Product distribution in preparative scale electrolysis

J. Electroanal. Chem., 123 (1981) 231--242 Elsevier Sequoia S.A., Lausanne - - Printed in The Netherlands

PRODUCT

DISTRIBUTION

IN PREPARATIVE

231

SCALE ELECTROLYSIS

PART IV. EC REACTION SCHEMES FOLLOWED BY COMPETITION BETWEEN FIRST-ORDER CHEMICAL REACTION AND FURTHER ELECTRON TRANSFER. ELECTROCATALYTIC SYSTEMS

C. AMATORE, J. PINSON and J.M. SAVEANT Laboratoire d'Electrochimie de l'Universitd de Paris 7, 2, place Jussieu, 75251 Paris Cedex 05 (France) A. THIEBAULT Laboratoire de Chimie Analytique des Milieux Reactionnels Liquides, E.S.P.C.I., 10, rue Vauquelin, 75231 Paris Cedex 05 (France) (Received 6th October 1980)

ABSTRACT The dependence of product distribution on the intrinsic and operational parameters of the system is established for electrochemically catalyzed processes, in which catalysis is in competition with electrode or solution electron transfer leading to an overall two-electron reduction or oxidation of the starting material. The main interest of such relationships is the prediction of the yield and the selection of the best experimental conditions for optimizing the production of the desired product. The extent of the competition between catalysis and electron transfer is also reflected by the apparent number of electrons, which varies between zero and two. Two different potentiostatic electrolysis regimes are considered, in which the substrate is either kept in constant concentration or exhaustively electrolyzed. Two limiting situations are of particular interest, corresponding to an easy characterization of the system. They involve the predominance o f one of the modes of electron transfer, either heterogeneous or homogeneous. The operational parameters have no influence on the course of the competition in the first case, while electrocatalysis is favored by low concentrations and large diffusion layer thickness in the second. The electrochemically catalyzed substitution of 2-chloroquinoline by benzenethioalate in liquid ammonia is discussed as an example of the application of the theoretical relationships.

INTRODUCTION T h e p u r p o s e o f t h e p r e s e n t p a p e r is t o r e l a t e t h e p r o d u c t d i s t r i b u t i o n t o t h e intrinsic (rates) and operational (concentration, diffusion layer thickness) parameters for a reaction scheme, involving a fast and irreversible first-order chemical reaction following the initial electron transfer:

A+ l e ~ B S - kl + C 0022-0728/81/0000--0000/$02.50, © 1981, Elsevier Sequoia S.A:

(0) (1)

232 leading to a species C which undergoes two competitive series of reactions. One of these is a chemical reaction leading to a species, F, which is reoxidized (starting with a reduction process and rereduced when starting with an oxidation process) in the potential range of interest either at the electrode or in the solution. The second is a further reductive (or oxidative respectively) electrode or solution electron transfer to C occurring at a less positive (for a reduction process, negative for an oxidation process) potential than the reduction (or oxidation) of the starting material: C~ F

(2)

C+le~D

(3)

kd

B+C-~A+D

(4)

F~ le~E

(5)

kd

A+F-~B+E

(6)

Under conditions where the C -~ F reaction predominates over the concurrent electron transfers (3) and/or (4), the balance reaction of the overall process is A-+E implying the consumption of a vanishingly small a m o u n t of electricity. In other words, the electrons provided by the electrode then play the role of a catalyst for the A -~ E reaction [ 1]. If the concurrent electron transfers (3) and/or (4) interfere significantly, the number of electrons per molecule will be between zero and two. Coulometry thus appears as a means of gaining mechanistic information for such an electrocatalytic process. Standard electrochemical kinetic techniques such as cyclic voltammetry can also give such information, even in those cases where the B -+ C reaction is so fast that the A/B reversibility cannot be restored by raising the sweep rate [2,3]. The main interest in analyzing product distribution for the present reaction scheme is therefore n o t the establishment of the reaction mechanism, but rather the prediction of the yields and the solution of experimental conditions for optimizing the yield in the desired product, E, in the present case. A typical example of such a competition between electrocatalysis and twoelectron reduction is provided by the electrochemical reduction of aromatic halides in the presence of soft nucleophiles (Nu-) [1--6]. When the reaction is carried out in liquid ammonia, the reaction mechanism exactly fits the above reaction sequence: ArX + 1 e ~ ArX:

(0)

ArX; -+ At" + XAt" + Nu- -+ ArNu"

(1) (k2 = k~lNu-I)

Ar" + 1 e $ AtArX: + Ar" -+ ArX + Ar-

(2) (3) (4)

233 ArNu: -- 1 e ~ ArNu

(5)

ArX + ArNu: -~ ArX: + ArNu

(6)

completed by proton abstraction by Ar- to lead to ArH, since another route to ArH, H-atom abstraction from the solvent by Ar', can be neglected in the case of liquid NH3. Another example is provided by the reduction of aromatic halides in the presence of aliphatic alcoholates as H-atom donor [7]:

(0) (1) (2) (3) (4) (5) (6)

ArX + 1 e ~ ArX" ArX: -* Ar" + XAt" + ~ C H O - -* ArH + ~C--OAt" + l e ~

At-

ArX" + Ar" ~ ArX + Ar~C--O- -- 1 e ~- ~C==O ArX + ~ C - O - ~ ArX; + ~C==O The chemical reaction being catalyzed by the electrons provided by the electrodes is ArX + ~CH--O- -~ ArH + X- + ~C==O

In both cases a complete quantitative analysis of the reaction mechanism has been carried o u t using cyclic voltammetry. Basic assumptions, symbolism, adimensionalization and resolution procedures will be the same as in the preceding papers of this series [8--10]. In particular, it will be assumed in the treatments given below that the chemical reactions occur within a reaction layer, the thickness of which is smaller than the diffusion layer. Since the current can be vanishingly small in cases where the electrocatalytic process predominates, galvanostatic electrolysis regimes do n o t appear suited to the present situation. We will therefore only discuss the cases of constant concentration potentiostatic electrolysis (CCPE) and exhaustive potentiostatic electrolysis (EPE). It is assumed that reactions (4) and (6) have the same second-order rate constant, kd, bearing in mind the frequent cases in which they are both at the diffusion limit. FORMULATION

OF THE PROBLEM

The problem can be formulated in dimensionless terms as a set of differential equations: O
+ ~.daf

d2b/dy 2 = )tlb + Xabc

-- Xdaf

d2c/dy 2 = --Xlb + X2c + XdbC d 2d/dy 2 = --Xd bc

(7)

(8) (9) (10)

234 d 2 e / d y 2 = --)~daf

(11)

d 2 f / d y 2 = --)~2c + ~,daf

(12)

p'
1:

d2a/dy 2 = 0

(13)

d2d/dy 2 = 0

(14)

d:e/dy 2 = 0

(15)

b -= 0,

c-

0,

(16)

f-- 0

F o r b o u n d a r y c o n d i t i o n s see T a b l e 1. T h e p r o b l e m t h e n consists in d e t e r m i n i n g t h e yields in D and E c o r r e s p o n d i n g respectively t o a t w o - e l e c t r o n process and t o a z e r o - e l e c t r o n e l e c t r o c a t a l y t i c process. T h e a p p a r e n t n u m b e r o f e l e c t r o n s will t h e n be related t o yields according to: nap = 2R D = 2(1 - - R E) A d d i t i o n o f eqns. ( 7 ) - - ( 1 2 ) and ( 1 3 ) - - ( 1 6 ) leads to: d2(a + b + c + d + e + f ) / d y 2 = 0 valid f r o m y = 0 to y = 1. It follows that: (dd/dy)w

+ (de/dy)l_

(17)

= --(da/dy)l_

expressing t h a t the overall p r o d u c t i o n o f D and E is equal t o the c o n s u m p t i o n o f A. On t h e o t h e r h a n d it is readily seen t h a t : d2(b + c + f + 2 d ) / d y 2 = 0

TABLE1 Electrolysis regime

EPE

y=0 (r > 0)

a=O,

y-~u'(T > 0)

b ~ 0, d b / d y ~ O, c--*O, dc/dy-~O, and continuity conditions for: a, d, e, da/dy, dd/dy, de/dy

= 1

~r~> O)

CCPE

(da/dy)+(db/dy =0,

(dc/dy) + (dd/dy) = O,

dab/dz

=

--(da/dy)l-

c=O

(de/dy) + (df/dy) = 0,

a b

=

1

(a b= 1 for r =0) ddb/dr =--(dcl/dy)l- , deb/dr =--(de/dY)l- ,

(d b = 0 for r = O) (eb = 0 for r = 0)

f=O

f-~ 0,

df]dy--, 0

235

and thus: (dd/dy)1_ = (1/2)[(db/dy)o -- (dc/dy)o + (df/dy)o]

or alternatively, (de/dy)l_ =--(da/dy)~_ + (1/2)[--(db/dy)o + (dc/dy)o-

(df/dy)o]

(18)

It can be shown that the system and therefore the yields depend upon only two dimensionless parameters: and

o = kl/k2

p = (kdk-~l/2k21)(c°D1/2tS-1)

which are the same as for the reaction schemes discussed in Parts II and III of this series. For CCPE conditions, a set of variable changes appropriate to show that dependence is as follows: a* = ak~ n ,

c* = ckl n,

b* = bk~/2,

f* = f~]/2,

y* = y k ] n

The system to be solved then involves the following differential equations: d2a*/dy .2 = - - ( p / a ) b ' c * + (p/a)a*f*

(19)

d2b*/dy .2 = b* + ( p / a ) b'c* - - (p/o)a*f*

(20)

d2c*/dy .2 = --b* + ( 1 / o ) c * + (p/o)b*c*

(21)

d:f*/dy .2 = - - ( 1 / o ) c * + (p/o)a*f*

(22)

with, as boundary conditions, y* = 0:

(da*/dy*) + (db*/dy*) = 0,

y*-~ ~ :

da*/dy*->l,

b*-* 0,

a* = c* = f* = 0 c*-* 0,

f*-~0

Equation (17) leads to: (ddb/dT) + (deb/dT) = 1 and thus to: db + eb = T

and eqn. (18) to: d e b / d r = 1 + (1/2) [(db*/dy*)o - - (dc*/dy*)o + (df*/dy*)0]

and thus to: e b = T( 1 + ( 1 / 2 ) [ ( d b * / d y * ) o - - ( d c * / d y * ) o + (df*/dy*)0]}

The yields are then obtained from the resolution of the above system according to: E D RCCPE = 1 -- RCCPE = 1 + ( 1 / 2 ) [ ( d b * / d y * ) o - - (dc*/dy*)o + (df*/dy*)0]

Under EPE conditions, a0 is still equal to zero, but the bulk concentration of A decreases exponentially with time: a b = exp(--r)

236 The following f u r t h e r changes of variables are appropriate for taking this into account: a ° = a* exp(r),

b ° = b* exp(r),

f ° = f* exp(T),

pO = P exp(--r)

c ° = c* exp(r)

Then: d 2 a ° / d y .2 = ---(p°/a ) b % ° + ( p ° / o ) a ° f °

d2bO/dy .2 = b ° + ( p ~ / o ) b ° c ~ - - ( p ° / o ) a D f ° d 2 c ° / d y .2 = --b ° + ( 1 / o ) c ~ + ( p ° / a ) b ° c ° d2fO/dy .2 = _ ( 1 / o ) c ° + (p ° / o ) a ° f °

with, as b o u n d a r y conditions, y* = 0:

( d a ° / d y *) + ( d b ~ / d y *) = O,

a ° = c ° = fo = 0

y*-* ~:

(da°/dy *)-.1,

c °-+0,

b ° ~ 0,

fo ~ O

E q u a t i o n (17) n o w leads after t i m e integration to: d b + e b = 1 -- exp(--r) and eqn. (18) to: deb/dr = [exp(--r)] { 1 + ( 1 / 2 ) [ ( d b ~ / d y * ) o - - ( d c ° / d y * ) o + (df°/dy*)0]} and thus to: T

eb = f o

{ 1 + ( 1 / 2 ) [ ( d b ° / d y * ) o - - ( d c ° / d y * ) o + ( d f ° / d y * ) o ] } (~7) e x p ( - ~ ) d1?

The yields are t h e n expressed as: P REEpE = 1 --RDEPE

= (P _ _ p • ) - I

;

R E CCPE(~7) dT?

(23)

pO

showing h o w the yields in EPE c o n d i t i o n s can be derived f r o m those corresponding to CCPE conditions. The exact relationship depends u p o n the electrolysis time and t h u s u p o n the conversion ratio. For ~ -~ 0, i.e. for a very low conversion ratio, pO _, p and thus: R EPE E '-> R CCPE E T h e y will be m a x i m a l l y d i f f e r e n t for c o m p l e t e e x h a u s t i o n of the solution (~ ~ 0, i.e. pO ~ 0). Then: P

RE

= (l/p) f R cpE( )

(24)

0

The p a r a m e t e r p / o -- kd k] 3n governs the t w o - t e r m c o m p e t i t i o n b e t w e e n h o m o g e n e o u s and h e t e r o g e n e o u s electron transfer as discussed previously [8].

237

For ( p / a ) -+ 0, the electrode electron transfers will predominate over the solution electron transfers. For the present problem the three-cornered competition will be then reduced to a two-term competition, electrocatalysis vs. ECE depending upon a single parameter o. Conversely, for (p/o) --* oo the competition will be between electrocatalysis and Disp, depending upon the single parameter p. It is of more interest to investigate these two limiting situations systematically rather than the general case, since the system is much easier to characterize experimentally. E L E C T R O C A T A L Y S I S v s . ECE

The system of eqns. (19)--(22) n o w becomes: d2a*/dy .2 = 0

(25)

d2b*/dy .2 = b*

(26)

d2c*/dy .2 = --b* + (1/o)c*

(27)

d2f */dy*2 = _ ( 1 / o ) c*

(28)

with the same boundary conditions. It follows from eqn. (25) that (da*/dY*)o= 1 and thus (db*/dy*)0 = --1. Integration of eqn. (26) then leads to b* = exp(--y*). On the other hand, addition of eqns. (26)--(28) followed by integration shows that: (df*/dy* )0 = --(db*/dy*)0 -- (dc*/dy*)o Thus, the yield in E can be expressed as E

RccPE = 1 -- (dc*/dy*)o Finally, integration of eqn. (27) leads to: E _ RCCPE1

D -- R CCPE

= (1 +

O1/2)-1

RE

0.5

OO

I

i

- 4

i

j

- 2

i

i

0

i

i

2

i

i

i

logo"

Fig. 1. E l e c t r o c a t a l y t i c - - E C E c o m p e t i t i o n . Yield in the electrocatalytic p r o d u c t and apparent n u m b e r of electrons as functions of the parameter o = k 1/k2.

238

Since the yields are independent of p, application of eqn. (23) immediately shows that: REpE -- RECCPE = (1 + O1/2)-I = 1 -- nap~2 The resulting variations of the yield with kl and k2 are shown in Fig. 1. ELECTROCATALYSIS

vs. D I S P

Since (p/o) -~ oo, homogeneous stationary-state approximation is valid both for C and F: c* = ob*/(1 + pb*),

f* = (1/p)c*/a*

The differential equation system then becomes: d2(a * + b*)/dy .2 = b*

(29)

d2b*/dy .2 = 2pb'2/(1 + pb*)

(30)

In the CCPE case, integration of eqn. (29) leads to: b* dy* = ( d a * / d y * ) y . ~ = 1

(31)

and the yields are given by RECPE = 1 --RDcPE = 1 + (1/2)(db*/dy*)o

The problem is thus entirely defined by eqns. (30) and (31) and by the boundary conditions, y* -~ oo, b* -* 0. A very similar problem has already been solved for another reaction scheme previously analyzed in this series [9] with the same notation; it follows that: E D RccPE = 1 -- RCCPE = 1 --nap/2

= 1 -- (1/2112p)[z~-- 2Z0 + 2 ln(1 + z0)] 1/2

z0 being defined by the following integral equation: z0

21/2p=:

z[z 2-2z

+ 2 1 n ( 1 + z ) ] -~/2dz

0

The resulting variations of R E CCPE are represented in Fig. 2a. In the EPE case the yield in E is immediately obtained as a function of p by application of eqn. (23). Figure 3a shows the variations of REpE in the case of complete exhaustion of the solution [eqn. 24 applied to the REcPE(p) function as calculated above]. DISCUSSION

From the variations of the yields in the two limiting situations, as represented in Figs. 1, 2a and 3a, one can predict the magnitude of the yields when the rates

239 -1

0 v

1

2

r

w

o

I

2

a

1°9e

log e

E E

0.5

0.5

O0

0.0

b log e k2 Disp

X,,,/ A /

Ele~--trOCatI Disp K ElectrocQt.

~

Electrocot./Ece

I

, o

"

Ece

kd'C°

b log e

i j

Electrocat./DisoK ~ t ~ ~

Ece

Electrocat.

I

-5

I

,

0

I

'7

Fig. 2. Constant concentration potentiostatic electrolysis: (a) yield in the electrocatalytic product and apparent number of electrons as functions of the parameter p = ( k d k ~ 1/2 k2 1 ) ×

(c0 D

1/2

a - I ) for the electrocat.--Disp competition; (b) zone diagram (KG: general case).

Fig. 3. Exhaustive potentiostatic electrolysis: (a) yield in the electrocatalytic product and apparent number of electrons as functions of the parameter p = ( k d k ~ 1/2 k'21 )(c ° D 1/2 a -1 ) for the electrocat.mDisp competition; (b) zone diagram (KG: general case). (1--3) Working points representing runs 1, 2 and 3 as shown in Table 2.

of the controlling steps are known and select the best values of the operational parameters c o and 6, to optimize the production of the desired product. Alternatively, these working curves can be used to evaluate rate constants in the same way as discussed in Parts II and III of this series [9,10]. It is noted that the operational parameters have no effect on the competition when electron transfer occurs predominantly at the electrode, reflecting the first-order character of all steps. Conversely, when electron transfer predominantly occurs homogeneously, the yields depend upon the operational parameters. All other factors being kept constant, low concentrations and large diffusion layer thicknesses (low stirring rates) will favor the production of the desired product. The zone diagrams represented in Figs. 2b and 3b, based upon a 5% error in the yield determination, shows h o w one passes from one t y p e of competition

240 to the other as a function of the intrinsic and operational parameters of the system. As expected, an increase of k2 favors the formation of E whatever the type of competition. The effect of k 1 is worth noting. Its increase is the essential factor for passing from a situation where competition is with homogeneous electron transfer to one where competition is with heterogeneous electron transfer. When these last conditions are fulfilled, a further increase of k~ will lower the yield in E. Conversely, for homogeneous electron transfer an increase in k, favors the formation of E. AN EXPERIMENTAL EXAMPLE. THE ELECTROCATALYZED SUBSTITUTION OF 2-CHLOROQUINOLINE BY BENZENETHIOLATE IN LIQUID AMMONIA A cyclic voltammetric study of this system [2,6] has shown that it follows the reaction mechanism depicted by eqns. (0)--(6) as discussed in the Introduction. Within the time and concentration scale of cyclic voltammetry, the system was shown to undergo an electrocat.--Disp type competition for the higher scan rate. A tendency toward an electrocat.--ECE type competition was observed for the lower scan rate, i.e. for the most efficient induction. This trend was demonstrated to be in accordance [ 2] with the value of the cleavage rate constant of the 2-chloroquinoline anion radical in liquid ammonia (kl = 1.7 X 104 s-1 at --40°C). The second-order rate constant for reaction (2) was determined as 1.4 X 10 7 mol -~ 1 s -1. We report here the results of an analysis of product distribution for this system as a function of two operational parameters, the initial 2-chloroquinoline concentration, c °, and the concentration of benzenethiolate, [Nu-]. The electrolysis cell, instrumentation and purification procedures of the solvent have been previously described [ 11,12]. The working electrode was a platinum grid of about 15 cm 2 surface area. The solution was stirred by a magnetic Teflon-coated stirrer. From the time variations of the electrolysis current of 2-chloroquinoline alone, the cell constant was estimated as

DS/6V= 3.9 X 10 -3 s -~ since V = 50 cm 3 and D = 3 × 10 -s cm 2 s-1, it follows that 5 -~ 2.3 X 10 -3 cm. The electrode potential was maintained by a potentiostat (Tacussel PRT, 2 A--20 V) on the plateau of the 2-chloroquinoline reduction wave (E = --1.41 V vs. Ag/0.01 M Ag÷). Electrolysis was pursued until complete exhaustion of the starting material. Identification and titration of the electrolysis product were carried out by gas chromatography (3% OV17 column, flame ionization detector). Thus, reproducibility of the yields was of the order of 2%. The yields were also determined from the number of electrons per molecule at the end of electrolysis which was obtained by current integration (Tacussel IG5 Integrator). The results obtained with different values of the concentration of starting material and nucleophile are given in Table 2. According to the values of 5 and of the rate constants, as determined by cyclic voltammetry, the working points representing the three experiments on the zone diagram (see Fig. 3b), are located in the zone corresponding to the electrocat.--ECE competition, with negligible interference of the solution electron transfers. Analysis of the yields

241 TABLE 2 Run

1 2 3

c°/mM

[Nu-]/M

1.5 2.1 8.9

nap

1.5 x 10 -2 2.6 x 10 -2 0.14

Yield in ArNu/%

0.38 0.27 0.19

o exp

From titration of ArNu

From nap

78 85 90

81 86 91

(1.1 +- 0.6) x 10 -2 (3 +_ 1.0) x 10 -2 (7.0 +_ 2.5) x 10-2

w a s t h e n m a d e in t h e c o n t e x t o f this c o m p e t i t i o n (Fig. 4a), a n d t h e r e s u l t i n g values o f t h e p a r a m e t e r s o, o exp are listed in T a b l e 2. F i g u r e 4 b s h o w s t h a t a exp is p r o p o r t i o n a l t o [ N u - ] -1 w i t h i n e x p e r i m e n t a l u n c e r t a i n t y . T h e s l o p e o f t h e p r o p o r t i o n a l i t y s t r a i g h t line gives t h e v a l u e o f t h e r a t e f a c t o r k lk'2-~ = 0 . 9 5 X 10 -3. Since k l = 1.7 X 104 s -1 [ 6 ] , it f o l l o w s t h a t k~ = 1.8 X 107 mo1-1 l s -1, w h i c h c o m p a r e s s a t i s f a c t o r i l y w i t h t h e value, 1.4 X 107 mo1-1 1 s -1, d e t e r m i n e d I

2 - log ( [ N u ] / i v l )

1,0

R ArNu

0.~

log ,

_~

-I

~)

010

1

. e" e x p

0.05

n

3

U i

i

• 20

I

I

40

I

I

I

I

60

Fig. 4. Electrocatalysis of the substitution of 2-chloroquinoline by benzenethiolate in liquid ammonia at --40°C. (a) Experimental points compared to the theoretical curve (solid line) for an electrocat.--ECE competition; (b) proportionality of the experimental values of o to 1/[Nu-]: yields determined from titration of ArNu (o), and from nap (o).

242

by cyclic voltammetry. This further shows the correctness of the kinetic model developed in the preceding section. ACKNOWLEDGEMENT

This work was supported in part by the C.N.R.S. (A.T.P. "Energie et Mati~res Premieres" 1979. Electrochimie S~lective.) REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12

J.M. Sav6ant, Acc. Chem. Res., 13 (1980) 323. C. Amatore, J.M. Sav6ant and A. Thi6bault, J. Electroanal. Chem., 103 (1979) 303. C. Amatore, J. Pinson, J.M. Sav6ant and A. Thi6bault, J. Electroanal. Chem., 107 (1980) 75. J. Pinson and J.M. Sav6ant, J. Chem. Soc. Chem. Commun., (1974) 933. J. Pinson and J.M. Sav6ant, J. Am. Chem. Soc., 100 (1978) 1506. C. Amatore, J. Chaussard, J. Pinson, J.M, Sav6ant a nd A. Thi6bault, J. Am. Chem. Soe., 101 (1979) 6012. C. Amatore, J. Badoz-Lambling, C. Bonnel-Huyghe, J. Pinson, J.M. Sav6ant and A. Thi~batflt, in preparation. C. Amatore and J.M. Say,ant, J. Electroanal. Chem., 123 (1981) 189. C. A m a t o r e and J.M. Sav6ant, J. Eleetroanal. Chem., 123 (1981) 203. C. Amatore, F. M'Halla and J.M. Sav~ant, J. Electroanal. Chem., 123 (1981) 219. M. Herlem, Bull. Soe. Chim. Fr. (1967) 1687. M. Herlem, J.J. Minet and A. Thi~bault, J. Electroanal. Chem.. 30 (1971) 203.