b. Then
AFp(b)
-
(1
+ b + b 2 / 2 ) [ ( 1 / 2 b ) ( l+ l / b +
+ . . .) - ( 1 + e-b] -b/4 - 1/4 + 1/2b + O(b-2)
2!/b2
(A10)
Combining the asymptotic values of the three functions, the final result is
F(b)
-
3 / 4 - 1?/2 - (In b ) / 2 - 1/2b
-
(All)
For very large values of b
F(b)
-(In b ) / 2
(A 12)
as announced earlier.
KINETICS OF THE ACID-CATALYZED HYDROLYSIS OF ACETAL IS WATERACETONE SOLVENTS AT 15, 85, AND 35' BY RICHARD K. WOLBORD Solution Chemistry Section, National Bureau of Standards, Washington 66, D. C. Received August SO, 1968 Rate constants for the acid-catalyzed hydrolysis of acetal in water-acetone mixtures have been obtained as a function of solvent composition and temperature. The reaction rate passes through a minimum a t an approximately equimolar mixture of water and acetone. The activation energy determined for solutions of the same composition tends to increase as acetone content increases while the activation energy determined for solutions of the same dielectric constant increases as the dielectric constant of the solvent increases.
Introduction There are many examples in the literature of the effect of solvent change on acid-catalyzed hydrolysis reactions of esters,'S2 but the number of such studies dealing with the effect of solvent on acid-catalyzed hydrolysis reactions of acetals has been small.3 The purpose of this investigation, therefore, was to study the effects of solvent change and temperature on the hydrolysis of acetal, CH3CH(OC2H&,in water-acetone mixtures and to compare these results with those obtained for ester hydrolyses by other workers. I n addition, a correlation of the kinetic behavior with other measures of acidity in these mixed solvents has been attempted. The relation between the activation energy a t constant composition and the activation energy a t constant dielectric constant was examined to understand better specific solvation and electrostatic effects. Acetal hydrolysis in aqueous solution is extremely sensitive to hydrogen ion and undergoes specific hydrogen ion c a t a l y ~ i s . ~ The reaction has been studied in amide-water mixtures as a function of temperature and solvent cornpo~ition.~An explanation of the rate be(1) E. Tommila and A. Hella, Ann. Acad. Sci. Fennicae, Ser. A , 11, No. 53, 3 (1954). ( 2 ) H. S. Harned and A. 1LI. Ross, J . Am. Chem. Soc., 63, 1993 (1941). (3) P. Salomaa, Acta Chem. Scand.. 11, 461 (1987). (4) J. N. Bronsted and W. F. K. Wynne-Jones, Trans. Faradag Sac., 28, 59 (1929). (6) R. I AE and on the other side the reverse is true. ' Correlations with Ho.-Braude and Sternginterpreted their results as indicating that the proton affinity of water is greater in aqueous acetone solvents than in pure water and base their arguments on the fact that the quasi-crystalline structure of water is broken down as acetone is added. We have interpolated values of log IC2 from our data a t the compositions a t which Braude (19) Equation 3 is obtained as follows: ikerlof's data may be exprerised a s Do = a exp(-bt) for each solvent mixture, where a and b are constants independent of temperature. Differentiation of this equation and sub. atitution into (2) gives (3).
W. KEITHHALLASD J. A. HASSELL
636
and Stern determined H o for aqueous acetone solutions that were 0.1 M in hydrochloric acid. h plot of log k2 against H , gives a good straight line of slope 0.83. A linear plot of the logarithm of the rate constant against Ho with unit slope has been used for many years as a criterion for an -4-1 mechanism iii comentrated aqueous solutions of mineral acids.l2jZ0 The usefulness of this criterion has been questioned for the past several years, aiid ot,her proposals have been advanced to take its 22 It has been pointed out that the N o concept loses some of its generality as (20) Reference 10, p. 273.
(21) J. F. Bunnett, J . A m . Chem. Soc., 83, 4968 (1961). ( 2 2 ) E. Whalley, Trans. Faraday Soc., 65, 798 (JQ59).
Vol. 67
one goes from aqueous solution to media of lower dielectric constant. 23 This has been demonstrated many times. It appears then that one cannot assign a niechanism to a reaction occurring in mixed solvents on the basis of a rate-Ho correlation. Although the Ha scale has not been established on an absolute basis in aqueous binary solvents or nonaqueous solvents, there are many instancesz4of good correlations of rates with indicator acidities to which the results of this work may be added. (23) B. Gutbezahl and E. Grunwald, J. Am. Chem. Soc., 76, 559 (1953). (24) See, for example, ref. 3 and C. A. Bunton, J. B. Ley, A. J. RhindT u t t , and C. A. Vernon, J. Chem. Soc., 2327 (1957); E. A. Braiide and E. 8. Stern, (bid., 1982 (1948).
MICROCATALYTIC STUDIES OF TILE HYDROGENATION OF ETHYLENE. I. THE PROMOTING EFFECT OF ADSORBED I-IUDROGEN ON THE CATALYTIC ACTIVITY OF METAL SURFACES BY W. KEITHHALLAND J. A. HASSELL Mellon Institute, Pittsburgh, Pa. Received August SO, 196g The enhanced activity of copper-nickel alloy catalysts, brought about by pretreatment with hydrogen, is shown to result from alteration of a surface property; it is not a bulk effect as previously supposed. The activity difference is maintained a t sub-zero reaction temperatures, even in a floving stream of hydrogen. The metals of the first transition series have been surveyed, and it has been found that iron, cobalt, and nickel are poisoned by activated hydrogen chemisorption, while copper and copper-nickel alloys are promoted. Small amounts of oxygen left Rithin the catalysts following reduction do not alter their activities substantially. When hydrogen was substituted for helium as carrying gas, the ortho-para hydrogen conversion could be measured concomitantly and was affected by pretreatment in the same Tvay as the ethylene hydrogenation. The rates of these two reactions were generally correlative, but it was also observed that the 0-p conversion vias catalyzed, rather than poisoned, by the carbonaceous residues left from the hydrogenation. Similar behavior was observed for the Hz-DZ exchange. It was concluded, therefore, that the activity variations result from alterah surfaces tion of the ability of the catalyst t o activate hydrogen. Studies of the interaction of C2Ha ~ i t the did not show a correlation with pretreatment, as C2He was produced only on hydrogen treated surfaces, regardless of the catalyst composition. These results, nevertheless, provide some insight into the situation on the surface during hydrogenation.
Introduction I n earlier workf with a series of copper-nickel alloy catalysts, it was observed that cooling from the reduction temperature (250 or 350’) to the reaction temperature (,- -SOo) in the presence of hydrogen resulted in catalysts from two- to tenfold more active for the hydrogenation of ethylene than were produced when the alloys were outgassed at the reduction temperature and cooled in vacuo or in flowing helium. Further experiments2 showed that the amounts of hydrogen reversibly sorbed (corresponding to the difference in pretreatment) varied somewhat with pretreatment conditions but were many times their BET monolayer equivalents. This work also revealed that the hydrogen, in excess of that adsorbed on the catalyst surface, was in some way associated with small amounts of oxygen (less than 5 atom yo) left trapped within the matrix of the metal following the reduction of the mixed oxides. This knowledge led to the supposition that the oxygen, and/or the hydrogen associated with it, had a controlling influence on the catalytic activity. I n discussing this paper2 a t the Second International Congress on Catalysis, H. S. Taylor suggested that our observations offered an explanation for the well known (1) W. K. Hall and P. H. Emmett, J . Phys. Chem., 6 3 , 1102 (1959). (2) W. K. Hall, F. J. Chesdske, a n d F. E. Lutinski, “Congres International de Catalyse,” 2ieme, Paris. 1960. Aotes. Pans,Editions Teohnip, Vol. 2. 1961, p. 2199.
difference in the behavior of evaporated copper films and bulk copper catalysts. His idea mas that the small amount of oxide dissolved in the metal provided the vacant d-orbitals required for the adsorption of hydrogen. The need for further work to ascertain the relationship of our observations to the basic theory of catalysis was pointed The present work was undertaken with this view and it has been found that the catalytic actix-ity does not depend upon either the small amount of encapsulated oxide or on t‘?e rather large portion of hydrogen associated with it, but only upon that relatively small portion held on the catalyst surface or in solution in the metal. This finding is in accord with our earlier results1 for a pure nickel catalyst, which was poisoned by cooling in hydrogen but which had sufficient hydrogen associated with it to cover only about SO% of its surface. It is also in accord with the recent findings of Gharpurey and Emmett4 that the activity pattern obtained from evaporated copper-nickel alloy films, which were presumably free from oxygen, was substantially the same as that observed for our reduced oxide alloys.1 The phenomenon of chemical promotion has long been known, e.g., the effect of 0.5% K20 added to iron catalysts used for the ammonia synthesis, but it still is (3) P. H. Emmett, ref. 2, Vol. 2, p. 2218. (4) M. K. Gharpurey and P. H. Emmett, J . Phys. Chem., 65, 1182 (1961).
