HYDROLYSIS KIXETICSOF DILUTEAQUEOVSCHROMIUM(III) PERCHLORATE
713
Hydrolysis Kinetics of Dilute Aqueous Chromium(II1) Perchlorate1
by Larry D. Rich, David L. Cole, and Edward M. Eyring2 Department of Chemistry, Unioersity of Utah, Salt Lake City, Utah 8411.9
(Received August $8, 1968)
Dissociation field effect relaxation times in dilute aqueous chromium(II1) perchlorate solutions have been measured and attributed to the hydrolysis equilibrium Cr3+
+ H20
kl
+ H+
CrOH2+ k-l
7.8 X 108 J4-1 sec-l at an ionic strength p Ei 5 X 10-4 M. This kFl is apA t 25' the specific rate k-1 proximately six times smaller than that measured previously for reaction between a proton and A10H2+.
Introduction The aqueous solution chemistry of chromium(II1) has been summarized by Earley and C a n n ~ n . Dilute ~ aqueous solutions of chromium(II1) perchlorate reportedly contain the hydrolysis products CrOH2+and Cr(OH)2+ as well as polymeric species such as Cr2(OH)24+. The water molecules in the first coordination spheres of these species have been omitted in this notation simply for convenience. I n the absence of evidence for complexing of aquated chromium(II1) species by perchlorate, we expect that the major equilibria in acidic, dilute aqueous chromium(II1) perchlorate solutions will be ki
+ HzO Z I Z CrOH2++ H+ ki CrOH2++ HzOZ X Cr(OH)2++ H + Cra+
(1) (2)
ka
2CrOH2+Z Z Crz(OH)24+
(3)
Two of the corresponding equilibrium constants IC1
&= k-1
= [H+][CrOH*+]/[Cr"+]
k-i
= 1.05 X 10-4M
(4)
IC2 K, = -
= [H+][Cr(OH)2+]/[CrOHz+]
AIOHz+
+ H+ ---+
+ H30
A13+
(1) This research was supported by the Directorate of Chemical Sciences, Air Force Office of Scientific Research, Grant AF-AFOSR-
IC-2
=
M
(5)
were determined spectroscopically by Emerson and Graven4for chromium(II1) perchlorate solutions a t 25" and ionic strengths p ranging from 0.01 to 0.05 M . Tsuchiya and Umayahara5 have obtained a conductometric value of K1 = 1.1 X M for aqueous chromium(II1) sulfate at 25' extrapolated to p = 0 in excellent agreement with the K1 of Emerson and Graven.4 A dimerization equilibrium constant
Ka
can be deduced316from the data of Bjerrum' and Finholt.8 In 10-3 M chromium(II1) perchlorate solutions maintained at 30" and ranging in pH from 2 to 3, Postmus and Kingg found no evidence of polymerization after 1.5 years. The very slow polymbrization and depolymerization reactions of aqueous chromium(II1) have also been noted by other w o r k e r ~ . ~ J True ~J~ equilibrium can only be achieved by aging for very long periods or by heating aqueous chromium(II1) solutions well above room temperature. We chose to explore the kinetics of chromium(II1) perchlorate hydrolysis in freshly prepared acidic solutions kept a t 25" or below. Thus the system is clearly out of true equilibrium and the concentration of Crz(OH)24+and higher polymers can be assumed to be negligible. Our immediate goal is to determine the rate constants IC1 and k-1. We wish eventually to correlate values of IC1 us. reciprocal metal ion radii for a large number of isovalent ions. For the present we must content ourselves with a comparison of k-1 for chromium(II1) with a value k-1 = 4.4 x IO9 M-l sec-l found'z for the reaction
k8
=IC-8
= [ C ~ Z ( O I € ) Z ~ + ] / [ C ~ O H ~l o+4]M-1 ~
(6)
476-66. (2) To whom communications should be addressed, (3) J. E. Earley and R. D. Cannon, "Transition Metal Chemistry,"
Vol. 1, R. L. Carlin, Ed., Marcel Dekker, Inc., New York, N. Y . , 1966, p 34 ff. (4) K. Emerson and W. 31. Graven, J. Inorg. NucZ. Chem., 11, 309 (1959). (5) R. Tsuchiya and A. Umayahara, BdZ. Chem. SOC.Jap. 36, 554 (1963). (6) J. I. Morrow and J. Levy, J.Phys. Chem., 72, 885 (1968). (7) N.Bjerrum, "Studier over Basiske Kromiformbindelser," I n a u p ural Dissertation, Copenhagen, 1908. (8) J. Finholt, Thesis, Berkeley, UCRL Report No. 8879 (1960). (9) C. Postmus and E. L. King, J . Phys. Chem., 59, 1208 (1955). (10) J. N. Bronsted and K. Volquartz, 2. Phys. Chem., 134, 97 (1928). (11) H. T. Hall and H. Eyring, J . Amer. Chem. Soc., 72, 782 (1950). (12) L. P. Holmes, D. L. Cole, and E. M. Eyring, J . Phys. Chem., 72, 301 (1968).
Volume 73, Number 3 March 1969
L. D. RICH, D. L. COLE,AND E. M. EYRING
714
Table I : Calculated Molar Concentrations and Experimental Dissociation Field Effect Relaxation Times in Dilute Aqueous Chromium(II1) Perchlorate a t 25’ pHb
c0,a
10-6M
14.86 11.14 9.20 7.43 5.58 3.71 2.23
M,D
Wd
10-4 M
3.984 3.978 3.828 4.210 4.310 4.240 4.638
7.52 5.77 5.30 3.54 2.59 1.89 0.956
0.969 0.972 0.967 0.979 0.981 0.984 0.989
[H+I,e 10-6M
[Cr’+l,f
10.72 10.80 15.35 6.22 4.99 5.84 2.33
7.42 5.58 5.42 2.68 1.73 1.28 0.368
10-6M
[CrOH~+],f [Cr(OH)a+],f 10-5 M M
7.28 5.43 3.70 4.52 3.64 2.31 1.66
1.92 1.44 0.68 2.05 2.06 1.12 2.01
nh
729
paeo
3.74 i 0.41 4.59 i 0.17 3.03 1 0 . 1 7 4.03 i 0.18 4.69 i 0.32 5.26 i 0.41 5.77 =k 0.31
8 8 9 7 6 5 10
a Total molar concentration of chromium(II1) perchlorate. Glass electrode pH of the sample solution. c Ionic strength of the sample solution. Activity coefficient of hydrogen ion calculated from the limiting form of the Debye-Huckel relation. e Molar concentration of hydrogen ion, [H+] = 10-pH/va+. f Molar ionic concentrations calculated from eq 4, 5, and 7 through 10 of the text. Average experimental dissociation field effect relaxation time with standard deviation calculated from the range. * Number of independent determinations of the relaxation time.
in aqueous aluminum(II1) chloride a t 25’ and ionic strength p S 10-3 M . Eigen’s relaxation methods are well suited to kinetic studies of protolytic equilibria such as that in eq 1. The dissociation field effect or electric field jump (Ejump) relaxation methodls permits the ready determination of chemical relaxation times of to sec that we would anticipate for such a monomeric hydrolysis step in lo-^ M aqueous chromium(II1) solutions. Experimental Section
G. F. Smith Co. reagent grade chromium(II1) perchlorate, Cr(C104)s*3H20,was dissolved in distilled, deeminized, boiled water t o yield an approximately 5 X M stock solution. The exact chromium concentration was determined volumetrically : oxidation to dichromate using ammonium persulfate was followed by a titration of the dichromate with ferrous ion, the latter solution having been previously standardized with a primary standard potassium dichromate solution.l4 Sample solutions for the E-jump experiments were prepared by adding small aliquots of this stock solution under a Linde high-purity dry nitrogen atohm-l cm-’ conductivity water premosphere to pared by an electrophoretic ion-exclusion technique.16 The pH of each sample solution was determined with a Beckman 1019 pH meter fitted with 41263 glass and 39071 calomel electrodes. Our E-jump apparatus for conductometric determination of chemical relaxation times resulting from the application of a square, high-voltage wave has been described previously.la, l 7 Our experimental results are summarized in Table I. The concentrations shown were calculated from the measured pH, known total concentration of chromium(II1) denoted hereafter by CO, eq 4 and 5, and the additional equations
+ [CrOH2+]+ [Cr(OH)2+] +(9[Cra+]+ 4[CrOH2+]+ [CI(OH)~+] + 3c0) co = [Cr*+]
p =
The Journal of Physical Chemistry
(7)
(8)
= 0.509.\/II.
(9)
[H+] = 10-PH/yH+
(10)
-log
YH+
The relaxation times T were obtained from the oscilloscope traces by plotting the relative voltage (ordinate) vs. time (abscissa) on semilog paper and drawing a single straight line through the data. I n no case did a photographed oscilloscope trace give rise to multiple slopes in the corresponding semilog plot. Results The available equilibrium data, eq 1-6, and the Smoluchowsky-Debye-Eigen phenomenological equationl* for the limiting values of diff usion-controlled ionic reactions led us to anticipate observing two E-jump relaxation times each of the order of a few microseconds and caused by the coupled monomeric hydrolyses, eq 1 and 2. For instance, let us assume that k-1 = 9 X los M-’ sec-l and Lz = 4 X 109 M-’ sec-l. These specific rates are plausible since they are considerably smaller than the upper limit for the diffusion-controlled reaction rate constants calculated from the Smoluchowsky-Debye-Eigen equation for the general reactions li -1
H+
+ R2+ --+
and Hf
+ B+
k-2 --.+
in water at 2 6 O , and since this phenomenological equation would also predict that k-2 > k - l . Using the equilibrium concentrations calculated for the first (13) M . Eigen and L. De Maeyer, “Technique of Organic Chemistry, Vol. VIII, Part 11, S. L. Friess, E. S. Lewis, and A. Weissberger, Ed., Intersoience Publishers, Inc., New York, N. Y., 1963, p 988 ff. (14) D. A. Skoog and D. M. West, “Fundamentals of Analytical Chemistry,” Holt, Rinehart and Winston, Ino., New York, N. Y., 1963, p 457. (15) W.Haller and H. C. Dueoker, J . Res. Nut. Bur. Stand., A64, 527 (1960). (16) D. T.Rampton, L. P. Holmes, D. L. Cole, R. P. Jensen, and E. M. Eyring, Rev.Sci. Instrum., 38,, 1637 (1967). (17) D. L. Cole, E. M. Eyring, D. T. Rampton, A. Silzars, and R. P. Jensen, J . Phys. C h e w , 71, 2771 (1967). (18) Reference 13, p 1032.
715
HYDROLYSIS KINETICSOF DILUTEAQUEOUSCHROMIUM (111) PERCHLORATE experiment of Table I (ie., [H+] = 1.07 X loA4M , M , [Cr(OH)z+] = 1.92 X [CrOH2+] = 7.28 X 10-6M), kl = Klk-l = 9.45 X lo4 sec-l and kz = K z k z = 1.13 X lo4sec-1, me may calculate from the appropriate expression for the relaxation times 0111
r1,z-1
+
0122
= ____
2
[ f.dl -
4 (allazz - a12aZ1) (a11
where all =
aZl =
= kz
a22)*
+ KF1( [H+] + [CrOH2+]) k-l([H+l + [CrOH2+l)
kl
a12 =
a22
+
(IC2 - k-~[Cr(OH)2+1)
+ k-z([H+I + [Cr(OH)z+I)
(12) (13) (14) (15)
that T~ = 3.93 psec and r 2 = 2.22 psec. There is no serious obstacle to resolving two relaxation times this widely spaced as is evident, for example, from a rate study’g of nickel(I1) diglycine and imidazole complex formation. Thus, the simplest inference to dram from our observation of a single microsecond time range relaxation is that only one protolytic equilibrium is present in these aqueous chromium(II1) perchlorate sample solutions, We can easily provide a tentative identification of this equilibrium by plotting the data of Table I first in terms of the equation ~ 1 - l=
ICI
+
k-1(
[H+]
+ [CrOH2+])
(16)
and then in terms of the equation ~ 2 - l
=
1 % ~3. k-z([H+] I- [Cr(OH)2+1)
(17)
The least-squares straight line through the data plotted in terms of eq 16 has a slope = 7.8 X lo8 M-l sec-I and an intercept kl = 1.4 X lo5. The quotient kl/ = 1.8 X loM4 M is in quite good agreement with K1 = M of eq 4. Equation 17 also gives a good 1.1 x straight line fit of the data with a slope 1%-2 = 1.1 X 10°M-lsec-l and intercept kz = 1.5 X 105sec-l. HowM is in very poor ever, the quotient k2/k-z = 2.4 X agreement with K z = 2.8 X loe6 M of eq 5. Thus we have evidently observed the first monomeric hydrolysis step, eq 1.
Discussion There are actually at least two plausible explanations for our failure to observe a second relaxation time attributable to the second monomeric hydrolysis step of eq 2. It may indeed by true that K z is much smaller than in freshly prepared, dilute aqueous chromium( 111) perchlorate solutions. In this case the correct calculation of kl and kal from the experimental relaxation times requires the iterative solution of K1 = [H+][CrOH2+]/[Cr3+]
+ [CrOH2+] = ‘/2(9[Cr3+] + 4[CrOH2+]+ 3ca) co = [Cr3+]
p
(18) (19) (20)
and eq 9, 10, and 16 starting from K1 = 1.05 X M and rapidly attaining a different, constant value of K1 = k ~ / k - ~ .Since the dominant term in eq 16 is [ H t ] and not [CrOH2+], the constant values 1%1 = 1.4 X lo5sec-l, = 6.7 X lo8 M - l sec-l, and K1 = kl/lc-1 = 2.1 X M obtained from eq 18-20, 9, 10, and 16 in four iterations do not differ significantly from those reported in the preceding paragraph. The other plausible explanation for our observation of one rather than two relaxations in the microsecond time region was suggested by Hammes and Steinfeld.1g-20 For a coupled system of two equilibria, such as eq 1and 2, one of the two normal concentration variables, yij2l proportional to the amplitude of the observed voltage change, is a sum of two large terms in the concentrations, rate constants, reciprocal relaxation times, etc., whereas the other normal concentration variable is equal to a difference of two such terms. Thus the amplitude of the latter relaxation effect could be too small for detection even though both of the coupled chemical equilibria were present in the sample system. Returning now to a discussion of the kinetics of eq 1, it is interesting to compare the previously found12 Ll= 4.4 X 109 M-l sec-l and kl = 4.2 X lo4 sec-l for aluminum(II1) with the present k-1 = 7.8 X los M-l sec-l and kl = 1.4 X lo5 sec-l for chromium(111). Taking the dielectric constant E to be that of bulk solvent, 78.5 for water a t 25”, and assuming an interionic reaction distance u = 7.5 A previously found suitable for diff usion-controlled reactions in water, 22 we calculate from the Smoluchowsky-Debye-Eigen equation‘s that the upper limit of k-l for the reaction H+ M 0 H Z +4 M3+ H20is -2 X 1Olo M - l sec-l. Our experimental 1%-1 values for aluminum(II1) and chromium(II1) both lie comfortably below this limit for diffusion-controlled reaction, but why is k-1 for Cr(II1) only one-sixth that for Al(III)? An explanation might involve either differences in dielectric constant near CrOH2+compared to A10H2+or differences in the distances to which solvent water molecules are highly structured away from these two ions. Differences in both properties for these two ions would arise from differences in ionic radii (for A13+r = 0.50 A and that in turn yield differences in for Cr3+r = 0.69 electrostatic potential gradient near the surfaces of these isovalent ions. Since the reverse reaction
+
+
ki
Cr (H2O)eS+ +Cr (H2O)bOH2+
+ H+
(19) G. G. Hammes and J. I. Steinfeld, J. Amer. Chem. SOC.,84, 4639 (1962). (20) J. I. Steinfeld, B. 8 . Thesis, M.I.T., 1962, pp 51-54. (21) See ref 13, p 908 ff. (22) M. Eigen and L. De Maeyer, Proc. Roy. SOC.,A247, 505 (1958). (23) L. Pauling, “The Nature of the Chemical Bond and the Struc-
ture of Molecules and Crystals,” 3rd ed, Cornell University Press, Ithaca, N. Y . , 1960. Volume 75, Number 8 March 1060
716
A. V. DEO AND I. G. DALLALANA
involves the separation of repulsive charges as well as the migration of a very mobile proton, we are not surprised that kl = 1.4 X lo6 see-l for this reaction is a great deal larger than the 25' first-order rate constant kl* to sec-I reportedz4for the much studied reaction
-
ki*
Cr (HzO)
-+
Cr (HzO)b3+
+ HzO
that bears it a superficial resemblance. The iondipole attractive interaction in this latter reaction as well as the lower mobility of HzOthan H+ could account for a markedly lower kl* than kl. (24) M. Eigen and R. G. Wilkins in "Mechanisms of Inorganic Reactions," Advances in Chemistry Series, No. 49, R. F. Gould, Ed., American Chemical Society, Washington, D. C., 1965, p 64.
An Infrared Study of the Adsorption and Mechanism of Surface Reactions of 1-Propanol on y-Alumina and ?-Alumina Doped with Sodium Hydroxide and Chromium Oxide by A. V. Deo and I. G. Dalla Lana Department of Chemical and Petroleum Engineering, University of Alberta, Edmonton, Alberta, Canada (Received September 9 , 1 9 6 8 )
Infrared studies of the adsorption of 1-propanol on y-alumina and the effect of doping the y-alumina with sodium hydroxide and/or chromium oxide in the temperature range from room temperature to 400" are described. Four different types of surface species were observed : (i) strongly physically hydrogen-bonded propanol to the surface hydroxyl groups; (ii) an ahminum propoxide type structure chemisorbed on Al" ions; (iii) a carboxylate structure in which both surface hydroxyl and A13+ ions are involved; and (iv) a conjugated hydrocarbon species bonded probably to the A13+ ions. Dehydration mainly occurred on the pure y-alumina surface, particularly on the high-frequency hydroxyl groups. On the addition of sodium hydroxide, the dehydration reaction was suppressed and the dehydrogenation reaction became dominant. The addition of chromium oxide apparently creates more dehydrogenating sites. The dehydrogenation possibly proceeds via a mechanism involving both carbonium and carbanion ions. The results are correlated by both infrared spectra and mass spectral analysis of the gaseous products.
Introduction One of the earliest studies of the catalytic dehydrogenation of primary alcohols was reported by Ipatieff in 1936. Komarewsky2 used this method to prepare symmetrical ketones. I n a similar study, with 1propanol as the feed to a fixed-bed reactor using a sodium hydroxide-treated chromia-Alundum catalyst, D a h Lana,3 et al., proposed a chemical model for the multiple reaction sequence. By isolating and identifying chemical intermediates and by examining the chemical reactions of several intermediates under identical conditions, they showed the chemical sequence involved dehydrogenation of the 1-propanol to propionaldehyde followed by parallel condensation of the aldehyde to either its aldol or to propyl propionate under the elevated temperature a t 400". They also encountered some thermal reactions.4 The present paper discusses some mechanistic aspects of this reaction system, obtained by studying the infrared spectra of 1-propanol adsorbed on the catalyst and of the interThe Journal of Physical Chemistry
mediate surface species formed thereof. Some attention is also devoted to the catalytic influence of yalumina on 1-propanol. Infrared spectral studies of the adsorption of primary alcohols on alumina have been previously reported. Babushkin and Uvarov6 studied the adsorption of ethanol on alumina at 20" and found that the alcohol was adsorbed in fragments such as OH, -CH2-CHZ--, and also as an ethoxy group bound directly t o an aluminum atom on the surface, Al-O-CH,-CHZ. (1) V. N. Ipatieff, "Catalytic Reactions at High Pressures and Temperatures," The Macmillan Go., New York, 73. Y., 1936. pp
411-45 1. ( 2 ) V. I. Komarewsky and J. R. Coley, J . Amer. Chem. S O C . ,63, 700,3269 (1941): Advan. Calal., 8, 207 (1956). (3) I. G.Dalla Lana, K. Vasudeva, and D. B. Robinson, J . Catalysis, 6 , 100 (1966). (4) I. G. Dalla Lana, 5. E . Wanke, and A. V. Deo, paper presented
a t the Second Symposium on Catalysis, Hamilton, Ontario, Canada, June 16, 1967. (5) A. A. Babushkin and A. V. Uvarov, Dokl. Akad. N a u k S S S R , 110, 581 (1956).
