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A model analysis of a membrane-partitioned electrode reactor
The Chemical Engineering
Journal, 47 (1991)
25-32
25
A model analysis of a membrane-partitioned electrode reactor Tsung Min Hung* Department
and Chau Jen Lee?
of Chemical Engineering,
National
Tsing Hua University,
Hsinchu
(Taiwan)
(Received June 14, 1990)
Abstract A model for a reactor has been developed and utilized to investigate the reduction of trivalent europium ions to divalent em-opium in a recirculating system. The reactor consists of a set of flow-through porous electrodes and an anion exchange membrane which divides the reactor into two compartments. The europium chloride catholyte and the ferrous chloride anolyte each flow through their respective compartments. By means of this configuration, the trivalent em-opium ions are continuously reduced to divalent europium in the cathodic compartment; simultaneously, the ferrous ions are oxidized to ferric ions in the anodic compartment. The transient behaviour of the electrochemical system has been analysed both experimentaNy and theoretically. A mathematical model has been formulated to describe the performance characteristics of the system, and the values obtained from the model computation correlate closely with the experimental results.
1. Introduction There has been growing interest in the use, in electrochemical processes, of the flowthrough porous electrode, which provides a very large specific surface area and allows intimate contact between the electrode surface and the electrolyte solution. Many papers have been published in recent years, including review articles [ 11, papers on its application in metal removal [ 21 and work on the chlorine electrode for a zinc-chlorine battery [3, 41. In the electrochemical reduction of europium, inert porous carbon electrodes were first used by Onstott [ 5 1, who claimed that europium ions could be selectively reduced from a lanthanide mixture in a bromide medium by operating a continuous flow system. In order to prevent bromine evolution and to avoid contaminating the electrolytes around each electrode, a membrane-partitioned flow-through porous graphite electrode cell [6] was adapted; the lanthanide chloride catholyte and the ferrous chloride anolyte were respectively introduced into sep*Present address: Institute of Nuclear Energy Research, Lung-Tan, Taiwan. +Author to whom correspondence should be addressed.
arate compartments in order to achieve the desired high reduction rate of europium. Instead of using highly porous graphite .electrodes, two graphite sheets in which a number of holes 1 mm in diameter were drilled were assembled together with an anion exchange membrane to form a redox flow cell [ 71. The trivalent em-opium was reduced in such a redox cell; subsequently, the divalent europium was separated from other trivalent lanthanides by precipitation of europous sulphate. The present work is a study of em-opium reduction carried out in a membrane-partitioned flow-through reactor with porous graphite electrodes in a recirculating mode. The two streams, of europium chloride catholyte and ferrous chloride anolyte, each flow through the corresponding electrode. The reduction rate of the em-opium can be investigated by varying the applied current. In addition, a model of the reactor has been developed to describe the mechanisms of the redox reactions. Theoretical analyses of the performance of flowthrough porous electrodes may be found in some earlier published papers. A one-dimensional model [8, 91 for the flow-through elec-
Elsevier Sequoia, Lausanne
26
trode was developed previously, and this can be used to study certain cases restricted by assumptions concerning limited current. As to predictions of any effect on an electrolytic product, the recirculating mode of operation is more convenient to use in the laboratory. Models of such a recirculating mode have also been developed by several authors [ 10, 111. However, since reduced em-opium is easily reoxidized, especially in the reservoir, the model proposed here has also specifically inchided such a reoxidation reaction in the theoretical analysis.
2. Theory
-
)H,
(1)
EO=O.OO v Eu’+
Eu3’ + e- EO= -0.43
(2)
v
Anode: Fe’+ EO= -0.77
- 1.20-0.059
Fe3+ +e-
(3)
v
If what is required is the cell potential for the redox reaction alone, then the equilibrium form of the Nernst equation may be formulated:
log
[Eu2+I[Fe3’
]
(4)
[Eu3’][Fe2’]
It is obvious that fEu3’] and (Fe”] would decrease while [Eu’+ ] and [Fe3+ ] increase during the process; and the applied voltage must be increased to maintain the driving force to keep the redox reaction proceeding. However, it is undesirable but inevitable that hydrogen evolution will take place simultaneously with europium reduction at the cathode, because the europium is less noble than hydrogen. Divalent europium in aqueous solution is extremely unstable and can easily be photooxidized [ 121 in water: Eu’+(H,O)
2.1. Redox potentials Of the fifteen lanthanide elements, there are only three (samarium, europium and ytterbium) whose valence state may be changed owing to the tendency of their divalent cations to attain or approach the favourable f7 or f14 (halffilled and filled shell) configuration. The M3’/ M2+ redox potentials are - 1.55, - 0.43 and - 1.15 V for samarium, europium and ytterbium respectively. The potential for europium is relatively small compared with those for the other two. Therefore, by applying a moderate potential, divalent em-opium may be obtained exclusively through the electrolysis of trivalent lanthanide mixtures without the formation of divalent samarium or ytterbium. In the electrolytic cell used here, em-opium chloride solution and ferrous chloride solution served as the catholyte and the anolyte respectively. The following electrode reactions may be involved. Cathode: H++e-
E=
250,
Eu3+ +H’+OH-
and it can also be rapidly reoxidized [ 131 in the presence of oxygen: Eu2+ +H+ + 40, -
Eu3+ + fH20
(5)
with acid
(6)
These photochemical and/or chemical electron exchange reactions would indeed increase the complexity of such an electrochemical system. 2.2. Mathematical model The basic assumptions involved in the mathematical model development may be outlined as follows. (1) The porous electrode is considered to be of uniform porosity and specific area throughout. (2) Idealized plug flow exists in the porous electrode. (3) The reservoir is considered to be perfectly mixed. (4) The mass transfer coefficient is constant throughout the reactor. (5) The transport of the reactive ions occurs under convective-diffusion control and hence the supporting electrolyte is assumed to be present in sufficient quantity. (6) The physical properties of the electrolyte remain constant with time. (7) Chemical reaction is considered only in the reservoir, because of the short residence time in the electrolytic cell. During the recycling mode of operation, the reactant concentration C in the porous electrode is a function of both position x and time t. The mass-conservation equation may be written as
27
c
awJ9t> ~ u -w;‘(x, t> +oJ=o ax
at
(7)
where J is the pore-wall flux of reactive species, E is the porosity of the electrode, a is the specific surface area and u is the superficial fluid velocity. Also, referring to the reservoir, the equation for the change of concentration with time is 9-p
act-4 9 at
=C(L,
t)-C(0,
t)+7R
(8)
where R represents the rate of chemical reaction and I-(= V/Q) the residence time. C(L, t) and C(0, t) are the concentrations at the outlet (x=L) and the inlet (z= 0) of the electrode pore respectively. Rigorous analytical solutions for the above equations without the chemical reaction term have been obtained by means of the Laplace transform method [ 10 1. When the volume ratio of reservoir to electrode bed is large, eqn. (7) may be assumed to represent a steady state condition, so that it is possible to obtain a satisfactory approximate solution. Therefore the electrolytic reactor was assumed to be at steady state in the following mathematical manipulation. In the present europium reduction operation, the rate of reoxidation was determined and found to be zero order with respect to divalent europium. The following derivation will be based on zero order reaction for the reaction term in eqn. (8). Two cases are discussed based on the relative magnitude of the applied current I, and the limiting current IL. 2.2.1. Case I: The diffwional
where k, is the mean mass transfer coefficient. By integration of eqn. (lo), the exit concentration at x= L relative to the inlet concentration at 5 = 0 is given as C(L, t) = C(0, t) exp (-%$A) Substituting eqn. (11) into eqn. (8) for a zeroorder reoxidation, the equation is 7
dC(O, t) dt
= - C(0, t)R, + 7k
(12)
where R,=lexp(
- y)
stands for the yield of product in one passage through the pore electrode. By integration of eqn. (12), the concentration of product ions C ’ in the reservoir may be obtained:
C’(O, 0 = C(O, 0)
( 1
_
7k R,C(O, 0)
X[l-exp(
- $1))
(13)
where C ’ is the europium(I1) concentration in the reservoir. The mean current efficiency q over the period between the initial time and the instant t is defined by the following: increase in mass of product species in reservoir q= mass of product species equivalent to electricity consumed (14)
condition
I,>IL. In this case, the applied current I, is always greater than the limiting current I,. however the reactive ions change during the recycling operation. The rate of electroreduction is controlled by diiusion of ions from the bulk solution to the pore wall. So the flux term in eqn. (7) can be represented by
By this definition, the mean efficiency becomes
J = k, C(x, t)
2.2.2. Case U: The electrochemical condition I,
(9)
and, at steady state, eqn. (7) may be rewritten as
dC(x, t> = -km aAC(x, t)
Q
dx
(10)
i=~{cwmg] .{I--exp(
- $t)]
(15)
28
For an electroreduction accompanied by hydrogen evolution, there is a ratio factor f between the effective current and the applied current, which represents the effective conversion, in the desired direction, of the reactive ions. For the sake of model simplification, the factor f is assumed to be independent of time, if the limiting reactant is a minor constituent. This assumption has been tested experimentally and found to be justified, particularly for lower values of the operating flow rate of electrolyte. In view of this, the flux term J can be replaced, following Faraday’s law, and the steady state eqn. (7) becomes u
dC(x, 0 =
--
dx
C(0, tJ=
f&T ___
WR,
Using eqns. (19) and (22), the value of t, can be obtained from the initial concentration and from the operating conditions:
Once the operation time goes beyond t,, the current 1, becomes larger than the limiting current& and the electrolysis reaction is shifted into the diffusional condition. Therefore the model developed as Case I holds; it gives
(17)
where Q is the recycling flow rate. Substituting C(L, t) from eqn. (17) into eqn. (8), the performance equation for a zero-order reoxidation in the reservoir becomes
(18) where k is the rate constant. Integration of eqn. (18) leads to a solution for the variation with time of the product ion concentration: 1
f&-k WA 01 ( FJ7
where
(16)
, t) =C(O , t) - fA FQ
C’(O, t> -=____ C(O, 0)
(22)
(23)
fr, FAL
where F is Faraday’s constant. The exit concentration in the electrolyte C(L, t) is obtained by integrating eqn. (16): C(L
pressed as
t )
C(O,t)=
g
+(G(O,t,)-
Xexp{
- :
g}
(t-t,)}
By taking eqns. (22) and (23) into account, the concentration C’ in the reservoir and the mean current efficiency become C’(O, t> =l_ C(O,O)
+c R,C(O, 6)
(19)
Following the definition in eqn. (14), the mean current efficiency becomes
7j=
C’(0,
t)Fv
It
(20)
a
(25)
By taking eqn. (19) into account, the mean current efficiency (less than unity) can also be expressed as
fjzf-
F
(21) a
During the progress of the reaction, 1, decreases and should become (for a critical time) smaller than the operating current 1,. At the critical point C(0, t,), t, at which the applied current 1, is equal to the limiting current, the yield of product in one passage may be ex-
(26) which are valid for t > t,.
29
3. Experimental procedure
apparatus
maximum reaction rate at the front and to minimize the overall ohmic potential drop in the solution. The catholyte was composed of lanthanide chloride solution, and the anolyte of ferrous chloride solution. Both streams were pumped and recycled with an FM1 metering pump. The flow rates were measured using microflowmeters. The electrolyte leaving the cell was recycled to a reservoir of volume 0.3 1, which was maintained as a well-mixed tank by using a magnetic stirrer. The cathodic chamber, reservoir and polyethylene connecting tube were darkened with oily black paper to prevent reoxidation of reduced europium. In addition, argon was used to purge the catholyte reservoir and so to maintain an oxygen-free environment. The combination pH electrode immersed in the catholyte reservoir was used to monitor and record the pH variation. Before each run, 300 ml of 0.1 M hydrochloric acid followed by deionized water were allowed to flow through the cell. After that, the water residue was rinsed
and
A schematic diagram of the recirculating system for reducing europium in a flow-through porous graphite electrode cell is shown in Fig. 1. The porous electrodes were machined from a block of EG-NPL (Nippon Carbon Co.) graphite. Each electrode was 5 mm thick, with 88 cm2 of apparent surface area coming into contact with the electrolyte. Two graphite electrodes were clamped together in two acrylic frames, between which was an anion-exchange membrane (IONAC MA-3475, Sybron Co.) dividing the cell into two compartments. A rubber gasket, 4 mm thick, swathed with Teflon sealing tape, was placed between the membrane and the electrode plate. The space on the acrylic frame side was filled with glass beads, 2.4 mm in diameter, to reduce the hold-up volume. The electrolyte streams flowed separately from the front face in order to produce the aAnion
exchange membrane
aGraphite
electrode
aAcrylic
frame
@Gasket
& spacer
@Ar-purging
tube
1. Schematic diagram of electrolytic
@pH
electrode
aMagnetic
stirrer set
@Metering
pump
@Fl
ow meter
0 o Glass
reduction
bead
of europium in recirculation
mode.
30
out with a solution containing the electrolytes to be used in the test. The cathodic solution was saturated with argon each time before use. In this investigation, the anodic feed solution contained exclusively 0.3 M ferrous chloride in 0.3 N hydrochloric acid solution. The electrolysis proceeded at room temperature (cu. 299 K) galvanostatically, using a d.c. power supply. During the time course of the redox reaction, the concentrations of Eu2+ and Fe2 + were analysed by the Ce4 + titration method with Ferroin as the indicator.
4. Results and discussion 4.1. Reoxidation of divaknt europium Divalent europium is readily oxidized photochemically and in acid as mentioned above. Some change from europium(II) to europium(II1) was detected, although preventive measures had been taken during our experiments. After the end of electrolysis experiment, the catholyte in the reservoir was kept purged with argon and stirred continuously with a magnetic bar, and the pH was adjusted to about 2. It was observed that the concentration of europium(I1) was depleted linearly with time and the pH value changed from 1.6 to 4.5 within about two hours. As shown in Fig. 2, an average value of the rate constant equal to 1.486~10~6mo11-‘s-‘wasobtai.nedbylinear regression with four sets of measurements. From this observation it was inferred that the order of the reaction in the reservoir was zero during the recirculating operation.
4.2. Electroreduction of europium During the redox reaction, the pH value of the catholyte slowly increased. During the final stage of the operation, the pH value rose steeply to 6 and the reduction reaction was rendered ineffective. The hydroxide which formed at this high pH value fouled the electrode pores and the reactor became inoperable. Thus a high pH value must be avoided during the operation of this electrochemical system. Figure 3 shows the relationship between the europium(I1) concentration and time in the cathodic reservoir with different applied currents. A linear relationship appeared only during a short period of time at the beginning of the measurement using 0.5 A, which indicates that the reduction reaction was proceeding under the electrochemical conditions described in Section 2.2.2. as Case II. A current of 0.175 A is ideally sufficient, in terms of electric charge, to obtain a complete conversion to europium(II). This means that the effective current ratio distributed to europium reduction is about 0.35 for such electrochemical conditions. As shown in Fig. 3, a higher ratio of europium(I1) to total europium ions was obtained when a higher current was applied. With both 0.75 A and 1 .OA, the same quantity of europium was reduced with the same quantity of integrated electric charge. This implies that a higher current efficiency can be achieved when a higher current is applied, but only up to 0.75
4 al-
,,,.
1.1
N
ZE . N
I-’
0
‘;;
$
l
1.0
A
.
0.75 fl A 0.6 A 0 0.5 A 0
Klc
&I-
d;NmIJ6<*em
,“ 1;
D’ ,Q I /
l.D-
_-*-
/d
,HG
/’
,K
/ ‘A
__-<
--*
0 p_-” cc -‘6 AA *--
,/doeo
,,/
_.-
__--
0
X0
A
, e ’ t
Li ’
0.5.
----
&t
Id
curve
fitting
with
eq.(l3>
l2D
150
1
”
0.
0
I
2
Time Fig. 2. Relationship between time.
3
xIOb3.
4
6
0
7
set
europium(I1) reoxidation and
0
30
m
al
la0
210
Time. min Fig. 3. Effect of applied current on europium reduction. Initial catholyte: total lanthanide, 0.465 M; europium(III), 0.05 M; pH=l; Q=20 ml min-‘.
31
0 0.75 A A 0.6 fl 0 0.5 A
IO0)
0
Fig.
-y-
JI
Thyret;
m
,
,
,
,
90
la3
150
lm
210
Time.
min
4. Mean current efficiency VS. time during recircu-
lation.
A. Thus an applied current of 0.75 A may be considered as an optimal value. This effect on the current efficiency would be clearly exhibited if a plot of overall mean current efficiency 2)s. [Eun]/[EuT] ratio was drawn. During the recycling operation, the electrode potential progressively decreased, while the [ Eu’] /[EuT] ratio and the pH value of the catholyte increased. Hence the efficiency decreased with time as shown in Fig. 4. In contrast with the no-gas-evolution electrode, a higher current efficiency was obtained when a higher current was applied, and this was larger than that corresponding to the limiting current in the europium reduction system, when there was hydrogen evolution. The higher current efficiency with a higher applied current may be explained by the fact that the overpotential for europium relative to hydrogen is less significant with a high current than with a low current. With hydrogen evolution at an
electrode, however, gas bubbles substantially reduced the active electrode area, and hence the pore electrolyte resistance was increased. This could result in the absence of any further increase in the current efficiency when the applied current was raised yet higher (as when 1.O A was applied). As a first approximation, the apparent overall mass transfer coefficient k, ( = k,a) was estimated from eqn. (13) by curve-fitting with the experimental data given in Fig. 3. The value of k, may also be calculated theoretically from experimental data on the conversion factor R, for a single pass through a pore in an electrode. The values of k, obtained from singlepass experiments compared with the values obtained by curve fitting (shown in Fig. 3) are listed in Table 1. It seems reasonable that the values from data fitting are smaller (about - lo%), because these stand for the average from the whole range of operation. Based on the values of the rate constants k and k, which were obtained from curve fitting in Fig. 3, the variation with time of the overall mean current efficiency could also be calculated. Figure 4 gives a comparison between the experimental and calculated values; the dashed lines l-4 correspond to the respective values of the current as indicated, which range from 1.0 down to 0.5 A. It can be seen that the calculated values are smaller than the experimental values at the initial stage, but become larger towards the final stage. These results indicate that the mass transfer coefficient decreases progressively with time, presumably owing to the generation of hydrogen.
5. Conclusion A membrane-partitioned flow-through porous graphite electrode reactor, designed for
TABLE 1. Comparison of experiment and calculation for k, values Applied current (AI 0.5 0.6 0.75 1.0
Experiment
Model fitting
&
K. (s-l)
Rt
K. @-‘I
0.115 0.155 0.210 0.270
9.255 x 1o-4 1.276x 1O-3 1.786X1O-3 2.384 x 1O-3
0.109 0.144 0.195 0.242
8.743X 1.178~ 1.643X 2.099 x
10-d 1O-3 1O-3 1o-3
32
the study of europium reduction kinetics, has been experimentally and theoretically examined. Preliminary operational runs with the system which has been designed suggest that it will be an effective system for extraction and purification of em-opium from a mixture of lanthanides. A theoretical model which specifically considered the reoxidation of europium(I1) produced a good description of the transient performance characteristics of the system. The model computations compare closely with the experimental results.
Acknowledgment
Appendix
a A
C(x, t>
,“I, f F
I.% 4. J
Financial support in part through Grant NSC77-0402-E007-17, from the National Science Council of Taiwan, is gratefully acknowledged.
k
A: Nomenclature specific surface area of the electrode (cm’ cmm3) geometrical cross-sectional area of the electrode (cm2) reactant concentration at electrode position x and instant time t (mol cmp3) product concentration (mol cm-“) electrode potential (V) ratio factor Faraday’s constant (96487 C mol-‘) applied cell current (A) limiting current (A) mass flux from bulk electrolyte to electrode (mol cmp2 s-i) rate constant for the zero-order reaction (mol cmp3 s-i) apparent mass transfer coefficient,
k,a (s-l) km L
Q R
7
9 10
13
J. Newman and W. Tiedemann, Adv. Ekctrochem. Ekctrochem. Eng., II (1978) 353-438. K. Kusakabe, H. Nishida, S. Morooka and Y. Kato, J. Ap~l. Ekctrochem., 16 (1986) 121-126. E. Roayaie and J. Jorne, J. Electrochem. Sot., 132 (1985) 1273-1276. J. Jome and E. Roayaie, J. Ekctrochem. Sot., I33 (1986) 696-701. E. I. Onstott, U.S. Patent 3,616,326, 1971. S. J. Dong, Z. X. Li, G. B. Tang, X. L. Zhao, X. Z. Cui and X. W. Yan, Hua Hsueh Tung Pao, 5 (1980) 285-288. D. Lu, Y. W. Miao and C. P. Tung, Sep. Froc. Hgdnnnetall., 41 (1987) 428-436. D. N. Bennion and J. Newman, J. Appl. Electrochem., 2 (1972) 113-122. J. A. Trainham and J. Newman, J. Electrochenz. Sot., 124 (1977) 1528-1540. A. T. S. Walker and A. A. Wragg, Electrochim. Acta, 22 (1977) 1129-l 134. M. Enriquez-Granados, G. Valentin and A. Storck, Electrochim. Acta, 28 (1983) 1407-1414. T. Donohue, Opt. Eng., I8 (1979) 181-186. C. T. Stubblefield and L. Eyring, J. Am. Chem. Sot., 77 (1955) 3004-3005.
Rt t U V X
mass transfer coefficient (cm s- ‘) electrode thickness (cm) flow rate of electrolyte (cm3 s-i) chemical reaction rate (mol cmp3 s-i> conversion factor, R,= 1 - exp( -
k,~/Q)
instant time (s) electrolyte flow velocity, u = Q/A (cm s- ‘) volume of reservoir (cm3) geometrical location of the electrode
Greek symbols E porosity of the electrode overall mean current efficiency; deii fined in eqn. (14) 7 residence time, V/Q (s) Subsctipt
i
initial state
Superscept
T
total europium
Journal, 47 (1991)
25-32
25
A model analysis of a membrane-partitioned electrode reactor Tsung Min Hung* Department
and Chau Jen Lee?
of Chemical Engineering,
National
Tsing Hua University,
Hsinchu
(Taiwan)
(Received June 14, 1990)
Abstract A model for a reactor has been developed and utilized to investigate the reduction of trivalent europium ions to divalent em-opium in a recirculating system. The reactor consists of a set of flow-through porous electrodes and an anion exchange membrane which divides the reactor into two compartments. The europium chloride catholyte and the ferrous chloride anolyte each flow through their respective compartments. By means of this configuration, the trivalent em-opium ions are continuously reduced to divalent europium in the cathodic compartment; simultaneously, the ferrous ions are oxidized to ferric ions in the anodic compartment. The transient behaviour of the electrochemical system has been analysed both experimentaNy and theoretically. A mathematical model has been formulated to describe the performance characteristics of the system, and the values obtained from the model computation correlate closely with the experimental results.
1. Introduction There has been growing interest in the use, in electrochemical processes, of the flowthrough porous electrode, which provides a very large specific surface area and allows intimate contact between the electrode surface and the electrolyte solution. Many papers have been published in recent years, including review articles [ 11, papers on its application in metal removal [ 21 and work on the chlorine electrode for a zinc-chlorine battery [3, 41. In the electrochemical reduction of europium, inert porous carbon electrodes were first used by Onstott [ 5 1, who claimed that europium ions could be selectively reduced from a lanthanide mixture in a bromide medium by operating a continuous flow system. In order to prevent bromine evolution and to avoid contaminating the electrolytes around each electrode, a membrane-partitioned flow-through porous graphite electrode cell [6] was adapted; the lanthanide chloride catholyte and the ferrous chloride anolyte were respectively introduced into sep*Present address: Institute of Nuclear Energy Research, Lung-Tan, Taiwan. +Author to whom correspondence should be addressed.
arate compartments in order to achieve the desired high reduction rate of europium. Instead of using highly porous graphite .electrodes, two graphite sheets in which a number of holes 1 mm in diameter were drilled were assembled together with an anion exchange membrane to form a redox flow cell [ 71. The trivalent em-opium was reduced in such a redox cell; subsequently, the divalent europium was separated from other trivalent lanthanides by precipitation of europous sulphate. The present work is a study of em-opium reduction carried out in a membrane-partitioned flow-through reactor with porous graphite electrodes in a recirculating mode. The two streams, of europium chloride catholyte and ferrous chloride anolyte, each flow through the corresponding electrode. The reduction rate of the em-opium can be investigated by varying the applied current. In addition, a model of the reactor has been developed to describe the mechanisms of the redox reactions. Theoretical analyses of the performance of flowthrough porous electrodes may be found in some earlier published papers. A one-dimensional model [8, 91 for the flow-through elec-
Elsevier Sequoia, Lausanne
26
trode was developed previously, and this can be used to study certain cases restricted by assumptions concerning limited current. As to predictions of any effect on an electrolytic product, the recirculating mode of operation is more convenient to use in the laboratory. Models of such a recirculating mode have also been developed by several authors [ 10, 111. However, since reduced em-opium is easily reoxidized, especially in the reservoir, the model proposed here has also specifically inchided such a reoxidation reaction in the theoretical analysis.
2. Theory
-
)H,
(1)
EO=O.OO v Eu’+
Eu3’ + e- EO= -0.43
(2)
v
Anode: Fe’+ EO= -0.77
- 1.20-0.059
Fe3+ +e-
(3)
v
If what is required is the cell potential for the redox reaction alone, then the equilibrium form of the Nernst equation may be formulated:
log
[Eu2+I[Fe3’
]
(4)
[Eu3’][Fe2’]
It is obvious that fEu3’] and (Fe”] would decrease while [Eu’+ ] and [Fe3+ ] increase during the process; and the applied voltage must be increased to maintain the driving force to keep the redox reaction proceeding. However, it is undesirable but inevitable that hydrogen evolution will take place simultaneously with europium reduction at the cathode, because the europium is less noble than hydrogen. Divalent europium in aqueous solution is extremely unstable and can easily be photooxidized [ 121 in water: Eu’+(H,O)
2.1. Redox potentials Of the fifteen lanthanide elements, there are only three (samarium, europium and ytterbium) whose valence state may be changed owing to the tendency of their divalent cations to attain or approach the favourable f7 or f14 (halffilled and filled shell) configuration. The M3’/ M2+ redox potentials are - 1.55, - 0.43 and - 1.15 V for samarium, europium and ytterbium respectively. The potential for europium is relatively small compared with those for the other two. Therefore, by applying a moderate potential, divalent em-opium may be obtained exclusively through the electrolysis of trivalent lanthanide mixtures without the formation of divalent samarium or ytterbium. In the electrolytic cell used here, em-opium chloride solution and ferrous chloride solution served as the catholyte and the anolyte respectively. The following electrode reactions may be involved. Cathode: H++e-
E=
250,
Eu3+ +H’+OH-
and it can also be rapidly reoxidized [ 131 in the presence of oxygen: Eu2+ +H+ + 40, -
Eu3+ + fH20
(5)
with acid
(6)
These photochemical and/or chemical electron exchange reactions would indeed increase the complexity of such an electrochemical system. 2.2. Mathematical model The basic assumptions involved in the mathematical model development may be outlined as follows. (1) The porous electrode is considered to be of uniform porosity and specific area throughout. (2) Idealized plug flow exists in the porous electrode. (3) The reservoir is considered to be perfectly mixed. (4) The mass transfer coefficient is constant throughout the reactor. (5) The transport of the reactive ions occurs under convective-diffusion control and hence the supporting electrolyte is assumed to be present in sufficient quantity. (6) The physical properties of the electrolyte remain constant with time. (7) Chemical reaction is considered only in the reservoir, because of the short residence time in the electrolytic cell. During the recycling mode of operation, the reactant concentration C in the porous electrode is a function of both position x and time t. The mass-conservation equation may be written as
27
c
awJ9t> ~ u -w;‘(x, t> +oJ=o ax
at
(7)
where J is the pore-wall flux of reactive species, E is the porosity of the electrode, a is the specific surface area and u is the superficial fluid velocity. Also, referring to the reservoir, the equation for the change of concentration with time is 9-p
act-4 9 at
=C(L,
t)-C(0,
t)+7R
(8)
where R represents the rate of chemical reaction and I-(= V/Q) the residence time. C(L, t) and C(0, t) are the concentrations at the outlet (x=L) and the inlet (z= 0) of the electrode pore respectively. Rigorous analytical solutions for the above equations without the chemical reaction term have been obtained by means of the Laplace transform method [ 10 1. When the volume ratio of reservoir to electrode bed is large, eqn. (7) may be assumed to represent a steady state condition, so that it is possible to obtain a satisfactory approximate solution. Therefore the electrolytic reactor was assumed to be at steady state in the following mathematical manipulation. In the present europium reduction operation, the rate of reoxidation was determined and found to be zero order with respect to divalent europium. The following derivation will be based on zero order reaction for the reaction term in eqn. (8). Two cases are discussed based on the relative magnitude of the applied current I, and the limiting current IL. 2.2.1. Case I: The diffwional
where k, is the mean mass transfer coefficient. By integration of eqn. (lo), the exit concentration at x= L relative to the inlet concentration at 5 = 0 is given as C(L, t) = C(0, t) exp (-%$A) Substituting eqn. (11) into eqn. (8) for a zeroorder reoxidation, the equation is 7
dC(O, t) dt
= - C(0, t)R, + 7k
(12)
where R,=lexp(
- y)
stands for the yield of product in one passage through the pore electrode. By integration of eqn. (12), the concentration of product ions C ’ in the reservoir may be obtained:
C’(O, 0 = C(O, 0)
( 1
_
7k R,C(O, 0)
X[l-exp(
- $1))
(13)
where C ’ is the europium(I1) concentration in the reservoir. The mean current efficiency q over the period between the initial time and the instant t is defined by the following: increase in mass of product species in reservoir q= mass of product species equivalent to electricity consumed (14)
condition
I,>IL. In this case, the applied current I, is always greater than the limiting current I,. however the reactive ions change during the recycling operation. The rate of electroreduction is controlled by diiusion of ions from the bulk solution to the pore wall. So the flux term in eqn. (7) can be represented by
By this definition, the mean efficiency becomes
J = k, C(x, t)
2.2.2. Case U: The electrochemical condition I,
(9)
and, at steady state, eqn. (7) may be rewritten as
dC(x, t> = -km aAC(x, t)
Q
dx
(10)
i=~{cwmg] .{I--exp(
- $t)]
(15)
28
For an electroreduction accompanied by hydrogen evolution, there is a ratio factor f between the effective current and the applied current, which represents the effective conversion, in the desired direction, of the reactive ions. For the sake of model simplification, the factor f is assumed to be independent of time, if the limiting reactant is a minor constituent. This assumption has been tested experimentally and found to be justified, particularly for lower values of the operating flow rate of electrolyte. In view of this, the flux term J can be replaced, following Faraday’s law, and the steady state eqn. (7) becomes u
dC(x, 0 =
--
dx
C(0, tJ=
f&T ___
WR,
Using eqns. (19) and (22), the value of t, can be obtained from the initial concentration and from the operating conditions:
Once the operation time goes beyond t,, the current 1, becomes larger than the limiting current& and the electrolysis reaction is shifted into the diffusional condition. Therefore the model developed as Case I holds; it gives
(17)
where Q is the recycling flow rate. Substituting C(L, t) from eqn. (17) into eqn. (8), the performance equation for a zero-order reoxidation in the reservoir becomes
(18) where k is the rate constant. Integration of eqn. (18) leads to a solution for the variation with time of the product ion concentration: 1
f&-k WA 01 ( FJ7
where
(16)
, t) =C(O , t) - fA FQ
C’(O, t> -=____ C(O, 0)
(22)
(23)
fr, FAL
where F is Faraday’s constant. The exit concentration in the electrolyte C(L, t) is obtained by integrating eqn. (16): C(L
pressed as
t )
C(O,t)=
g
+(G(O,t,)-
Xexp{
- :
g}
(t-t,)}
By taking eqns. (22) and (23) into account, the concentration C’ in the reservoir and the mean current efficiency become C’(O, t> =l_ C(O,O)
+c R,C(O, 6)
(19)
Following the definition in eqn. (14), the mean current efficiency becomes
7j=
C’(0,
t)Fv
It
(20)
a
(25)
By taking eqn. (19) into account, the mean current efficiency (less than unity) can also be expressed as
fjzf-
F
(21) a
During the progress of the reaction, 1, decreases and should become (for a critical time) smaller than the operating current 1,. At the critical point C(0, t,), t, at which the applied current 1, is equal to the limiting current, the yield of product in one passage may be ex-
(26) which are valid for t > t,.
29
3. Experimental procedure
apparatus
maximum reaction rate at the front and to minimize the overall ohmic potential drop in the solution. The catholyte was composed of lanthanide chloride solution, and the anolyte of ferrous chloride solution. Both streams were pumped and recycled with an FM1 metering pump. The flow rates were measured using microflowmeters. The electrolyte leaving the cell was recycled to a reservoir of volume 0.3 1, which was maintained as a well-mixed tank by using a magnetic stirrer. The cathodic chamber, reservoir and polyethylene connecting tube were darkened with oily black paper to prevent reoxidation of reduced europium. In addition, argon was used to purge the catholyte reservoir and so to maintain an oxygen-free environment. The combination pH electrode immersed in the catholyte reservoir was used to monitor and record the pH variation. Before each run, 300 ml of 0.1 M hydrochloric acid followed by deionized water were allowed to flow through the cell. After that, the water residue was rinsed
and
A schematic diagram of the recirculating system for reducing europium in a flow-through porous graphite electrode cell is shown in Fig. 1. The porous electrodes were machined from a block of EG-NPL (Nippon Carbon Co.) graphite. Each electrode was 5 mm thick, with 88 cm2 of apparent surface area coming into contact with the electrolyte. Two graphite electrodes were clamped together in two acrylic frames, between which was an anion-exchange membrane (IONAC MA-3475, Sybron Co.) dividing the cell into two compartments. A rubber gasket, 4 mm thick, swathed with Teflon sealing tape, was placed between the membrane and the electrode plate. The space on the acrylic frame side was filled with glass beads, 2.4 mm in diameter, to reduce the hold-up volume. The electrolyte streams flowed separately from the front face in order to produce the aAnion
exchange membrane
aGraphite
electrode
aAcrylic
frame
@Gasket
& spacer
@Ar-purging
tube
1. Schematic diagram of electrolytic
@pH
electrode
aMagnetic
stirrer set
@Metering
pump
@Fl
ow meter
0 o Glass
reduction
bead
of europium in recirculation
mode.
30
out with a solution containing the electrolytes to be used in the test. The cathodic solution was saturated with argon each time before use. In this investigation, the anodic feed solution contained exclusively 0.3 M ferrous chloride in 0.3 N hydrochloric acid solution. The electrolysis proceeded at room temperature (cu. 299 K) galvanostatically, using a d.c. power supply. During the time course of the redox reaction, the concentrations of Eu2+ and Fe2 + were analysed by the Ce4 + titration method with Ferroin as the indicator.
4. Results and discussion 4.1. Reoxidation of divaknt europium Divalent europium is readily oxidized photochemically and in acid as mentioned above. Some change from europium(II) to europium(II1) was detected, although preventive measures had been taken during our experiments. After the end of electrolysis experiment, the catholyte in the reservoir was kept purged with argon and stirred continuously with a magnetic bar, and the pH was adjusted to about 2. It was observed that the concentration of europium(I1) was depleted linearly with time and the pH value changed from 1.6 to 4.5 within about two hours. As shown in Fig. 2, an average value of the rate constant equal to 1.486~10~6mo11-‘s-‘wasobtai.nedbylinear regression with four sets of measurements. From this observation it was inferred that the order of the reaction in the reservoir was zero during the recirculating operation.
4.2. Electroreduction of europium During the redox reaction, the pH value of the catholyte slowly increased. During the final stage of the operation, the pH value rose steeply to 6 and the reduction reaction was rendered ineffective. The hydroxide which formed at this high pH value fouled the electrode pores and the reactor became inoperable. Thus a high pH value must be avoided during the operation of this electrochemical system. Figure 3 shows the relationship between the europium(I1) concentration and time in the cathodic reservoir with different applied currents. A linear relationship appeared only during a short period of time at the beginning of the measurement using 0.5 A, which indicates that the reduction reaction was proceeding under the electrochemical conditions described in Section 2.2.2. as Case II. A current of 0.175 A is ideally sufficient, in terms of electric charge, to obtain a complete conversion to europium(II). This means that the effective current ratio distributed to europium reduction is about 0.35 for such electrochemical conditions. As shown in Fig. 3, a higher ratio of europium(I1) to total europium ions was obtained when a higher current was applied. With both 0.75 A and 1 .OA, the same quantity of europium was reduced with the same quantity of integrated electric charge. This implies that a higher current efficiency can be achieved when a higher current is applied, but only up to 0.75
4 al-
,,,.
1.1
N
ZE . N
I-’
0
‘;;
$
l
1.0
A
.
0.75 fl A 0.6 A 0 0.5 A 0
Klc
&I-
d;NmIJ6<*em
,“ 1;
D’ ,Q I /
l.D-
_-*-
/d
,HG
/’
,K
/ ‘A
__-<
--*
0 p_-” cc -‘6 AA *--
,/doeo
,,/
_.-
__--
0
X0
A
, e ’ t
Li ’
0.5.
----
&t
Id
curve
fitting
with
eq.(l3>
l2D
150
1
”
0.
0
I
2
Time Fig. 2. Relationship between time.
3
xIOb3.
4
6
0
7
set
europium(I1) reoxidation and
0
30
m
al
la0
210
Time. min Fig. 3. Effect of applied current on europium reduction. Initial catholyte: total lanthanide, 0.465 M; europium(III), 0.05 M; pH=l; Q=20 ml min-‘.
31
0 0.75 A A 0.6 fl 0 0.5 A
IO0)
0
Fig.
-y-
JI
Thyret;
m
,
,
,
,
90
la3
150
lm
210
Time.
min
4. Mean current efficiency VS. time during recircu-
lation.
A. Thus an applied current of 0.75 A may be considered as an optimal value. This effect on the current efficiency would be clearly exhibited if a plot of overall mean current efficiency 2)s. [Eun]/[EuT] ratio was drawn. During the recycling operation, the electrode potential progressively decreased, while the [ Eu’] /[EuT] ratio and the pH value of the catholyte increased. Hence the efficiency decreased with time as shown in Fig. 4. In contrast with the no-gas-evolution electrode, a higher current efficiency was obtained when a higher current was applied, and this was larger than that corresponding to the limiting current in the europium reduction system, when there was hydrogen evolution. The higher current efficiency with a higher applied current may be explained by the fact that the overpotential for europium relative to hydrogen is less significant with a high current than with a low current. With hydrogen evolution at an
electrode, however, gas bubbles substantially reduced the active electrode area, and hence the pore electrolyte resistance was increased. This could result in the absence of any further increase in the current efficiency when the applied current was raised yet higher (as when 1.O A was applied). As a first approximation, the apparent overall mass transfer coefficient k, ( = k,a) was estimated from eqn. (13) by curve-fitting with the experimental data given in Fig. 3. The value of k, may also be calculated theoretically from experimental data on the conversion factor R, for a single pass through a pore in an electrode. The values of k, obtained from singlepass experiments compared with the values obtained by curve fitting (shown in Fig. 3) are listed in Table 1. It seems reasonable that the values from data fitting are smaller (about - lo%), because these stand for the average from the whole range of operation. Based on the values of the rate constants k and k, which were obtained from curve fitting in Fig. 3, the variation with time of the overall mean current efficiency could also be calculated. Figure 4 gives a comparison between the experimental and calculated values; the dashed lines l-4 correspond to the respective values of the current as indicated, which range from 1.0 down to 0.5 A. It can be seen that the calculated values are smaller than the experimental values at the initial stage, but become larger towards the final stage. These results indicate that the mass transfer coefficient decreases progressively with time, presumably owing to the generation of hydrogen.
5. Conclusion A membrane-partitioned flow-through porous graphite electrode reactor, designed for
TABLE 1. Comparison of experiment and calculation for k, values Applied current (AI 0.5 0.6 0.75 1.0
Experiment
Model fitting
&
K. (s-l)
Rt
K. @-‘I
0.115 0.155 0.210 0.270
9.255 x 1o-4 1.276x 1O-3 1.786X1O-3 2.384 x 1O-3
0.109 0.144 0.195 0.242
8.743X 1.178~ 1.643X 2.099 x
10-d 1O-3 1O-3 1o-3
32
the study of europium reduction kinetics, has been experimentally and theoretically examined. Preliminary operational runs with the system which has been designed suggest that it will be an effective system for extraction and purification of em-opium from a mixture of lanthanides. A theoretical model which specifically considered the reoxidation of europium(I1) produced a good description of the transient performance characteristics of the system. The model computations compare closely with the experimental results.
Acknowledgment
Appendix
a A
C(x, t>
,“I, f F
I.% 4. J
Financial support in part through Grant NSC77-0402-E007-17, from the National Science Council of Taiwan, is gratefully acknowledged.
k
A: Nomenclature specific surface area of the electrode (cm’ cmm3) geometrical cross-sectional area of the electrode (cm2) reactant concentration at electrode position x and instant time t (mol cmp3) product concentration (mol cm-“) electrode potential (V) ratio factor Faraday’s constant (96487 C mol-‘) applied cell current (A) limiting current (A) mass flux from bulk electrolyte to electrode (mol cmp2 s-i) rate constant for the zero-order reaction (mol cmp3 s-i) apparent mass transfer coefficient,
k,a (s-l) km L
Q R
7
9 10
13
J. Newman and W. Tiedemann, Adv. Ekctrochem. Ekctrochem. Eng., II (1978) 353-438. K. Kusakabe, H. Nishida, S. Morooka and Y. Kato, J. Ap~l. Ekctrochem., 16 (1986) 121-126. E. Roayaie and J. Jorne, J. Electrochem. Sot., 132 (1985) 1273-1276. J. Jome and E. Roayaie, J. Ekctrochem. Sot., I33 (1986) 696-701. E. I. Onstott, U.S. Patent 3,616,326, 1971. S. J. Dong, Z. X. Li, G. B. Tang, X. L. Zhao, X. Z. Cui and X. W. Yan, Hua Hsueh Tung Pao, 5 (1980) 285-288. D. Lu, Y. W. Miao and C. P. Tung, Sep. Froc. Hgdnnnetall., 41 (1987) 428-436. D. N. Bennion and J. Newman, J. Appl. Electrochem., 2 (1972) 113-122. J. A. Trainham and J. Newman, J. Electrochenz. Sot., 124 (1977) 1528-1540. A. T. S. Walker and A. A. Wragg, Electrochim. Acta, 22 (1977) 1129-l 134. M. Enriquez-Granados, G. Valentin and A. Storck, Electrochim. Acta, 28 (1983) 1407-1414. T. Donohue, Opt. Eng., I8 (1979) 181-186. C. T. Stubblefield and L. Eyring, J. Am. Chem. Sot., 77 (1955) 3004-3005.
Rt t U V X
mass transfer coefficient (cm s- ‘) electrode thickness (cm) flow rate of electrolyte (cm3 s-i) chemical reaction rate (mol cmp3 s-i> conversion factor, R,= 1 - exp( -
k,~/Q)
instant time (s) electrolyte flow velocity, u = Q/A (cm s- ‘) volume of reservoir (cm3) geometrical location of the electrode
Greek symbols E porosity of the electrode overall mean current efficiency; deii fined in eqn. (14) 7 residence time, V/Q (s) Subsctipt
i
initial state
Superscept
T
total europium