228
T. W. NEWTONAND F. B. BAKER
or lattice models sometimes give reasonable agreement with experimentally determined quantities, ft cannot be taken as an indication of their validity, since it is to be expected that the properties of a superheated solid will not differ greatly from those of a liquid. In summary, we have proposed a model of liquid water which by using the theory of significant structures has assumed that water is composed primarily of two species: an ice-like component (but we are not imply-
ing that the spatial arrangement is the same as ice) and a freely rotating monomer. The model demonstrates reasonable agreement with experiment. A model successfully applied to one liquid means little, but this model is strengthened since significant structure theory has been applied successfully to so many classes of liquids. Certainly, this is not the final work on water, but it opens up an interesting line of approach.
The Kinetics of the Reaction between Vanadium(I1) and Vanadium(1V)l
by T. W. Newton and F. B. Baker University of California, Los Alamos Scientific Laboratory, Lo8 Alamos, N e w Mexico (Received September SO, 1963)
+
The kinetics of the reaction V(I1) V(1V) = 2V(III) have been studied in acid perchlorate solutions from 0.2 to 2.0 M in HClOd over a temperature range from 0.4 to 34.5' a t p = 2.0 M . The rate law is -d[V(IV)]/di = (Lo k,[H+]) [V(II)][V(IV)]. The L term accounts for nearly all of the rate, and values of AH* and AS* for this path were found to be 12.3 f 0.1 kcal./mole and -16.5 f 0.3 e.u. Chloride ion increases therate slightly while sulfate increases the rate markedly. The effect of ionic strength was studied between 0.2 and. 2.0 M at 25' and is in accord with the extended form of the Debye-Huckel equation.
+
Introduction The kinetics of the reaction between V(I1) and V(1V) have been studied in order to learn the rate law and the thermodynamic quantities of activation for comparison with other oxidation-reductfon reactions. Earlier workers have reported that the reaction is rapid2 or instantaneous. 8 Recently, however, catalytic polarographic currents for the reduction of V(II1) in the presence of V(1V) have been used to estimate the rate of the reaction in sulfate solutions. In the present work it was found that the rate of the reaction in perchlorate solutions is conveniently measurable using spectrophotometric techniques. The reaction proceeds partly by way of a highly colored intermediate which has been identified as a hydrolytic T h e Journal of Physical Chemistry
dimer of V(II1). A study of the properties of this substance will be published elsewhere.6
Experimental
Reagents. V(1V) perchlorate solutions were prepared from V(V) in HC104 by electrolytic reduction at a mercury cathode. Small amounts of V(II1) were (1) Work done under the auspices of the U. S. Atomic Energy Commission. (2) K. V. Krishnamurty and A. C. Wahl, J . Am. Chem. Sac., 80, 6921 (1968). (3) W. R. King, Jr., and C. 5. Garner, J. Phys. Chem., 58, 29 (1964). (4) J. W. Olver and J. W. Ross, Jr., ibid., 66, 1699 (1962). (5) T. W,Newton and F. B. Baker, Inorg. Chem., in press.
229
KINETICSOF REACTION BETWEEN VANADIUM(II) AND VAIVADIUM(IV)
removed by reaction with V(V). The V(V) solutions were prepared by the dissolution of v&, in HClOr. The V(1V) solutions were analyzed by reduction to V(I1) on zinc amalgam, adding an aliquot to excess standard Ce(1V) in 5 M H&04 and back-titrating with standard Fe(I1) to the ferroin end point. The V(I1) solutions were prepared by the reduction of V(1V) on zinc amalgam. All of the V(I1) solutions were protected from air oxidation by means of blankets of argon. The HClO,, LiC104, and NaC104 solutions were prepared and standardized as described previously.6 Procedure. Appropriate amounts of V(II), V(IV), HC104, and salt (LiC104 or NaC1O4) stock solutions were brought to the desired temperature and mixed in special absorption. cells. The solutions and cells were thoroughly swept with argon before use. The cells were either two-chambered for hand mixing or arranged for injection with mechanical stirring. The cells were positioned in a small thermostat in the light beam of the Cary recording spectrophotometer, Model 14. Additiond details have been given in previous a r t i ~ l e s . ~ J The reaction was followed a t 7600 A. where the absorption is due primarily to V(IV). After the final absorbance readings were made, an aliquot of the mixture was added to excess standard Ce(1V) in 6 M HzS04and back-titrated with standard Fe(I1) in order to determine the initial V(I1) concentration. The initial V(1V) concentration was computed from the amount and concentration of the stock solution used. The concentration units used here are moles per liter ( M ) a t 23'. The actual concentrations are slightly different a t different temperatures, for example, being about 1%)higher a t 0". The apparent second-order rate constants were calculated from the absorbance data using the method of least squares described previously.6 Catalytic Impurities. The possibility of catalytic impurities was investigated by comparing the ratec;i obtained using specially prepared reagents with those obtained using the reagents described above. The use of recrystallized VO(C104)2, recrystallized LiC104, or redistilled HC104 gave essentially the same rates as, the use of the ordinary preparations. V(I1) prepared electrolytically gave the same results as that prepared on zinc amalgam. To minimize air oxidation, the V(I1) solutions were transferred using hypodermic syringes; replacing the stainless steel needle with a, glass one was without effect. Stoichiometry. The oxidation potentials of the various vanadium couples in acid solutions are such that the reaction
2H+
+ V+2 + VO+2
=
2Vfa
+ HzO
(1)
goes to completion. V(I1) is unstable with respect to oxidation by H + and both V(I1) and V(II1) can be oxidized by C104-; however, the rates of these reactions are low. It is reported that in HC1 solutions V(J1) is oxidized a t a rate iM-1 min.-'-Obad. Calcd.
+ VO+2 = [VOV+*]*
(4)
and that the two hydrogen ions required for the over-all reaction are acquired after the rate-determining step. The minor term in the rate law, kl[H+], can be due to an additional reaction path with the net activation process
V+2
+ VO+2 + H+
=
[V(OH)V+b]*
(5)
or it might equally well be due to a small medium efTable I11 : Apparent Second-Order Rate Constants a t Various Sulfate Concentrations. Conditions: 4.9 X I O + JZ V ( I I ) , 7.0 x 10-3 M V(IV), 24.8", p 0.8 A4'
-
fect. The t,emperature dependence of the rate has been interpreted under the assumption that both IC0 and kl follow the equationg
k i = ( k B / h ) T exp(ASi*/R) exp( - AHi*/RT) (6) 0.493 ,467 ,364 0 0,250 ,233 ,166 0
0 0.022 ,110 475 0 0.013 ,065 ,241
0 0 0 0.075 0 0 0 0.083
0 299 297 281 ,057 599 539 523 322
0 493 ,493 .*93 ,493 ,735 ,25 ,25 .25
0 0.018 ,091 ,457 0 0.009 ,046 ,232
0
0.004 ,018 093 0 0 004 018 ,093
40.5 73.6 217 732 39.7 70 196 772
a [H+], [HS04-], and [SO,-2] were calculated assuming K , of HS04- to be 0.1 N .
The Journal of Physical Chemistry
A least-squares program was used to find values of AS0*, AHo*, AS1*, and AH1* which minimize the sum of the squares of the per cent deviations between the observed and calculated rate constants at all values of [H+]and temperature simultaneously.6 The results of this calculation are included in Table V. The (9)
S. Glasstone, K. Laidler, and H. Eyring, "The Theory of Rate Processes,'' McGraw-Hill Book Co., Inc., New York, N. Y . , 1941, p . 19G.
KINETICSOF REACTIOK BETWEEN VANADIUM(II) AND VANADIUM(IV)
231
calculated rate constants given in Table I are based on these thermodynamic quantities of activation.
tion that C1- catalyzes the reactions of C O ( N H ~ ) ~ - + ~ with V+2 and with Cr+2, which involve outer-sphere activated complexes,lO and the observation that for inner-sphere activated complexes, C1- enhances trhe rate if it is in the bridging position but has only a Table V : Thermodynamic Quantities of Activation, 25" small effect if it is in a ligand position." Net Sulfate Catalysis. The data in Table I11 show that act. AF*, small amounts of sulfate markedly increase the rate of Reaction procAS, AH*, kcal./ S * o o m ~ ~ e x , a path e68 e.u. kcel./mole mole e.u. reaction between V(I1) and V(1V) and that the rate is essentially independent of [H+] and IHS04-] a t k0 ( 4 ) .-16.5 f 0 . 3 b 1 2 . 3 =t0 . 1 1 7 . 2 -65 kl[H+] ( 5 ) .-31.6 f 6 . 4 9 . 8 f 1 . 8 19.2 -81 constant [S04-2]. The rate was found to be nearly linear in [S04-2]up to concentrations of 0.018 M, but a The formal ionic entropy of the activated complex, a t 0.093 M the rate is somewhat below the line. This S*aomplex = A S * + 2Soreiietants. S n v + 2 was estimated to b'e -23 =t3 and Snv0+a is reported to be -26 f 3 e.u. See M. S. latter deviation is probably due to a small amount LaSalle and J. W. Cobble, J . Phys. Chem., 59, 519 (1955). of sulfate complexing or to the ever possible mediuim The uncertaintics listed are the standard deviations determined effect. These results lead to the conclusion that the by the least-squares program. activation process v+2
Although the values found for AS1* and AH1* arle quite reasonable, it should be re-emphasized that they may not actually apply to net activation process 5 because of medium effects. It has been shown6 that about half of the reaction between V(I1) and V(1V) proceeds by way of the colored intermediate mentioned previously. The most likely mechanism is
+ v0+2 = vov+4 H+ + v0v+4 = v+3+ V O H + ~ v+2
VOH-t2
+ H + = V+3 + HsO (rapid)
(7) (8) (9)
Thus, eel. 4 actually represents the formation of more than one activated complex with the formula [VOV+4] and the activation parameters listed in Table V are average values. Such a possibility is present, of course, in many reactions but is mentioned here specifically because the intermediate is actually detectable. Chloride Catalysis. The small effect of chloride ion, shown in Table 11, is consistent with the equation k' (in Cl-)
=
ko'(1
+ 2.46[C1-1)/(1 + 1.71[C1-1)
(10) where ko' is the rate constant in the absence of chloride ion. This expression suggests that there is a path involving chloride ion as well as a small amount of chloride complexing of one or both of the reactants. On the other hand, some or all of the effect may be due to the change in medium when chloride ion is substituted for perchlorate ion. The srnall effect of chloride observed here is in accord with an inner-sphere activated complex bridged with the vanadyl oxygen. This follows from the observa-
+ VO+2 -t SO4-2
=
[VOV(SO4)+2]* (11)
is important in the presence of S04-2 a t concentrations as low as 0.004 M. This conclusion is contrary to that reached by Olver and ROSS,~ who believe that activation process 4 is predominant even in high sulfate concentrations and that a bisulfate group is present in the activated complex rather than the sulfate group which is indicated in (11). We are unable to follow their arguments since the compositions of their experimental solutions were not given. It is to be noted, however, that the reaction rates determined by the catalytic reduction currents arid those determined directly by spectrophotometry agree fairly well in solutions of the same composition. Olver and Ross found the apparent second-order rate constant to be 10 M-I sec.-l a t 25' in a solution which was 0.4 M H$04 and 0.15 M KaHS04. The fourth solution listed in Table 111 has essentially this same composition; the apparent, second-order rate constant for it was found to be 732 M-l mine-' or 12.2 M - - l set.-'. Ionic Strength Dependence. The data in Table IV can be described satisfactorily by the extended form of the Debye-Huckel equation log k'
=
log ka'
Az'p''' + 1 0.509 + 0.3296p1/2+ BF
(12)
For the LiClO4 solutions ko' = 3.27, 8. = 9.17 k., and B = 0.2 M-l; these parameters reproduce the experimental data with a mean deviation of 1.2% and
(10) A. Zwiokel and H. Taube, J . Am. Chem. Soe., 83, 793 (1961). (11) R. K. Murmann, H. Taube, and F. A. Posey, (bid., 79, 262 (1967).
Volume 68, Number ?2 February, 1964
J. H. SIXFELT
232
a maximum deviation of 2.2%. For the KaClO4 solutions, the corresponding parameters are 3.57 M-l o.2 M - l , deviation, and 4.07’ maximum deviation. The calculated values given in Table IV were obtained using these parameters in eq. 12.12
Acknowledgments. The authors wish to acknowledge many helpful discussions with Dr. C. E. Holley, Jr.,
and especially with Dr. J. F. Lemons, under whose general direction this work was done. (12) NOTEADDED I N PROOF.-A least-squares method for determining the parameters ko’. 8, and B in eq. 12 has been provided by P. McWilliams of the Statistical Section of this laboratory. Results of treating the data in this way are for LiClO, solutions: 3.02 M-‘ min.-l, 8.96 .&., and 0.180 ilk1, and for NrlC104 solutions: 3.06 M-‘inin.-’, 8.82 A., and 0.161 k - l . The data were fitted well within their experimental errors; the mean and maximum deviations were 0 7 and 1.7% for LiClOd and 1.2 and 1.6% for NaClOd.
Kinetics of Ethylene Hydrogenation over Alumina
by J. H. Sinfelt Esso Research and Engineering Company, Linden, N e w Jersey
(Received September 87, 1963’)
The kinetics of hydrogenation of ethylene were studied over alumina in the temperature range 120 to 430”. The rate measurements were made in a flow reactor a t atmospheric pressure using helium as a diluent. The rate of hydrogenation to ethane was found to be first order in hydrogen partial pressure and to vary approximately with the square root of the ethylene partial pressure. The apparent activation energy of the reaction was observed to decrease with increasing temperature. At the lowest temperatures the apparent activation energy mas about 9 kcal./mole, but approached zero at temperatures above about 300’. Possible explanations for the variation in apparent activation energy are discussed. It is suggested that the mechanism of hydrogenation of ethylene over alumina involves reaction of a hydrogen molecule from the gas phase with an adsorbed ethylene molecule.
Alumina has been shown to be a catalyst for the hydrogenation of ethylene a t temperatures in the range of 250 to 600O.1 However, very little information appears to be available on the kinetics of the reaction over alumina, in marked contrast to the situation with metal catalysts, where many investigations have been reported, the results of which have been summarized by Eley2and Bond.3 Although alumina is a very inactive catalyst for the hydrogenat,ion of ethylene when compared with noble metals such as platinum or palladium, a study of the kinetics is still of interest from a mechanistic viewpoint. Furthermore, alumina is widely used as a catalyst or support for a variety of hydrocarbon reactions, many The Journal of Physical Chemistry
of which are carried out in the presence of hydrogen a t conditions where the hydrogenation properties of alumina can have a bearing on the results. For example, in the cracking of hydrocarbons over alumina catalysts, hydrogen pressure has been shown to have a marked effect on the distribution between saturated and unsaturated hydrocarbons in the products, and to have a pronounced effect on the rate of ~ r a c k i n g . ~ ______
(1) V. C. F. Holm and R. W. Blue, I n d . Eng. Chem., 43,501 (1951); 5.G. Hindin and S. W. WelleI, J . Phys. Chem., 6 0 , 1501 (1956).
(2) D. D. Eley, “Catalysis,” Vol. 111, Reinhold Publishing Gorp., New York, N. Y., 1965, pp. 49-77. (3) G. C. Bond, “Catalysis by Metals,” Academic Press, New I’ork, N.Y., 1962, pp. 239-252.
