- Email: [email protected]
The voltammetric behaviour of the Mn2+, Mn3+, Mn4+ system in 15 N H2SO4 on a smooth platinum microelectrode
Electrochimica Acta. 1968, Vol. 13. pp. 99 to 107. PergamonPress. Printedin NorthernIreland
THE VOLTAMMETRIC BEHAVIOUR OF THE Mn2+, Mn3+, Mn*+ SYSTEM IN 15N H,SO, ON A SMOOTH PLATINUM MICROELECTRODE* R.
GUIDELLI
and G.
Institute of Analytical Chemistry,
PICCARDI
University of Florence, Italy
Abstract-The voltammetric behaviour of Mn 8+, Mn*+ and mixtures of these ionic species in 15 N HBSOp on a smooth platinum micro-electrode with periodical renewal of the diffusion layer shows that the reduction occurs through the electro-active couple Mn*+, Mn*+. The value of the electron-transfer coefficient a relative to the electrode process Mn*+ + e z MnSf has been determined together with the diffusion coefficients of Mnz+, Mn8+ and Mn4+. Rt%nn&L’analyse des courbes intensit&potentiel de Mn $+, Mn4+ et melanges de ces esp&es en milieu acide sulfurique 15 N, d&ermin&s 51une microelectrode de platine poli avec renouvellement de la couche de diffusion, montre que la reduction a lieu par l’intermtdiaire du systeme electroactif Mn*+, Mns+. On a determine aussi la valeur du coefficient de transfert a du systeme oxydo-reducteur Mn8+ -I- e s Mn”+ et les coefficients de diffusion de Mn8+, Mn8+ et Mn4+. Zusammenfassung-Eine Untersuchung des voltametrischen Verhaltens von Mn*+, Mn*+ und ihren Gem&hen in 15 N HLlS04 an einer glatten Platin-Mikroelektrode mit periodischer Emeuerung der Diffusionsschicht ergab, dass die Reduktion tiber das elektrochemisch aktive Redoxpaar Mns+/Mn8+ verlluft. Man ermittelte den Durchtrittsfaktor cc des Elektrodenvorganges Mn*+ + e az Mn’f und die Diffusionskoefhzienten des Mna+, Mna+ und Mn4+. INTRODUCTION THE AIM of the present work was to study the influence of the disproportionation equilibrium 2 Mn3+ z? Mn2+ + Mn4+ upon the electroreduction of Mn*f and Mn3+ to the bivalent state in 15 N H,SO, and at the same time to show the potentialities of the electrode with periodical renewal of the diffusion layer (DLPRE)l in the elucidation of the mechanism of electrode processes. The behaviour of the Mn2+, Mn3+ and Mn 3+, Mn4f couples on a smooth platinum electrode in 15 N H,SO, has been studied by Vetter and Manecke2- 3 with a particular electrochemical technique at controlled current. However, these authors studied the behaviour of the two couples separately, considering the disproportionation equilibrium only in connexion with the Mn 3+, Mn*+ couple and neglecting it in the investigation of the Mn 2f, Mn3+ couple. This way of dealing the subject will be justified in the present paper where the reduction of Mn*+ as well as Mn3f to the bivalent state will be considered simultaneously on theoretical grounds.
THEORY
Consider the voltammetric behaviour of the Mn 2f, Mn4+ couple while taking into account the homogeneous chemical equilibrium Mn*+ + Mn2+ti 2 Mn3f.
(1)
Consider a thin layer of solution bounded by two surfaces parallel to the electrode and at distances s and s + ds respectively. The rate of change of the concentration of the manganese atoms contained in the three ionic species Mn2f, Mn3+ and Mn*+ within this layer is obviously equal* to the ratio of the difference between the fluxes * Manuscript received 20 March 1967. 99
R. GUIDELLIand G. PICCARDI
loo
of Mn at s + ds and ds by the increment ds. In the case of spherical diffusion this statement may be easily expressed by the differential equation 6,[M++] + 6,[Mn3+] + &[Mn*+] = 0,
(2)
where
and D,, Da, Da are the diffusion coefficients of the species Mn2f, MrP, Mn*+ respectively. Let us further consider the number of electrons present in the manganese atoms of the three ionic species under examination, in excess with respect to those contained in the atom of the species Mn4+, characterized by the highest oxidation state. Obviously this number is 2 for the species Mn2+ and 1 for the species Mn3+. The rate of change of the concentration of these electrons within the thin layer of solution previously considered is still equal to the ratio of the difference between their fluxes at r + dr and dr by the increment dr. This statement may be expressed as 2S2[Mn2+] + 6,[Mn3+] = 0. In order to exclude the possibility of accumulation electrode surface, the boundary condition a[Mn2+l
D
2
+
aW3+l
D
3 &
+
ar
Wn4+l
D
4
(3) of manganese atoms on the
=
o
&
,
for
r = r. t>o
(4)
will be written. The initial conditions are [Mn2+] = [Mn2+]* [Mn3+] = [Mn3+]*: [Mn4+] = [Mn4+]* ,
r 2 r,,
t = 0,
for
(5) r+a,t>O,
where [Mn2+]*, [Mn3+]* and [Mn4+]* express bulk concentrations and r. is the radius of the spherical electrode. In order to simplify the calculations it will be assumed that D, = D, = D4 = D.
(6)
This statement is justified by the actual values of the diffusion coefficients reported in the experimental part. (2), (4), (5) and (6) immediately yield [Mn2+] + [Mn3+] + [Mn4+] = [Mn2+]* + [Mn3+]* + [Mn4+]* = C.
(7)
If equilibrium (1) is perfectly mobile, (8) for any value of the electrolysis time and of the distance r - r. from the electrode surface. The polarographic current relative to the reduction to the bivalent state is given by
Voltammetric behaviour of the Mn I+, Mn8+, Mn*+ system in 15 N HoSOl on smooth Pt
101
The reduction of Mn4+ and Mn3+ to Mn2f on smooth platinum is characterized by a high electron-transfer overtension. Consequently the boundary condition
F& = 2 ,kr[Mn4+] + ,kf[Mn3+l may be written, where 4kr and 3kf are respectively the rate constants for the electrode processes relative to the reduction of Mn4+ and Mn3+ to the bivalent state. [MrP+] and [Mn3f] express surface concentrations. The rates of the backward electrode processes have been neglected. Let us assume that 3kf[Mn3f] > 2 4 k f [Mn”+l (11) for any value of the potential. This amounts to saying that the number of moles of Mn3+ that react on the electrode surface in unit time is much larger than the corresponding number of moles of Mn4+, so that Mn3+ is to be considered the electro-active species through which the electro-reduction occurs. Therefore (IO) becomes i
- = ,kf[Mn3+]. FA
(12)
The solution of the set of differential equations (2) and (3) based on conditions (4), (5), (6), (8) and (12) is quite arduous, and it has been found convenient to introduce some approximations. In this connexion it may be noted that the surface concentration of Mn3+ is sensibly larger than that of Mn4+ for most of the rising portion of the cathodic waves of Mn 4+, Mn3+ and mixtures of the two. In fact, through a suitable combination of (7) and (8), one has [Mn3+] -=
WeI
-K+
4CK K2 - 4K ’ [Mn4+]
J(
2
,
(13)
which holds at any distance from the electrode surface, r - r,, = 0 included. Since the value of K is about 2 x lo2 in 15 N HaSO at 25°C,3*5for C = 10d2 M the ratio expressed by (13) is equal to O-99, 72.63, 123.16 and 358.04 when [Mn4+] equals 5 x lo”, lOA, 5 x W6 and 10m5respectively. In the upper part of the rising portion of the cathodic wave of Mn4f one has therefore
[Mn3+l> [Mn4+1
1
.
(14)
Obviously, when considering mixtures of Mn3+ and Mn4f, the larger the ratio [Mn3+]*/[MnQ]* in the bulk of the solution, the wider the part of the rising portion where condition (14) holds. When this is the case, (12) may be written approximately i - = 3kr[Mn3+] w 3kf{ [Mn3+] + 2 [Mn”+]}. FA
(15)
By combining (2) and (3) linearly, one has 6{[Mn3+] + 2[Mn4+]} = 0.
(16)
R. GUIDELLI and G. PICCARDI
102
In view of (5), (9), (15) and (16), the linear combination {[Mn3f] + 2 [Mn4+]} behaves formally like the concentration of the oxidized component of a simple redox couple characterized by a slow electron transfer. The expression of the instantaneous polarographic current for spherical diffusion may then be found in the literature6 as i=
FAD1’23’f(2’M~~*
+ IMn3+‘*) (1 + (2
_ 1) exp (/JZt) erfc (/jr13)
(17)
where
The analogous expression of the mean current obtainable with the DLPRE may be derived by integrating (17) and taking into account the washing period, tr,. Then1s7 i=
FAD1j2 ,kr(2[Mn*+]* + [Mn3+]*) It,,, + (B$ r&tot
1) [““p (82rt,;j)fc
(18)
2(&112_ $12)
exp (p2tp) erfc @ti”) + where ttot is the period. that
(/%3
&2
B
When 3kf + co, i tends to the limiting diffusion current,
id,
so
id = lim i
skr+
= FAD(2[Mn4+]* + [Mna+]*)(k + 2’~t~,~$‘2)
.
(19)
~0
Dividing i by id, one obtains
exp (b2tp) erfc (&l’“) +
2(tg
ttot +
-
1 (20)
q2>
7+2/?
(20) expresses 3kf in an implicit form as a function of i/id. The experimental current voltage characteristics furnish j/G as a function of the applied potential. Therefore (20) allows ,kf to be determined as a function of E, if rO, D, ttot and tp are known. If the assumptions previously made are correct, log ,kf must be proportional to E according to the well known expression 3kr = 3kr” exp [-(aF/RT)(E
- EON,
(21)
where 3kf” is the value of the heterogeneous rate constant for E = E,. EXPERIMENTAL
TECHNIQUE
The voltammetric measurements were carried out using the electrode with periodical renewal of the diffusion layer, described by Cozzi, Raspi and Nucci.l The electrode surface consisted of a spherical bowl of radius r, = O-088 cm and height h = O-107 cm. Consequently the geometrical area of the electrode was 0.0592 cm2. When using (18)
Voltammetricbehaviour of the Mn*+,Mns+,Mn4+system in 15 N HpSO,on smooth Pt 103 and (19) the effective area, A, of the electrode was employed. The value of A was derived from the experimental limiting diffusion current of a 4 x 10-s M K,Fe(CN), solution in O-1 M KCl. The diffusion coefficient of Fe(CN),“- under these conditions may be found in the literature,* allowing the value of A (=0*0628 cm”) to be obtained through the use of an equation analogous to (19). The agreement between the effective and geometrical areas is satisfactory. The current/voltage curves were recorded at a 0.47 mV/s sweep rate with a Polarecord Metrohm E 261 and have been suitably corrected for the ohmic drop. The Mns+ and Mn4f solutions were prepared from KMnO, and MnSO, aqueous solutions titrated according to the traditional methods of analysis. The stoichiometric quantities of MnSO, and KMnO, solutions were added to water-H,SO, TABLE 1. LIMITING CATHODIC CURRENTS OF Mn4+AT DIFFERENT CONCENTRATIONS OF THE DEPOLARIZER; tt,,t = 5.76s
[Mn’+]l M 1x 2x 4x 6x 8x 1x 2x
10-z 10-B 10-a lo-* 10-a 10-8 10-e
x/[Mna+]* A ml/mole 5.27 10.65 21.2 31.0 41.7 52.5 104.5
5.27 5.32 5.30 5.17 5.21 5.25 5.22
mixtures suitably cooled. The disappearance of the absorption maxima of MnO, in the visible range of the spectrum shows that the reaction between Mn2+ and MnO, with Mn3+ formation is practically instantaneous, while that relative to Mn4+ formation is slower and requires about + h to go to completion. The spectrophotometric measurements were carried out with an UNICAM SP 800 spectrophotometer. Both the Mn3f and Mn4+ solutions remained satisfactorily stable for about 12 h. However, after one day the oxidizing power of the above solutions showed a sensible decrease. Consequently freshly prepared solutions were used every day. The instantaneous currents along the rising portion of the polarographic waves of Mn3+ and Mn4+ were measured with a Tektronix 502 oscilloscope. Their behaviour, together with that of the mean currents, confirms the theoretical predictions. RESULTS AND DISCUSSION Table 1 shows that the mean limiting current relative to the reduction of Mn4+ is proportional to the concentration of this species. The use of (19) allows the diffusion coefficient D to be derived from the experimental value of the ratio &/[MI$+]*, noting that [Mn3+]* = 0, r0 = 0.088 cm, A = O-0628 cm2, t, = 2.82 x 1O-2s and t tot = 576 s. The diffusion coefficient so obtained is practically that of the species Mn4+, ie D,. In fact, under the above conditions, Mn4f is the only species diffusing towards the electrode. Table 2 shows the variations of the mean limiting current of 1O-2M Mn4+ in 15 N H,SO, with a change of the period ttot. The experimental currents (&,) are in good agreement with the theoretical ones (&,_) obtained on the basis of (19) for the following data: [Mn4+]* = 1O-2M, [Mn”+]* = 0, r,, = O-088 cm, tp == 2.82 x 1O-2s, D = D, = O-90 x 1O-s cm2/s. The agreement between
104
R. GUIDELLIand G. PICCARDI TABLE2. LIMITINGCATHODIC ~~RRRNTS OF IO-* M Mn‘+ in 15 N HISO, FOR DIFFERENT
VALUES
OF tt,t
ttot
i,e.p
s
PA
PA
61.0 59.5 57.0 55.0 53.5 52.0 50.7 49.4 48.0 46.5 44.7 43.7 42.2 41.6
61.2 59.9 57.6 55.4 54.0 52.5 51.2 50.0 48.6 46.8 45.1 44.0 42.1 41.1
4.13 4.33 4.72 5.11 5.41 5.75 6.07 6.41 6.81 7.35 7.99 8.42 9.21 9.69
i&or
the theoretical and experimental values reveals that the limiting current is diffusioncontrolled. Figure 1 shows the polarogram of 1O-2M Mn4+ in 15 N H,S04. Tables 3 and 4 are analogous to Tables 1 and 2 respectively but refer to Mn3+ solutions. The diffusion coefficient D, = 1.10 x lo4 cmZ/s of the tervalent species was obtained from these data in the usual way. In fact, although Mn3f is present in the bulk of the solution together with the products Mn2+ and Mn4f of its disproportionation, Mn3+ may be considered the only species diffusing towards the electrode in sensible amounts. The value 1.22 of the ratio D,/D, is in good agreement with the value 1.20 obtained by Vetter and Manecke, 2*3although the single values of the diffusion coefficients D3 and Da reported by these authors (Da = 0.75 x 10e5 cm2/s; D, = 0.62 x 10m5cm2/s)
FIG. 1. Polarogram of lo-* M MI++ in 15 N H,SO ,; t tot = 8.62 s; 25°C. The vertical limerefers to +0*5 V vs the saturated H&JO, electrode.
Voltammetric
behaviour of the Mn *+, Mns+, Md+
system in 15 N HaSO, on smooth Pt
TABLE 3. LIMITING CATHODIC CURRENTS OF Mn*+ ATDIFFERENTCONCENTRATIONSOFTHE DEPOLARIZER; ttot = 5.82 s [MnS+] * M 1 2 4 6 8 1 2
x x x x x x x
G/[Mn”+]* A ml/mole
10-S 10-S 10-S 1O-3 1O-3 IO-’ 10-s
2.85 5.70 11.47 17.5 23.1 28.7 60.8
2.85 2.85 2.87 2.90 2.89 2.87 3.05
TABLE 4. LIMITING CATHODIC CURRENTS OF 1O-p M Mn3+ IN 15 NHISOl FOR DIFFERENT VAL.UES OF ttot
ttot
T
I-
‘dexp
%mr
S
PA
PA
444 4.63 4.85 5.16 5.45 5.78 6.12 6.51 6.93 7.53 7.73 7,95 8.55 8.95 9.62
32.8 32.2 31.4 30.4 29.6 28.8 28.0 27.2 26.4 25.8 25.2 25.0 24.2 23.6 22.8
32.8 32.2 31.5 30.6 29.9 29.0 28.3 27.5 26.7 25.7 25.4 25.1 24.3 23.7 22.9
TABLE 5. LIMITING ANODIC CURRENTS OF Mn*+ ATDIPEERENTCONCENTRA~ONS OF THE DEPOLARIZER; tt,,t = 5.78 S [Mn3+] * M 1 2 3 4 5 6 7 8 9 1
x x x x x x x x x x
10-s 10-s 10-S 10-S IO-3 1O-3 IO-3 1O-3 10-S 10-e
z PA 2.89 5.62 8.65 10.8 13.6 16.4 18.7 22.0 23.5 26.0
&/ [Mnl+] * A ml/mole 2.89 2.81 2.88 2.71 2.73 2.74 2.68 2.75 2.61 2.60
105
106
R. GUIDELLIand G. PICCARDI
I
0.5v
’
I
lop A
FIG. 2. Polarogram of a mixture of 5 x lo-‘M Mnz+ and 5 x 10-3M Mn3- in 15 N H,SO,; ttot = 8.05 s; 25°C . The vertical line refers to to.5 V vs the saturated HgzSOI electrode.
I
I
I
-25-
-3 o-
d
Y
.p’”
c H -3.5-
-4.0 -
0.7
I
06
04 E ,V( $.”
I
03
HgpSOqsot.)
FIG. 3. Log akr VS. E plot as derived from the approximate equation (20). The curves refer to different values of [Mn8+]*/[MnP+]*: f, co; 0, 1.25; 0, 1.00; 0, 0.50; n , 0.062; x, 0.
Voltammetric behaviour of the Mn 2+, MnS+, MI++ system in 15 N H$O, on smooth Pt 107
are about seven times larger than those obtained using (19). It should be noted that Vetter and Manecke obtained D3 and D, by applying the approximate Nernst formula9 and ascribing the arbitrary value 5 x 10e3 cm to the thickness of the diffusion layer. Also, the mean limiting current relative to the oxidation of M$+ to Mn3+ has been determined as a function of the concentration of the bivalent species (Table 5). The constant ratio id/[Mn2f]* has been used in order to determine the diffusion coefficient D, on the basis of an equation analogous to (19). The resulting value of D, is O-98 x 1O-s cm2/s. When [Mn2f]* > 2 x lop2 M the anodic wave shows a round maximum, while the ratio id/[Mn2f]* decreases. The rising portion of the wave of Mn2f is poorly reproducible on account of the nearby discharge of the solvent, and has not been considered from a quantitative point of view. Figure 2 shows the current/ potential characteristic of a mixture of Mn2+ and Mn3+ in 15 N H,SO,. The sensible difference between the slopes of the anodic and cathodic waves reveals the considerable asymmetry of the potential-energy barrier relative to the electron-transfer process Mn3f + ee Mn2f. Polarograms relative to solutions of Mn3f, Mn*+ and mixtures of the two in different ratios have been determined, for a constant value of [Mn3+]* + 2[Mn4+]* = 1O-2 M. In Fig. 3 the value of log 3kr obtained through the use of (20) is plotted as a function of the applied potential E. In a Mn3+ solution, where Mn4+ arises from the disproportionation reaction (l), the latter species may be neglected with respect to Mn 3+ both in the bulk of the solution and at the electrode surface. Therefore the log 3kr USE plot is a straight line for the whole rising portion of the polarographic wave. A straight line for values of the ratio i/id larger than O-1 (log 3kf > -4.3) is obtained with mixtures of Mn3+ and Mn4+ where [Mn3f]*/ [Mn4+]* :> 1. In this connexion, the higher the values of [Mnsf]*/ [Mn4+]*, the wider the extent of the upper part of the rising portion where (20) holds, and the log 3kf us E plot is linear. Practically when only Mn4f is present in the bulk of the solution the log 3kf us E plot is linear for i/id > l/2 (log 3kf > -3.4). In view of (21) the slope of the straight line in Fig. 3 is given by -0.434 x (aF/RT). The value 0.22 has been obtained for the electron-transfer coefficient cc. The voltammetric waves are very reproducible as far as their shape is concerned, but tend to shift along the potential axis. The fluctuations occur within a range of 20 mV. The corresponding uncertainty about the intersection point of the log 3kf 2rsE line with the potential axis causes the value of the kinetic parameter 3kf” to be poorly reproducible. 1. 2. 3. 4. 5. 6. 7. 8. 9.
REFERENCES D. Cozzr, G. RASPI and L. Nuccr, J. electroanal. Chem. 12,36 (1966). K. J. VEER and G. MANECKE, 2. phys. Chem. 195,270 (1950). K. J. VETIXRand G. MANECKE; 2. >h&. Chem. 195; 337 (1950). P. DELAHAY. New InstrumentalMethods in Electrochemistrv. D. 48. Interscience. New York (1954). . ~I G. GRUBE&d H. HUBERICH, Z. Elektrochem. 29,s (192jj.’ I. SHAIN,J. phys. Chem. 65,259 (1961). D. COZZI, G. CIANTELLIand R. GUIDELU,in preparation. M. v. STACKELBERQ, M. RLGRAM and V. TOOME,Z. Elektrochem. 57, 342 (1953). P. DELAHAY,New Instrumental Methods in Electrochemistry, p. 218. Interscience, New York (1954).
THE VOLTAMMETRIC BEHAVIOUR OF THE Mn2+, Mn3+, Mn*+ SYSTEM IN 15N H,SO, ON A SMOOTH PLATINUM MICROELECTRODE* R.
GUIDELLI
and G.
Institute of Analytical Chemistry,
PICCARDI
University of Florence, Italy
Abstract-The voltammetric behaviour of Mn 8+, Mn*+ and mixtures of these ionic species in 15 N HBSOp on a smooth platinum micro-electrode with periodical renewal of the diffusion layer shows that the reduction occurs through the electro-active couple Mn*+, Mn*+. The value of the electron-transfer coefficient a relative to the electrode process Mn*+ + e z MnSf has been determined together with the diffusion coefficients of Mnz+, Mn8+ and Mn4+. Rt%nn&L’analyse des courbes intensit&potentiel de Mn $+, Mn4+ et melanges de ces esp&es en milieu acide sulfurique 15 N, d&ermin&s 51une microelectrode de platine poli avec renouvellement de la couche de diffusion, montre que la reduction a lieu par l’intermtdiaire du systeme electroactif Mn*+, Mns+. On a determine aussi la valeur du coefficient de transfert a du systeme oxydo-reducteur Mn8+ -I- e s Mn”+ et les coefficients de diffusion de Mn8+, Mn8+ et Mn4+. Zusammenfassung-Eine Untersuchung des voltametrischen Verhaltens von Mn*+, Mn*+ und ihren Gem&hen in 15 N HLlS04 an einer glatten Platin-Mikroelektrode mit periodischer Emeuerung der Diffusionsschicht ergab, dass die Reduktion tiber das elektrochemisch aktive Redoxpaar Mns+/Mn8+ verlluft. Man ermittelte den Durchtrittsfaktor cc des Elektrodenvorganges Mn*+ + e az Mn’f und die Diffusionskoefhzienten des Mna+, Mna+ und Mn4+. INTRODUCTION THE AIM of the present work was to study the influence of the disproportionation equilibrium 2 Mn3+ z? Mn2+ + Mn4+ upon the electroreduction of Mn*f and Mn3+ to the bivalent state in 15 N H,SO, and at the same time to show the potentialities of the electrode with periodical renewal of the diffusion layer (DLPRE)l in the elucidation of the mechanism of electrode processes. The behaviour of the Mn2+, Mn3+ and Mn 3+, Mn4f couples on a smooth platinum electrode in 15 N H,SO, has been studied by Vetter and Manecke2- 3 with a particular electrochemical technique at controlled current. However, these authors studied the behaviour of the two couples separately, considering the disproportionation equilibrium only in connexion with the Mn 3+, Mn*+ couple and neglecting it in the investigation of the Mn 2f, Mn3+ couple. This way of dealing the subject will be justified in the present paper where the reduction of Mn*+ as well as Mn3f to the bivalent state will be considered simultaneously on theoretical grounds.
THEORY
Consider the voltammetric behaviour of the Mn 2f, Mn4+ couple while taking into account the homogeneous chemical equilibrium Mn*+ + Mn2+ti 2 Mn3f.
(1)
Consider a thin layer of solution bounded by two surfaces parallel to the electrode and at distances s and s + ds respectively. The rate of change of the concentration of the manganese atoms contained in the three ionic species Mn2f, Mn3+ and Mn*+ within this layer is obviously equal* to the ratio of the difference between the fluxes * Manuscript received 20 March 1967. 99
R. GUIDELLIand G. PICCARDI
loo
of Mn at s + ds and ds by the increment ds. In the case of spherical diffusion this statement may be easily expressed by the differential equation 6,[M++] + 6,[Mn3+] + &[Mn*+] = 0,
(2)
where
and D,, Da, Da are the diffusion coefficients of the species Mn2f, MrP, Mn*+ respectively. Let us further consider the number of electrons present in the manganese atoms of the three ionic species under examination, in excess with respect to those contained in the atom of the species Mn4+, characterized by the highest oxidation state. Obviously this number is 2 for the species Mn2+ and 1 for the species Mn3+. The rate of change of the concentration of these electrons within the thin layer of solution previously considered is still equal to the ratio of the difference between their fluxes at r + dr and dr by the increment dr. This statement may be expressed as 2S2[Mn2+] + 6,[Mn3+] = 0. In order to exclude the possibility of accumulation electrode surface, the boundary condition a[Mn2+l
D
2
+
aW3+l
D
3 &
+
ar
Wn4+l
D
4
(3) of manganese atoms on the
=
o
&
,
for
r = r. t>o
(4)
will be written. The initial conditions are [Mn2+] = [Mn2+]* [Mn3+] = [Mn3+]*: [Mn4+] = [Mn4+]* ,
r 2 r,,
t = 0,
for
(5) r+a,t>O,
where [Mn2+]*, [Mn3+]* and [Mn4+]* express bulk concentrations and r. is the radius of the spherical electrode. In order to simplify the calculations it will be assumed that D, = D, = D4 = D.
(6)
This statement is justified by the actual values of the diffusion coefficients reported in the experimental part. (2), (4), (5) and (6) immediately yield [Mn2+] + [Mn3+] + [Mn4+] = [Mn2+]* + [Mn3+]* + [Mn4+]* = C.
(7)
If equilibrium (1) is perfectly mobile, (8) for any value of the electrolysis time and of the distance r - r. from the electrode surface. The polarographic current relative to the reduction to the bivalent state is given by
Voltammetric behaviour of the Mn I+, Mn8+, Mn*+ system in 15 N HoSOl on smooth Pt
101
The reduction of Mn4+ and Mn3+ to Mn2f on smooth platinum is characterized by a high electron-transfer overtension. Consequently the boundary condition
F& = 2 ,kr[Mn4+] + ,kf[Mn3+l may be written, where 4kr and 3kf are respectively the rate constants for the electrode processes relative to the reduction of Mn4+ and Mn3+ to the bivalent state. [MrP+] and [Mn3f] express surface concentrations. The rates of the backward electrode processes have been neglected. Let us assume that 3kf[Mn3f] > 2 4 k f [Mn”+l (11) for any value of the potential. This amounts to saying that the number of moles of Mn3+ that react on the electrode surface in unit time is much larger than the corresponding number of moles of Mn4+, so that Mn3+ is to be considered the electro-active species through which the electro-reduction occurs. Therefore (IO) becomes i
- = ,kf[Mn3+]. FA
(12)
The solution of the set of differential equations (2) and (3) based on conditions (4), (5), (6), (8) and (12) is quite arduous, and it has been found convenient to introduce some approximations. In this connexion it may be noted that the surface concentration of Mn3+ is sensibly larger than that of Mn4+ for most of the rising portion of the cathodic waves of Mn 4+, Mn3+ and mixtures of the two. In fact, through a suitable combination of (7) and (8), one has [Mn3+] -=
WeI
-K+
4CK K2 - 4K ’ [Mn4+]
J(
2
,
(13)
which holds at any distance from the electrode surface, r - r,, = 0 included. Since the value of K is about 2 x lo2 in 15 N HaSO at 25°C,3*5for C = 10d2 M the ratio expressed by (13) is equal to O-99, 72.63, 123.16 and 358.04 when [Mn4+] equals 5 x lo”, lOA, 5 x W6 and 10m5respectively. In the upper part of the rising portion of the cathodic wave of Mn4f one has therefore
[Mn3+l> [Mn4+1
1
.
(14)
Obviously, when considering mixtures of Mn3+ and Mn4f, the larger the ratio [Mn3+]*/[MnQ]* in the bulk of the solution, the wider the part of the rising portion where condition (14) holds. When this is the case, (12) may be written approximately i - = 3kr[Mn3+] w 3kf{ [Mn3+] + 2 [Mn”+]}. FA
(15)
By combining (2) and (3) linearly, one has 6{[Mn3+] + 2[Mn4+]} = 0.
(16)
R. GUIDELLI and G. PICCARDI
102
In view of (5), (9), (15) and (16), the linear combination {[Mn3f] + 2 [Mn4+]} behaves formally like the concentration of the oxidized component of a simple redox couple characterized by a slow electron transfer. The expression of the instantaneous polarographic current for spherical diffusion may then be found in the literature6 as i=
FAD1’23’f(2’M~~*
+ IMn3+‘*) (1 + (2
_ 1) exp (/JZt) erfc (/jr13)
(17)
where
The analogous expression of the mean current obtainable with the DLPRE may be derived by integrating (17) and taking into account the washing period, tr,. Then1s7 i=
FAD1j2 ,kr(2[Mn*+]* + [Mn3+]*) It,,, + (B$ r&tot
1) [““p (82rt,;j)fc
(18)
2(&112_ $12)
exp (p2tp) erfc @ti”) + where ttot is the period. that
(/%3
&2
B
When 3kf + co, i tends to the limiting diffusion current,
id,
so
id = lim i
skr+
= FAD(2[Mn4+]* + [Mna+]*)(k + 2’~t~,~$‘2)
.
(19)
~0
Dividing i by id, one obtains
exp (b2tp) erfc (&l’“) +
2(tg
ttot +
-
1 (20)
q2>
7+2/?
(20) expresses 3kf in an implicit form as a function of i/id. The experimental current voltage characteristics furnish j/G as a function of the applied potential. Therefore (20) allows ,kf to be determined as a function of E, if rO, D, ttot and tp are known. If the assumptions previously made are correct, log ,kf must be proportional to E according to the well known expression 3kr = 3kr” exp [-(aF/RT)(E
- EON,
(21)
where 3kf” is the value of the heterogeneous rate constant for E = E,. EXPERIMENTAL
TECHNIQUE
The voltammetric measurements were carried out using the electrode with periodical renewal of the diffusion layer, described by Cozzi, Raspi and Nucci.l The electrode surface consisted of a spherical bowl of radius r, = O-088 cm and height h = O-107 cm. Consequently the geometrical area of the electrode was 0.0592 cm2. When using (18)
Voltammetricbehaviour of the Mn*+,Mns+,Mn4+system in 15 N HpSO,on smooth Pt 103 and (19) the effective area, A, of the electrode was employed. The value of A was derived from the experimental limiting diffusion current of a 4 x 10-s M K,Fe(CN), solution in O-1 M KCl. The diffusion coefficient of Fe(CN),“- under these conditions may be found in the literature,* allowing the value of A (=0*0628 cm”) to be obtained through the use of an equation analogous to (19). The agreement between the effective and geometrical areas is satisfactory. The current/voltage curves were recorded at a 0.47 mV/s sweep rate with a Polarecord Metrohm E 261 and have been suitably corrected for the ohmic drop. The Mns+ and Mn4f solutions were prepared from KMnO, and MnSO, aqueous solutions titrated according to the traditional methods of analysis. The stoichiometric quantities of MnSO, and KMnO, solutions were added to water-H,SO, TABLE 1. LIMITING CATHODIC CURRENTS OF Mn4+AT DIFFERENT CONCENTRATIONS OF THE DEPOLARIZER; tt,,t = 5.76s
[Mn’+]l M 1x 2x 4x 6x 8x 1x 2x
10-z 10-B 10-a lo-* 10-a 10-8 10-e
x/[Mna+]* A ml/mole 5.27 10.65 21.2 31.0 41.7 52.5 104.5
5.27 5.32 5.30 5.17 5.21 5.25 5.22
mixtures suitably cooled. The disappearance of the absorption maxima of MnO, in the visible range of the spectrum shows that the reaction between Mn2+ and MnO, with Mn3+ formation is practically instantaneous, while that relative to Mn4+ formation is slower and requires about + h to go to completion. The spectrophotometric measurements were carried out with an UNICAM SP 800 spectrophotometer. Both the Mn3f and Mn4+ solutions remained satisfactorily stable for about 12 h. However, after one day the oxidizing power of the above solutions showed a sensible decrease. Consequently freshly prepared solutions were used every day. The instantaneous currents along the rising portion of the polarographic waves of Mn3+ and Mn4+ were measured with a Tektronix 502 oscilloscope. Their behaviour, together with that of the mean currents, confirms the theoretical predictions. RESULTS AND DISCUSSION Table 1 shows that the mean limiting current relative to the reduction of Mn4+ is proportional to the concentration of this species. The use of (19) allows the diffusion coefficient D to be derived from the experimental value of the ratio &/[MI$+]*, noting that [Mn3+]* = 0, r0 = 0.088 cm, A = O-0628 cm2, t, = 2.82 x 1O-2s and t tot = 576 s. The diffusion coefficient so obtained is practically that of the species Mn4+, ie D,. In fact, under the above conditions, Mn4f is the only species diffusing towards the electrode. Table 2 shows the variations of the mean limiting current of 1O-2M Mn4+ in 15 N H,SO, with a change of the period ttot. The experimental currents (&,) are in good agreement with the theoretical ones (&,_) obtained on the basis of (19) for the following data: [Mn4+]* = 1O-2M, [Mn”+]* = 0, r,, = O-088 cm, tp == 2.82 x 1O-2s, D = D, = O-90 x 1O-s cm2/s. The agreement between
104
R. GUIDELLIand G. PICCARDI TABLE2. LIMITINGCATHODIC ~~RRRNTS OF IO-* M Mn‘+ in 15 N HISO, FOR DIFFERENT
VALUES
OF tt,t
ttot
i,e.p
s
PA
PA
61.0 59.5 57.0 55.0 53.5 52.0 50.7 49.4 48.0 46.5 44.7 43.7 42.2 41.6
61.2 59.9 57.6 55.4 54.0 52.5 51.2 50.0 48.6 46.8 45.1 44.0 42.1 41.1
4.13 4.33 4.72 5.11 5.41 5.75 6.07 6.41 6.81 7.35 7.99 8.42 9.21 9.69
i&or
the theoretical and experimental values reveals that the limiting current is diffusioncontrolled. Figure 1 shows the polarogram of 1O-2M Mn4+ in 15 N H,S04. Tables 3 and 4 are analogous to Tables 1 and 2 respectively but refer to Mn3+ solutions. The diffusion coefficient D, = 1.10 x lo4 cmZ/s of the tervalent species was obtained from these data in the usual way. In fact, although Mn3f is present in the bulk of the solution together with the products Mn2+ and Mn4f of its disproportionation, Mn3+ may be considered the only species diffusing towards the electrode in sensible amounts. The value 1.22 of the ratio D,/D, is in good agreement with the value 1.20 obtained by Vetter and Manecke, 2*3although the single values of the diffusion coefficients D3 and Da reported by these authors (Da = 0.75 x 10e5 cm2/s; D, = 0.62 x 10m5cm2/s)
FIG. 1. Polarogram of lo-* M MI++ in 15 N H,SO ,; t tot = 8.62 s; 25°C. The vertical limerefers to +0*5 V vs the saturated H&JO, electrode.
Voltammetric
behaviour of the Mn *+, Mns+, Md+
system in 15 N HaSO, on smooth Pt
TABLE 3. LIMITING CATHODIC CURRENTS OF Mn*+ ATDIFFERENTCONCENTRATIONSOFTHE DEPOLARIZER; ttot = 5.82 s [MnS+] * M 1 2 4 6 8 1 2
x x x x x x x
G/[Mn”+]* A ml/mole
10-S 10-S 10-S 1O-3 1O-3 IO-’ 10-s
2.85 5.70 11.47 17.5 23.1 28.7 60.8
2.85 2.85 2.87 2.90 2.89 2.87 3.05
TABLE 4. LIMITING CATHODIC CURRENTS OF 1O-p M Mn3+ IN 15 NHISOl FOR DIFFERENT VAL.UES OF ttot
ttot
T
I-
‘dexp
%mr
S
PA
PA
444 4.63 4.85 5.16 5.45 5.78 6.12 6.51 6.93 7.53 7.73 7,95 8.55 8.95 9.62
32.8 32.2 31.4 30.4 29.6 28.8 28.0 27.2 26.4 25.8 25.2 25.0 24.2 23.6 22.8
32.8 32.2 31.5 30.6 29.9 29.0 28.3 27.5 26.7 25.7 25.4 25.1 24.3 23.7 22.9
TABLE 5. LIMITING ANODIC CURRENTS OF Mn*+ ATDIPEERENTCONCENTRA~ONS OF THE DEPOLARIZER; tt,,t = 5.78 S [Mn3+] * M 1 2 3 4 5 6 7 8 9 1
x x x x x x x x x x
10-s 10-s 10-S 10-S IO-3 1O-3 IO-3 1O-3 10-S 10-e
z PA 2.89 5.62 8.65 10.8 13.6 16.4 18.7 22.0 23.5 26.0
&/ [Mnl+] * A ml/mole 2.89 2.81 2.88 2.71 2.73 2.74 2.68 2.75 2.61 2.60
105
106
R. GUIDELLIand G. PICCARDI
I
0.5v
’
I
lop A
FIG. 2. Polarogram of a mixture of 5 x lo-‘M Mnz+ and 5 x 10-3M Mn3- in 15 N H,SO,; ttot = 8.05 s; 25°C . The vertical line refers to to.5 V vs the saturated HgzSOI electrode.
I
I
I
-25-
-3 o-
d
Y
.p’”
c H -3.5-
-4.0 -
0.7
I
06
04 E ,V( $.”
I
03
HgpSOqsot.)
FIG. 3. Log akr VS. E plot as derived from the approximate equation (20). The curves refer to different values of [Mn8+]*/[MnP+]*: f, co; 0, 1.25; 0, 1.00; 0, 0.50; n , 0.062; x, 0.
Voltammetric behaviour of the Mn 2+, MnS+, MI++ system in 15 N H$O, on smooth Pt 107
are about seven times larger than those obtained using (19). It should be noted that Vetter and Manecke obtained D3 and D, by applying the approximate Nernst formula9 and ascribing the arbitrary value 5 x 10e3 cm to the thickness of the diffusion layer. Also, the mean limiting current relative to the oxidation of M$+ to Mn3+ has been determined as a function of the concentration of the bivalent species (Table 5). The constant ratio id/[Mn2f]* has been used in order to determine the diffusion coefficient D, on the basis of an equation analogous to (19). The resulting value of D, is O-98 x 1O-s cm2/s. When [Mn2f]* > 2 x lop2 M the anodic wave shows a round maximum, while the ratio id/[Mn2f]* decreases. The rising portion of the wave of Mn2f is poorly reproducible on account of the nearby discharge of the solvent, and has not been considered from a quantitative point of view. Figure 2 shows the current/ potential characteristic of a mixture of Mn2+ and Mn3+ in 15 N H,SO,. The sensible difference between the slopes of the anodic and cathodic waves reveals the considerable asymmetry of the potential-energy barrier relative to the electron-transfer process Mn3f + ee Mn2f. Polarograms relative to solutions of Mn3f, Mn*+ and mixtures of the two in different ratios have been determined, for a constant value of [Mn3+]* + 2[Mn4+]* = 1O-2 M. In Fig. 3 the value of log 3kr obtained through the use of (20) is plotted as a function of the applied potential E. In a Mn3+ solution, where Mn4+ arises from the disproportionation reaction (l), the latter species may be neglected with respect to Mn 3+ both in the bulk of the solution and at the electrode surface. Therefore the log 3kr USE plot is a straight line for the whole rising portion of the polarographic wave. A straight line for values of the ratio i/id larger than O-1 (log 3kf > -4.3) is obtained with mixtures of Mn3+ and Mn4+ where [Mn3f]*/ [Mn4+]* :> 1. In this connexion, the higher the values of [Mnsf]*/ [Mn4+]*, the wider the extent of the upper part of the rising portion where (20) holds, and the log 3kf us E plot is linear. Practically when only Mn4f is present in the bulk of the solution the log 3kf us E plot is linear for i/id > l/2 (log 3kf > -3.4). In view of (21) the slope of the straight line in Fig. 3 is given by -0.434 x (aF/RT). The value 0.22 has been obtained for the electron-transfer coefficient cc. The voltammetric waves are very reproducible as far as their shape is concerned, but tend to shift along the potential axis. The fluctuations occur within a range of 20 mV. The corresponding uncertainty about the intersection point of the log 3kf 2rsE line with the potential axis causes the value of the kinetic parameter 3kf” to be poorly reproducible. 1. 2. 3. 4. 5. 6. 7. 8. 9.
REFERENCES D. Cozzr, G. RASPI and L. Nuccr, J. electroanal. Chem. 12,36 (1966). K. J. VEER and G. MANECKE, 2. phys. Chem. 195,270 (1950). K. J. VETIXRand G. MANECKE; 2. >h&. Chem. 195; 337 (1950). P. DELAHAY. New InstrumentalMethods in Electrochemistrv. D. 48. Interscience. New York (1954). . ~I G. GRUBE&d H. HUBERICH, Z. Elektrochem. 29,s (192jj.’ I. SHAIN,J. phys. Chem. 65,259 (1961). D. COZZI, G. CIANTELLIand R. GUIDELU,in preparation. M. v. STACKELBERQ, M. RLGRAM and V. TOOME,Z. Elektrochem. 57, 342 (1953). P. DELAHAY,New Instrumental Methods in Electrochemistry, p. 218. Interscience, New York (1954).