Kinetics of the reduction of inorganic ions by borohydride—I ferricyanide

J. Inorg. Nucl. Chem., 1959, Vol. 9, pp. 246 to 251. PergamonPress Ltd. Printed in Northern Ireland

KINETICS

OF THE REDUCTION OF INORGANIC IONS BY BOROHYDRIDE--I

FERRICYANIDE T. FREUND Convair Scientific Research Laboratory, San Diego, California (Received 2 September 1958)

Abstract--The reaction of borohydride with ferricyanide to give borate and ferrocyanide has been studied in buffered aqueous solutions. The rate of disappearance of ferricyanide ion was found to be first order in both borohydride and hydrogen ion and independent of the ferricyanide ion with a normal bimolecular frequency factor of 5"9 x 10n sec-1 and an activation energy of 7"2 kcal. A mechanism is proposed that is consistent with the kinetics of the hydrolysis of borohydride.

THE reactions of borohydride in aqueous solution with various inorganic species have not been extensively investigated. The reactions with iodine, permanganate, hypochlorite have been studied from an analytical standpoint Ill and several other reactions have been surveyed by other workers. ~2) The only inorganic oxidant for borohydride which has been investigated kinetically is water.~3,4~ The over-all stoicheiometry is: BH 4- q- 2H~O = 4H~ -+- BO 2-

(1)

The hexacyanoferrate ions are an attractive choice for oxidation-reduction studies because in both oxidation states they are extremely stable with respect to dissociation and have the same geometry and chemical composition. Furthermore, only a oneelectron transfer is involved. The over-all stoicheiometry involving the hexacyanoferrate ions is: 8 Fe(CN)s 3- q-- BH 4- + 2H20 = 8 Fe(CN)64- + BO2- --k 8H + EXPERIMENTAL

AND

(2)

RESULTS

The kinetic studies were carried out by continuously following the concentration of ferricyanide from its absorption at 415 m ~ with a Beckman spectrophotometer Model DK1 using 1 and 5 cm cells thermostated either with an air or water jacket. Sodium borohydride of 98 per cent purity was recrystallized ~5~ from diglyme* resulting in a product which gave by iodine titration c1~ better than 99 per cent of theoretical reducing capacity. All other substances used were A.C.S. Analytical Reagent grade. Each run was performed both at constant borohydride and constant hydrogen ion concentrations. The borohydride concentration was kept essentially constant by using a large excess. Each run was buffered with either borate-boric acid, carbonate-bicarbonate or sodium hydroxide. The sodium hydroxide concentration was determined by titration with standard acid. The pH * Diglyme has been suggested ~5~as a name for the dimethyl ether of ethylene glycol. tx~ E. H. JENSEN, A Study in Sodium Borohydride. Nyt Fordisk Forlga, Copenhagen, (1954). c2~For summaries see A. C. STEWART. Thesis, Reducing Properties of Sodium Borohydride, University of Chicago (1956); N. G. GAYLORD, Reductions with Complex Metal Hydrides. Interscience, New York (1956). ts~ R. L. PECSOK, J. Amer. Chem. Soc. 75, 2862 (1953). t4~ j. B. BROWN and M. SVENSEN,J. Amer. Chem. Soc. 79, 4241 (1957). c5~H. C. BROWN, E. J. MEAD and B. C. RAO, J. Amer. Chem. Soc. 77, 6029 (1955). 246

Kinetics of the reduction of inorganic ions by borohydride--I

247

before and after a run was measured with a glass electrode and the hydrogen ion concentration was found to change by less than 10 per cent in any given run. Three methods of mixing the reactants were used: (1) adding solid sodium borohydride to a solution containing potassium ferricyanide; (2) adding solid potassium ferricyanide to a solution containing sodium borohydride; (3) mixing two solutions each containing one of the reactants. As long as air was excluded no difference was found by the different mixing techniques. The concentration ranges in moles per litre in these experiments were: initial ferricyanide from 1"5 x 10-4 to 18 x 10-4, borohydride from 1 × 10-3 to 70 x 10-3 and hydrogen ion from 6 x 10-l° to 3 x 10-la. In most of the runs the concentration of ferricyanide was followed until it dropped to less than a tenth of its original concentration. The effect of continuous illumination of the reaction mixture in the spectrophotometer at 415 m/~ was negligible. This was tested three ways: by using 1 and 5 cm cells, by working at different slit widths, and by keeping the reaction cell shutter dosed 95 per cent of the time. Addition of ferrocyanide equal to the initial concentration of ferricyanide had no effect on the rate. Two typical series of runs showing the variation in rate as a function of borohydride ion concentration at constant hydrogen ion are shown in Fig. 1. On Fig. 2 the log of the rate of disappearance of ferricyanide divided by borohydride ion concentration is plotted on the ordinate against pH on the abscissae. The nearly unit slope indicates a first order dependence on hydrogen ion. Fig. 3 shows that the second order over-all rate constants, k, obey an Arrhenius temperature relation with an activation energy of 7"2 kcal, and a frequency factor, A, of 5"9 x 1011 sec-1. The remainder of this section is a description of some nonkinetic experiments which are pertinent to a discussion of the mechanisms of the reaction. Bubbles of gas were observed to form in the reaction solution as the ferricyanide reacted. The bubbles were presumably hydrogen formed from the hydrolysis of borohydride as described by equation (1). Because the side reaction produces hydrogen, the possibility that ferricyanide catalysed the hydrolysis and the stoicheiometry over a wide range of concentration conditions were studied. The possibility of catalysis of the hydrogen producing reaction by ferricyanide during conditions used in the kinetic studies was investigated. Aliquots of solutions in the concentration range used for the kinetic experiments, containing ferricyanide and an excess of borohydride, were analysed over the time range of the kinetic experiments. The JENSENtll iodimetric method for borohydride was modified to give the number of equivalents of borohydride present plus that portion of borohydride that had reacted with ferricyanide. This was done by adding zinc sulphate which insure the completion <6~of the reaction: 2Fe(CN)63- ÷ 21-

,- 2Fe(CN)64- + I2.

(3)

Therefore, the iodine titre gives Lhe difference between the number of equivalents of borohydride and ferricyanide. Since the titre remained constant within experiment error it was concluded that the ferricyanide does not catalyse the decomposition of borohydride. The rate of hydrolysis of borohydride ion has been reported t~ as having the same dependence on the concentrations of hydrogen and borohydride ions which we have found for the rate of disappearance of ferricyanide. This led us to study the competition for borohydride ion by water and ferricyanide. The information gained from these competition experiments will be used in conjunction with the kinetic results to propose a mechanism for the behaviour of the borohydride-ferricyanide aqueous system. Various ratios of ferricyanide to borohydride were prepared in 0"3 N NaOH. To these solutions, weak acids of different strengths were added at different rates while the reaction mixture was rapidly stirred. The hydrogen liberated from the hydrolysis reaction was determined volumetrically and the ferricyanide left was analysed spectrophotometrically. The conditions t6~ of the experiment were such that all the borohydride either reacted with the water or the ferricyanide. Ten experiments were conducted with mole ratios of ferricyanide to borohydride of between 3 and 18 and initial ferrieyanide concentrations from 0'03 to 0"4 M. In all cases the sum of the number of equivalents of hydrogen gas liberated and ferricyanide used up equalled within 3 per cent the initial amount of borohydride. The analyses showed that per mole of borohydride from 2'4 to 3'1 moles of ferricyanide were consumed with the corresponding liberation of 2'9-2'4 moles of H2 gas. Most of the ~6~I. KOL'rI-IOFFand E. SANDELI~,Textbook of Quantitative Analysis p. 624. Macmillan, London (1946).

248

T. F~UND

higher yields of ferricyanide reduction were found when the ratio of ferricyanide to borohydride was high and when the acid was added very slowly. For an interpretation of the kinetics we will consider it necessary that a proposed scheme should be consistent with the disappearance of 2-3 three moles of ferricyanide and the production of 2~-3 moles of hydrogen gas per mole of borohydride consumed. z

k

-30 M/ 0.0098 -20 NoOH/

,

I

12

II

1

-7

U

tt.

0 =E 0 Qc

T

NoOH

0.02

0.04

i

0-06

[BH~I] MOLES / LITER

I0

P

2.--Hydrogen ion dependence: log of rate of disappearance of ferricyanide divided borohydride ion concentration vs. pH.

1.--Rate of disappearance of ferricyanide vs. borohydride concentration. Upper curve at 0.0098 M NaOH, lower curve 0.032 M NaOH.

FIG.

FIG.

7c

i

H

5

E,s % -6 E 3

% x "~

2

i

'~

I/T

X

FIG. 3.--Arrhenius plot: second order rate constant, k, which is the rate of disappearance of ferricyanide divided by the concentrations of hydrogen ion and borohydride ion vs. reciprocal of absolute temperature. DISCUSSION The kinetics show t h a t the a c t i v a t e d c o m p l e x f o r the rate d e t e r m i n i n g step o f b o t h the hydrolysis (in the absence o f ferricyanide) a n d the o x i d a t i o n b y f e r d c y a n i d e is p r o b a b l y the same. Since the rates for b o t h r e a c t i o n s are p r o p o r t i o n a l to the first p o w e r o f b o t h the h y d r o g e n a n d b o r o h y d r i d e ions, it follows t h a t the c h e m i c a l c o m p o s i t i o n o f the activated c o m p l e x is H+BH4 - . F u r t h e r s u p p o r t for the identity o f the activated c o m p l e x c o m e s f r o m t e m p e r a t u r e studies. The over-all a c t i v a t i o n energy f o r the h y d r o l y s i s has been r e p o r t e d (3) to be within a kilocalorie o f the v a l u e

Kinetics of the reductionof inorganicions by borohydride--I

249

obtained in our experiments with ferricyanide. The first step for both reactions is therefore : BH4- + H + . k~ * H + B H 4 - . k-1

(4)

The redox steps following should involve 2 or 3 moles of ferricyanide per mole of borohydride consumed and produced 2~-3 moles of H 2. From the present studies there is no evidence concerning the molecularities involved in these individual radox steps. There is evidence from the hydrolysis of diborane (7) that intermediates of partially hydrolysed boron hydride compounds exist and that these intermediates differ by two electrons in reducing capacity. They have one or more hydride hydrogens replaced by hydroxide groups. A mechanism consistent with these ideas would involve one- or two-electron steps. Illustrated below are possibilities for one of the redox steps in the mechanism. Alternative one- and two-electron oxidations of the boron intermediate which has four equivalents of reducing capacity are given by equations (5-8). Equations (5) and (7) described a one-electron oxidation, by ferricyanide and water respectively, to produce the intermediate BH(OH)s- which has three equivalents of reducing capacity. The two-electron reductions to produce BH(OH)~, which has a two-electron reducing capacity, are described by equations (6) and (8). BH2OH q- Fe(CN)6a - -t- H20 k,F'). BH(OH)2_ q- Fe(CN)64- q- 2H + BHzOH q- 2Fe(CN)63- q- H20 BH2OH q- H20

J¢4F' k4H

(5)

~. q- BH(OH) 2 -}- 2Fe(CN)64- q- 2H + (6) ). BH(OH)~- -~ H q- H +

(7)

k4H'

BH2(OH ) + H20 • BH(OH)~ + H 2 (8) The formulas of the boron intermediates used are primalily intended only to show the reducing capacity of the intermediate. The elemental hydrogen producing reactions probably involve a two-electron transfer. (Complex aluminium hydrides on hydrolysis in heavy water yield HD3a~) * A kinetic scheme consisting of equation (4) followed by consecutive one-electron steps can be used as a basis to explain the experimental results. Each boron intermediate can react with either a ferricyanide or a hydrogen producing species such as water. Let the subscripts of the bimolecular rate constant, k, specify the reactants involved in the elementary step. The letter, i, which can be an integer from 1 to 8, refers to the reducing capacity of the boron intermediate, while "F" represents reaction with ferricyanide and "H" with a species producing hydrogen such as water. Assuming a steady state for each of the eight boron intermediates: kaF[F] q- ksH[H20] --d[Fe(CN)~-3]dt = kl[BH4-][H+] k_ 1 q- ksF[F] q- ksH[H20]

i = 8,7,6,.... 1

k,F[F ] kiF[F ] q- ki~[H20]. "

(9)

• Note added in proof: Analysis of the hydrogen produced from the hydrolysis of our sample of NaBH4 by heavy water was shown to contain over 90 per cent HD. {7~ H. G. WEISS and I. SHAPIRO,J. Amer. Chem. Soc. 75, 1211 (1953); I. SHAPIROand H. G. WEiss, J. Phys. Chem. $7, 219 (1953). is~ I. WENDER, R. A. FR1EDEL and M. ORCHIN, J. Amer. Chem. Soc. 71, 1140 (1949).

250

T. FREUND

Equation (9) consists of eight one-electron terms since each mole of borohydride has eight equivalents. Each term is obtained from the bimolecular rate constant, k~F, times the product of the concentrations of the ferricyanide and the boron intermediate having an ith reducing capacity. The steady state concentration for the first intermediate, BHs, is: kl[BH4-][H+] k_ 1 q- ksF[F] q- ksa[H~O ] "

(10)

The concentration for each succeeding steady intermediate with ith reducing capacity is equal to (ksF[F] q- ksH[H20] t [BHs] (k/F[F ] -q- km[H20]/.

(11)

The general expression, equation (9), will agree with the experimentally observed kinetics (first order each in BH£- and H + and zero order in Fe(CN)e-a) and the observed ratio of reacted ferricyanide to produced hydrogen if three restrictions are imposed. First, two or three of the k~F[F] terms must be large compared to the corresponding km[H20]. Second, the five or six remaining k~r[F] terms must be small compared to the corresponding km[H20] values. The first two restrictions make the summation factor in equation (9) equal to 2-3. Third, ksF[F] + ksa[H~O] must be large compared to k_l. The k_ 1 is probably small since it was found that the experimental over-all rate constant has a normal collision frequency, 6 × 1011. Using these restrictions, equation (9) becomes: --d[Fe(CN)e-a] dt

= kl[BH4- ] [H+] × (constant)

(12)

with the constant having a value between two and three. Therefore, from the measurements on the ferricyanide kinetics, kl, has a frequency factor of between 2 and 3 × 1011see-1 and an activation energy of 7.2 kcal. The essential feature is that any given intermediate reacts only with a hydrogen producing species, or else ferricyanide, i.e. that there be no competition for a given intermediate. The same rate law will exist for a scheme with successive two-electron steps as long as any given ith boron intermediate is attacked either solely by a hydrogen producing species or the ferricyanide. The proposed type of scheme also gives for the hydrogen gas produced which accompanies the reduction of ferricyanide: d[H2] -- kl[BH4-] [H+] × (constant) dt

(13)

with this constant having a value between 2.5 and 3. The ratio of reacted Fe(CN)e-a to produced H 2 should be independent of the initial ratio of ferricyanide to borohydride. This was confirmed experimentally, i.e. a wide variation in initial ratio resulted in a small change in the amount of ferricyanide reduced. Further support for our mechanism is found from the rate measurements of the hydrolysis of borohydride in the absence of ferricyanide. The mechanism for the

Kinetics of the reduction of inorganic ions by borohydride--1

251

hydrolysis may be represented by equation (4) followed by hydrogen-yielding steps of the type given by equations (7) or (8). Then if k_ 1 is small compared to ksrr[H20 ] the proposed mechanism predicts: --d[BH4- ]

dt

-- kl[BH4- ] [n +]

(14)

We have measured the rate of hydrolysis of borohydride in borate buffers and found that our sodium borohydride had a rate constant, k 1, corresponding to a frequency factor 2 × 1011 see -1. This is in agreement with the value determined frgm the kinetic studies with ferricyanide.

Acknowledgement--Many of the experiments were performed with the technical assistance of R. Fox and J. OPDYCr~.