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Correlations of polarographic and spectroscopic parameters of metal ions of the first transition series
inorg, nucL Chem• Vol. 42, pp. 863.-867 Pergamon Press Ltd.. 1980 Printed in Great Britain
CORRELATIONS OF POLAROGRAPHIC AND SPECTROSCOPIC PARAMETERS OF METAL IONS OF THE FIRST TRANSITION SERIES D. R. CROW and J. G. SHARP Department of Physical Sciences, The Polytechnic, Wolverhampton, England
(Received 15 August 1979; receivedfor publication 12 September 1979) Abstraet--A complementary relationship is reported between the activation energy of electrochemical reduction and the crystal field splitting parameter for divalent aquo ions of the First Transition Series. This is interpreted in terms of QE,2being the energy requirement in excess of Aofor the reduction process; the quantity (OF,,, + Ao) being approximately constant for the series•
INTRODUCTION
Correlations between the activation energies (Q) for polarographic reduction of metal complexes and spectroscopic parameters were first reported by Vlcek[1-3]. When considering substitution-inert complexes of the type MX6 by a hetero ligand species, Y, to yield MX5 Y or MX4 Y2, a linear relationship was observed between successive values of Q and corresponding values of the shift in the main UV-visible absorption bands relative to those of the parent, unsubstituted, complex. Similar correlations of half-wave potentials and/or activation energies with the frequencies of d-d transitions have been reported [4-7]. It would appear thai activation energies for electroreduction of related complexes of the same central metal ion are related to individual d-d transition energies and therefore ultimately to the values of the crystal field splitting parameter, Ao. In contrast to previous workers who were concerned with the correlation of spectroscopic and polarographic parameters for families of complexes with the same central metal ion, this paper reports the behaviour of complexes of different metal ions with constant ligand complement. EXPERIMENTAL Activation energies for the electroduction of a number of first-row transition metal ions characterised by M2+ +2~ ~ M o were determined from polarographic waves, plotted manually over a range of temperatures, by use of the equation[8]
Q
Qo log ~ - log A' 2.303RT ld--l where A', the apparent frequency factor, combines all the temperature-independent terms, Qo being the activation energy for the process of diffusion to the electrode as distinct from Q referring to the electrode process. Values of Q are readily determined from the slopes of graphs of log i/(id - i) vs lIT for a fixed value of applied potential. Aquated ions of Mn2+, Fe2÷, Co2+, Ni2+ and Zn2÷ were investigated at a concentration of 5 x l0 -4 tool dm-3 in the forms of MnSO4, (NH4)2SO4, FeSO4.6H20, Co(NO3)2, Ni(NO3)2 and ZnSO4 of AnalaR grade. The supporting electrolyte used in most cases was 0.1 tool dm-3 potassium nitrate although for the cases of Mn2+ and Fe2-~, potassium chloride was found to be more 863
suitable, giving rise to more stable and reproducible results. In all cases the minimum quantity of Triton-X-100 was used as maximum suppressor (usually at a level of 0.0005%). Standardisation of technique and conditions throughout the entire range of temperatures was of prime consideration. Since halfwave potentials depend upon the nature and temperature coefficient of the reference electrode used, a common saturated calomel electrode, thermostatted throughout at 298°K, was used for all determinations which were made a number of times for each metal ion in order to ensure consistency of values. An H-type cell, containing in one limb the dropping mercury indicator electrode, degassing components and working solution, was immersed in a lagged water bath whose temperature was controllable to within _+0.1°Cby a "Circon" thermostat unit. An agar plug, saturated with supporting electrolyte, and supported by a sintered disc, provided electrical contact with the other limb containing a solution of supporting electrolyte. A KCl/agar salt bridge connected this latter section with a saturated calomel electrode immersed in a second waterbath, maintained at 25_+ 0.1°C by means of a second thermostat unit. The details of construction and operation of this arrangement is described elsewhere[9]. By these means the run-to-run reproducibility of half-wave potential data at various temperatures via normal determination of current-potential curves was found to be greatly improved over that obtained using a cell in which the reference electrode temperature was varied with that of the working solution. Apparently the temperature hysteresis associated with the calomel electrode[10, l l] was effectively obviated. Potentials were applied to the cell via a Tinsley potentiometer Type 3387B, the resultant cell currents being detected by means of a Pye Scalamp D.C. microammeter with calibrated ranges of l-l,000#A. "White Spot" nitrogen was passed initially through and subsequently over the working solutions, after preliminary passage through a train of coils and flasks immersed in the variable temperature bath to attain the temperature of the working solutions. Confirmation of diffusion control was obtained from linear plots of limiting current vs square root of mercury column height; the polarograms for this ,exercise being obtained automatically with the aid of a Heathkit D.C. Polarograph. RESULTS AND DISCUSSION Attempted correlation between polarographic quantities and the frequencies of principal absorption bands for a series of different central metal ions is confused by the fact that the bands correspond to different electronic transitions for each metal ion. Consequently, the crystal field splitting parameter, Ao, has been chosen as a more appropriate quantity. The populations of some of the graphs which follow
864
D.R. CROW and J. G. SHARP
are subject to a number of limitations: (i) the variable stability of the (2+) oxidation state across the periodic table; (ii) the value of half-wave potential with respect to the d.m.e, working range, which sometimes precludes the use of strong field ligands such as CN-; (iii) variable geometry of members of a particular complex series which can be further influenced by Jahn-Teller distrotion. In Table I are collected a number of significant parameters for the complex species in question. It is noteworthy that while the variations of E,2, E ~, and ( G / 2 - E ~) with Ao are characterised by curved plots (Figs. 1A-1C), a linear correlation is obtained for all the metal ions between the function an(G/2-E e) and Ao (Fig. 1D). It is apparent from Table 1 that half-wave potentials become increasingly positive with increase in atomic number of the central ion and their values may be correlated with the number of t2~ electrons, assuming high-spin electronic configurations. In fact, linear correlations are obtained for aqua, trioxalato, thiocyanato [1216] and ammine[17-19] complexes as shown in Fig. 2. In contrast to previously reported positive dependence of Q on Ao, for related complexes of the same metal ion, jt is clear from Table 1 that, when considering complexes
co
14
3
,,,~ '~
:'"'-----~
°'~
I0 J
4
~
6
ntz°
Fig. 2. Variation of half-wave potential with the number of t2g electrons for first row metal ion complexes.
,so
\ I
140
\
\
/=
',I
t20
\
p.. "t('3
/
s
/
•
•
'~
J"%
/
/
/ •
J
s/
Table 1. Polarographic and spectroscopic parameters for some first row transition metal ions M2+(aq)
Cr2+ Mn:+
ElnlV vsSCE E°/V vs SCE an(Eln Ee)/V Qe,~/kJ mol-~ QEo/kJ m01 i Ao/cm-~
1.44
Fe2+ Co2+ Ni~+ Zn2+
1.48 1.31 1.34 0.68 -0.26 0.72 -109 43 -213 319 13900 7800 10400 --
-
1.20 0.52 0.41 104 9200
1.00 0.996 0.48 1.003 0.37 0 110 67 228 65 8500 --
~
6O
0 40
Cr'z+
i
i
i
L
i
i
Mnz+
ge 2+
Coz+
Niz+
Cu2+
Znz+
Fig. 3. Demonstration of the complementary relationship between QE~I=and ~ across the seriesof first row ions. (open squares
and circles are experimen!al points, full square and circle are estimated values). ~,,, 1 2 >
I0
\
1
A
8
0 6 >
9
10
~/~Fe
0 4
II
12
13
2+
/ Ni2+
B
/ q• o 2
Mn2+/
9,
~e,
IO ,
",
~2
13
Mn2+
-. 0 6 1~05 08
C
Fe2+ 8
~
I0
II
12
13
~
Ao/IO crn
Fig. 1. Variation of polarographic functions with magnitude of splitting parameter Ao.
of different metal ions, high values of Q accompany low values of Ao and vice versa (Fig. 3). The reciprocal relationship between Q and Ao with increasing atomic number would indicate that a reassessment of the significance of measured Q values is required. In this respect it is interesting to note that the quantity (Q + Ao) is approximately constant for the metal ions studied. If it is assumed that Q, either wholly or partly, is a measure of the energy requirements in excess of Ao for the reduction process, then this would explain why, on the basis of approximately constant total energy---equivalent to the electron affinity and analogous to the approximately constant values for total ionisation potential--the values of Q and A are complementary. Further correlations exist between parameters obtained in this study and kinetic data for the reaction of the metal ions with hydrated electrons. Thus Qe,2 values relate linearly to the logarithms of the corresponding rate constants for reaction with hydrated electrons as determined by Baxendale[20] (Fig. 4). It has been suggested[21] that the rate of reaction of e-(aq) with different transition metal ions is diffusion controlled, being determined only by their rates of diffusion, effective diameter and charge. This provides a qualitative explanation for the observed correlation between the
Correlations of polarographicand spectroscopicparameters of metal ions of the first transition series
I10
865
t +
I00 9C 8O 7O 0
,.;~60 50 40 3O
~Fe
2+ i
85
9 0
91.5
lO0
log k e-
Fig. 4. Graph of Q~,~2vs logarithmof rate constant for reaction of various ions with hydrated electrons.
107 Ni2+~ 9.7
,
C02+
9.5
_~ 8.9
Z
8.5
I.'6
117
, 1~
119
2'0
~
+
2'.1
2'.2
213
2'.4
AQD/IO-2nm.kJ Fig. 5. Logarithmof rate constantfor reactionwith hydratedelectrons plottedas a functionof the productof ion radius and diffusionactivation energy.
above values of log k and the corresponding product of the ionic radius[22] and activation energy of diffusion, AQo, as shown in Fig. 5. It is further found that A and Qo are related for all the metal ions concerned here. With regard to the non-linear dependence of values of E,/2 or overvoltage (Et/2-E °) upon Ao, it is clear that potential data above are insufficient to explain the behaviour of irreversible electrochemical reductions. While the availability of electrons is determined by the magnitude of the overvoltage, the efficiency with which they may be received by a complex is measured by an, which is related to the structural and/or electronic rearrangement prior to the formation of the activated state at the electrode surface. Thus the product an (E,/2-E°), related to the hypothetical activation energy at E ~, is found to correlate linearly with Ao. For all of the complexes considered, the relationship between values of E,/2 and the corresponding number of hR electrons in the high spin configuration of the central
metal ion, suggests that E,/2, often considered to be uniquely characterised by particular electrochemical conditions, is further dependent upon the configuration of the ground state reactant species. This is supported by similar relationships for the ligands oxalate, thiocyanate and ammonia. In the light of previous correlations it is a little difficult to explain the reciprocal relationship between QE]/2 and Ao, until the nature of the depolarisers and the probable mechanism of electroreduction are considered. Most previous correlations were reported for substitution-inert (low spin) complexes of Co(Ill) and Rh(III) where it was postulated that, during the formation of the activated state, vacation of previously filled low energy t2,~ orbitals occurred through "electrode field excitation", allowing direct transfer of electrons from mercury to such vacated orbitals in the electrode process proper. In such cases the structure of the primary product of the electrode process is essentially the same as that of the
866
D.R. CROWand J. G. SHARP
original depolariser. In the cases considered here, however, the product of the electrode reaction is the metal itself, as expected for the reduction of labile complexes and implying an SN 1 reaction rather than SN 2 to be expected with inert complexes. Further, if excitation of tzf electrons to the antibonding eg level were to occur, this would presumably only be necessary in the cases of Co 2+ and Ni 2+ since Mn2÷ and Fe 2+ have sufficient singly-filled t:, orbitals to apparently allow direct reaction with the electrode. The fact that data for all four ions correlate with the spectral data would suggest that the mechanism of reduction is essentially the same in all cases. If an SN 1 mechanism is considered, then the stages involved during the overall reduction process for a hexaqua ion are as follows: [M(H20),s]2+ "* [M(H20)sH20*] -* [M(HzO)s]2+ + H20* 2~
M(Hg) + 5H20 <
[M(HzO)sHg]"
more readily available; (ii) the field gradient across the electrode/solution interface increases. 3. A point is reached where the induced ligand field strength becomes comparable to that which would obtain in the transition state complex involving combination of mercury, so that a water molecule may be displaced from the depolarizer. 4. Electron transfer occurs from mercury to vacant orbitals on the depolarizer ion, the configuration of the neutral metal atom is reached and the ligand field collapses with the removal of the remaining water molecules. According to this model, the greater the value of Ao in a given depolarizer, the smaller will be the additional energy (the experimental activation energy) that the electrode and its field must provide. It is significant that (QE,2 + Ao) is approximately constant for the metal ions considered, i.e. the total energy which may be regarded as the total electron affinity (~) is approximately constant. For two similar complexes with different control metal ion, MX6, M'X6 this may be represented by
i.e. the activated state is one in which the electrode has effectively replaced one water molecule as a ligand. So far as the changes in the internal electronic structure in passing from depolarizer to final product are concerned, we are considering a transition from an aquated ion, in which the weak ligand field exerted by water has induced a characteristic b, -e~ splitting of magnitude ~o, to one in which a five-fold degeneracy obtains in the final product. In order to explain this transition in the light of the reported observations, it is necessary to consider (albeit qualitatively) what happens to the depolarizer within the high field exerted by the electrode and to bear in mind that, during the electrode process proper, unimpeded (zero activation energy) electron transfer must occur between mercury and depolarizer. That is, electron transfer must occur between states of equal energy (equal electron affinity) according to the requirements of the Franck-Condon principle. Also, the sign of the charge on the electrode must be considered in all cases reduction occurred at potentials well to the negative side of the electrocapiilary zero. Thus it is necessary to consider passage of depolarizer particles from the bulk solution into a region of very high field gradient across the diffuse and Helmholtz double layers, to a negatively charged surface. Four effects become apparent:
%0.,
T I
O'
l
~'o
Eo5
(~consl,
~ o MX s
M'X6
Such an hypothesis is supported by the analogous values of total ionisation potential which, when measured in a constant environment, are approximately constant. Conversely, when related complexes of the same central metal ion are considered, the electron affinity is expected to vary with change in ligand complement. If the relative magnitudes of the functions Q~,: and Ao are not appreciably disturbed, then the positive dependence of QEI/2 and Ao is predicted as has been observed with complexes of Ni2+ [4]. The energy requirements for the electroreduction of a series of related complexes MX6, MY6, MZ~ may then be envisaged as:
I
OY
I
*fX
q[/. ~y
(~o~
Ao,
MX6
1. The negative charge on the electrode will increase the ligand field of those ligands directly approaching the electrode surface, i.e. Ao will be effectively increased. 2. Increase of negative potential of the electrode gives rise to two interrelated effects: (i) electrons are made
MZ6
Further evidence for a constant reduction mechanism throughout the series is provided by the correlation of the Q~In data with the kinetic data of Baxendale for reaction with hydrated electrons. Little else can be coneluded from this observation since while the former
Correlations of polarographic and spectroscopic parameters of metal ions of the first transition series relate to heterogeneous reactions at an electrode/solution interface the latter apply to homogeneous processes. However, the correlation of Baxendale's data for rate constants of the diffusion-controlled reactions with our data for the diffusion activation energies would suggest the essential correctness of the latter. REFERENCES
1. A. A. Vlcek, Discuss. Faraday Soc. 24, 164 (1958). 2. A. A. Vlcek, Paper presented at 18th Meeting of CITCE (1%7). 3. A. A. Vlcek, Progress in Inorganic Chemistry (Edited by F. A. Cotton), Vol. V, p. 363. Interscience, New York. 4. S. I. Woodburn and R. J. Magee, Aust. J. Chem. 20, 439 (1%7). 5. D. R. Crow, lnorg. Nucl. Chem. Lett. 5, 291 0%9). 6. R. J. Magee and W. H. Douglas, J. Inorg. Nucl. Chem. 26, 1707 (1964). 7. R. J. Magee and 1. A. M. Beattie, Anal. Chim. Acta 28, 253 (1%3). 8. A. A. Vlcek, Coll. Czech. Chem. Communs. 24, 3538 (1959). 9. D. R. Crow and J. G. Sharp, Talanta, 26, 1043 (1979).
867
10. J. G. Ives and G. J. Janz, Reference Electrodes, Academic Press (1%1). 11. A. K. Covington, J. V. Dobson and Lord Wynne-Jones, Electrochemica Acta 12,525 (1967). 12. I. A. Korsunor and M. K. Scennikova, Z Anal. Chim. 4, 5 (1949). 13. J. J. Lingane and H. Kedinger, Ind. Engng Chem. Anal. Ed. 13, 77 (1941). 14. R. E. Frank and D. M. Hume, J. Am. Chem. S~c. 75, 1736 (1953). 15. R. Tanaka, R. Tamamushi and 1. Storn, mezinar, polarogr. sjezdu, dil I; str. 486 Privodoredecke nakladatelstri. Praha (1951). 16. E. T. Verdier, Coll. Czech. Chem. Communs. II, 216 (1939). 17. J. J. Lingane, Ind. Engng Chem. Anal. Ed. 18, 429 t1946). 18. P. N. Kovalenko and L. S. Nadezina, Z. Obx. Chim. 22. 740 (1952). 19. M. Voriskova, Coll. Czech. Chem. Communs. !i, 580 (1939). 20. J. H. Baxendale, Nature 201,468 (1964). 21. H. A. Schwarz, Radiation Res. Suppl. 4, 89 (1964). 22. F. Basolo and R. G. Pearson, Mechanisms of Inorganic Reactions, 2nd Edn, p. 81. Wiley, New York (1%7).
CORRELATIONS OF POLAROGRAPHIC AND SPECTROSCOPIC PARAMETERS OF METAL IONS OF THE FIRST TRANSITION SERIES D. R. CROW and J. G. SHARP Department of Physical Sciences, The Polytechnic, Wolverhampton, England
(Received 15 August 1979; receivedfor publication 12 September 1979) Abstraet--A complementary relationship is reported between the activation energy of electrochemical reduction and the crystal field splitting parameter for divalent aquo ions of the First Transition Series. This is interpreted in terms of QE,2being the energy requirement in excess of Aofor the reduction process; the quantity (OF,,, + Ao) being approximately constant for the series•
INTRODUCTION
Correlations between the activation energies (Q) for polarographic reduction of metal complexes and spectroscopic parameters were first reported by Vlcek[1-3]. When considering substitution-inert complexes of the type MX6 by a hetero ligand species, Y, to yield MX5 Y or MX4 Y2, a linear relationship was observed between successive values of Q and corresponding values of the shift in the main UV-visible absorption bands relative to those of the parent, unsubstituted, complex. Similar correlations of half-wave potentials and/or activation energies with the frequencies of d-d transitions have been reported [4-7]. It would appear thai activation energies for electroreduction of related complexes of the same central metal ion are related to individual d-d transition energies and therefore ultimately to the values of the crystal field splitting parameter, Ao. In contrast to previous workers who were concerned with the correlation of spectroscopic and polarographic parameters for families of complexes with the same central metal ion, this paper reports the behaviour of complexes of different metal ions with constant ligand complement. EXPERIMENTAL Activation energies for the electroduction of a number of first-row transition metal ions characterised by M2+ +2~ ~ M o were determined from polarographic waves, plotted manually over a range of temperatures, by use of the equation[8]
Q
Qo log ~ - log A' 2.303RT ld--l where A', the apparent frequency factor, combines all the temperature-independent terms, Qo being the activation energy for the process of diffusion to the electrode as distinct from Q referring to the electrode process. Values of Q are readily determined from the slopes of graphs of log i/(id - i) vs lIT for a fixed value of applied potential. Aquated ions of Mn2+, Fe2÷, Co2+, Ni2+ and Zn2÷ were investigated at a concentration of 5 x l0 -4 tool dm-3 in the forms of MnSO4, (NH4)2SO4, FeSO4.6H20, Co(NO3)2, Ni(NO3)2 and ZnSO4 of AnalaR grade. The supporting electrolyte used in most cases was 0.1 tool dm-3 potassium nitrate although for the cases of Mn2+ and Fe2-~, potassium chloride was found to be more 863
suitable, giving rise to more stable and reproducible results. In all cases the minimum quantity of Triton-X-100 was used as maximum suppressor (usually at a level of 0.0005%). Standardisation of technique and conditions throughout the entire range of temperatures was of prime consideration. Since halfwave potentials depend upon the nature and temperature coefficient of the reference electrode used, a common saturated calomel electrode, thermostatted throughout at 298°K, was used for all determinations which were made a number of times for each metal ion in order to ensure consistency of values. An H-type cell, containing in one limb the dropping mercury indicator electrode, degassing components and working solution, was immersed in a lagged water bath whose temperature was controllable to within _+0.1°Cby a "Circon" thermostat unit. An agar plug, saturated with supporting electrolyte, and supported by a sintered disc, provided electrical contact with the other limb containing a solution of supporting electrolyte. A KCl/agar salt bridge connected this latter section with a saturated calomel electrode immersed in a second waterbath, maintained at 25_+ 0.1°C by means of a second thermostat unit. The details of construction and operation of this arrangement is described elsewhere[9]. By these means the run-to-run reproducibility of half-wave potential data at various temperatures via normal determination of current-potential curves was found to be greatly improved over that obtained using a cell in which the reference electrode temperature was varied with that of the working solution. Apparently the temperature hysteresis associated with the calomel electrode[10, l l] was effectively obviated. Potentials were applied to the cell via a Tinsley potentiometer Type 3387B, the resultant cell currents being detected by means of a Pye Scalamp D.C. microammeter with calibrated ranges of l-l,000#A. "White Spot" nitrogen was passed initially through and subsequently over the working solutions, after preliminary passage through a train of coils and flasks immersed in the variable temperature bath to attain the temperature of the working solutions. Confirmation of diffusion control was obtained from linear plots of limiting current vs square root of mercury column height; the polarograms for this ,exercise being obtained automatically with the aid of a Heathkit D.C. Polarograph. RESULTS AND DISCUSSION Attempted correlation between polarographic quantities and the frequencies of principal absorption bands for a series of different central metal ions is confused by the fact that the bands correspond to different electronic transitions for each metal ion. Consequently, the crystal field splitting parameter, Ao, has been chosen as a more appropriate quantity. The populations of some of the graphs which follow
864
D.R. CROW and J. G. SHARP
are subject to a number of limitations: (i) the variable stability of the (2+) oxidation state across the periodic table; (ii) the value of half-wave potential with respect to the d.m.e, working range, which sometimes precludes the use of strong field ligands such as CN-; (iii) variable geometry of members of a particular complex series which can be further influenced by Jahn-Teller distrotion. In Table I are collected a number of significant parameters for the complex species in question. It is noteworthy that while the variations of E,2, E ~, and ( G / 2 - E ~) with Ao are characterised by curved plots (Figs. 1A-1C), a linear correlation is obtained for all the metal ions between the function an(G/2-E e) and Ao (Fig. 1D). It is apparent from Table 1 that half-wave potentials become increasingly positive with increase in atomic number of the central ion and their values may be correlated with the number of t2~ electrons, assuming high-spin electronic configurations. In fact, linear correlations are obtained for aqua, trioxalato, thiocyanato [1216] and ammine[17-19] complexes as shown in Fig. 2. In contrast to previously reported positive dependence of Q on Ao, for related complexes of the same metal ion, jt is clear from Table 1 that, when considering complexes
co
14
3
,,,~ '~
:'"'-----~
°'~
I0 J
4
~
6
ntz°
Fig. 2. Variation of half-wave potential with the number of t2g electrons for first row metal ion complexes.
,so
\ I
140
\
\
/=
',I
t20
\
p.. "t('3
/
s
/
•
•
'~
J"%
/
/
/ •
J
s/
Table 1. Polarographic and spectroscopic parameters for some first row transition metal ions M2+(aq)
Cr2+ Mn:+
ElnlV vsSCE E°/V vs SCE an(Eln Ee)/V Qe,~/kJ mol-~ QEo/kJ m01 i Ao/cm-~
1.44
Fe2+ Co2+ Ni~+ Zn2+
1.48 1.31 1.34 0.68 -0.26 0.72 -109 43 -213 319 13900 7800 10400 --
-
1.20 0.52 0.41 104 9200
1.00 0.996 0.48 1.003 0.37 0 110 67 228 65 8500 --
~
6O
0 40
Cr'z+
i
i
i
L
i
i
Mnz+
ge 2+
Coz+
Niz+
Cu2+
Znz+
Fig. 3. Demonstration of the complementary relationship between QE~I=and ~ across the seriesof first row ions. (open squares
and circles are experimen!al points, full square and circle are estimated values). ~,,, 1 2 >
I0
\
1
A
8
0 6 >
9
10
~/~Fe
0 4
II
12
13
2+
/ Ni2+
B
/ q• o 2
Mn2+/
9,
~e,
IO ,
",
~2
13
Mn2+
-. 0 6 1~05 08
C
Fe2+ 8
~
I0
II
12
13
~
Ao/IO crn
Fig. 1. Variation of polarographic functions with magnitude of splitting parameter Ao.
of different metal ions, high values of Q accompany low values of Ao and vice versa (Fig. 3). The reciprocal relationship between Q and Ao with increasing atomic number would indicate that a reassessment of the significance of measured Q values is required. In this respect it is interesting to note that the quantity (Q + Ao) is approximately constant for the metal ions studied. If it is assumed that Q, either wholly or partly, is a measure of the energy requirements in excess of Ao for the reduction process, then this would explain why, on the basis of approximately constant total energy---equivalent to the electron affinity and analogous to the approximately constant values for total ionisation potential--the values of Q and A are complementary. Further correlations exist between parameters obtained in this study and kinetic data for the reaction of the metal ions with hydrated electrons. Thus Qe,2 values relate linearly to the logarithms of the corresponding rate constants for reaction with hydrated electrons as determined by Baxendale[20] (Fig. 4). It has been suggested[21] that the rate of reaction of e-(aq) with different transition metal ions is diffusion controlled, being determined only by their rates of diffusion, effective diameter and charge. This provides a qualitative explanation for the observed correlation between the
Correlations of polarographicand spectroscopicparameters of metal ions of the first transition series
I10
865
t +
I00 9C 8O 7O 0
,.;~60 50 40 3O
~Fe
2+ i
85
9 0
91.5
lO0
log k e-
Fig. 4. Graph of Q~,~2vs logarithmof rate constant for reaction of various ions with hydrated electrons.
107 Ni2+~ 9.7
,
C02+
9.5
_~ 8.9
Z
8.5
I.'6
117
, 1~
119
2'0
~
+
2'.1
2'.2
213
2'.4
AQD/IO-2nm.kJ Fig. 5. Logarithmof rate constantfor reactionwith hydratedelectrons plottedas a functionof the productof ion radius and diffusionactivation energy.
above values of log k and the corresponding product of the ionic radius[22] and activation energy of diffusion, AQo, as shown in Fig. 5. It is further found that A and Qo are related for all the metal ions concerned here. With regard to the non-linear dependence of values of E,/2 or overvoltage (Et/2-E °) upon Ao, it is clear that potential data above are insufficient to explain the behaviour of irreversible electrochemical reductions. While the availability of electrons is determined by the magnitude of the overvoltage, the efficiency with which they may be received by a complex is measured by an, which is related to the structural and/or electronic rearrangement prior to the formation of the activated state at the electrode surface. Thus the product an (E,/2-E°), related to the hypothetical activation energy at E ~, is found to correlate linearly with Ao. For all of the complexes considered, the relationship between values of E,/2 and the corresponding number of hR electrons in the high spin configuration of the central
metal ion, suggests that E,/2, often considered to be uniquely characterised by particular electrochemical conditions, is further dependent upon the configuration of the ground state reactant species. This is supported by similar relationships for the ligands oxalate, thiocyanate and ammonia. In the light of previous correlations it is a little difficult to explain the reciprocal relationship between QE]/2 and Ao, until the nature of the depolarisers and the probable mechanism of electroreduction are considered. Most previous correlations were reported for substitution-inert (low spin) complexes of Co(Ill) and Rh(III) where it was postulated that, during the formation of the activated state, vacation of previously filled low energy t2,~ orbitals occurred through "electrode field excitation", allowing direct transfer of electrons from mercury to such vacated orbitals in the electrode process proper. In such cases the structure of the primary product of the electrode process is essentially the same as that of the
866
D.R. CROWand J. G. SHARP
original depolariser. In the cases considered here, however, the product of the electrode reaction is the metal itself, as expected for the reduction of labile complexes and implying an SN 1 reaction rather than SN 2 to be expected with inert complexes. Further, if excitation of tzf electrons to the antibonding eg level were to occur, this would presumably only be necessary in the cases of Co 2+ and Ni 2+ since Mn2÷ and Fe 2+ have sufficient singly-filled t:, orbitals to apparently allow direct reaction with the electrode. The fact that data for all four ions correlate with the spectral data would suggest that the mechanism of reduction is essentially the same in all cases. If an SN 1 mechanism is considered, then the stages involved during the overall reduction process for a hexaqua ion are as follows: [M(H20),s]2+ "* [M(H20)sH20*] -* [M(HzO)s]2+ + H20* 2~
M(Hg) + 5H20 <
[M(HzO)sHg]"
more readily available; (ii) the field gradient across the electrode/solution interface increases. 3. A point is reached where the induced ligand field strength becomes comparable to that which would obtain in the transition state complex involving combination of mercury, so that a water molecule may be displaced from the depolarizer. 4. Electron transfer occurs from mercury to vacant orbitals on the depolarizer ion, the configuration of the neutral metal atom is reached and the ligand field collapses with the removal of the remaining water molecules. According to this model, the greater the value of Ao in a given depolarizer, the smaller will be the additional energy (the experimental activation energy) that the electrode and its field must provide. It is significant that (QE,2 + Ao) is approximately constant for the metal ions considered, i.e. the total energy which may be regarded as the total electron affinity (~) is approximately constant. For two similar complexes with different control metal ion, MX6, M'X6 this may be represented by
i.e. the activated state is one in which the electrode has effectively replaced one water molecule as a ligand. So far as the changes in the internal electronic structure in passing from depolarizer to final product are concerned, we are considering a transition from an aquated ion, in which the weak ligand field exerted by water has induced a characteristic b, -e~ splitting of magnitude ~o, to one in which a five-fold degeneracy obtains in the final product. In order to explain this transition in the light of the reported observations, it is necessary to consider (albeit qualitatively) what happens to the depolarizer within the high field exerted by the electrode and to bear in mind that, during the electrode process proper, unimpeded (zero activation energy) electron transfer must occur between mercury and depolarizer. That is, electron transfer must occur between states of equal energy (equal electron affinity) according to the requirements of the Franck-Condon principle. Also, the sign of the charge on the electrode must be considered in all cases reduction occurred at potentials well to the negative side of the electrocapiilary zero. Thus it is necessary to consider passage of depolarizer particles from the bulk solution into a region of very high field gradient across the diffuse and Helmholtz double layers, to a negatively charged surface. Four effects become apparent:
%0.,
T I
O'
l
~'o
Eo5
(~consl,
~ o MX s
M'X6
Such an hypothesis is supported by the analogous values of total ionisation potential which, when measured in a constant environment, are approximately constant. Conversely, when related complexes of the same central metal ion are considered, the electron affinity is expected to vary with change in ligand complement. If the relative magnitudes of the functions Q~,: and Ao are not appreciably disturbed, then the positive dependence of QEI/2 and Ao is predicted as has been observed with complexes of Ni2+ [4]. The energy requirements for the electroreduction of a series of related complexes MX6, MY6, MZ~ may then be envisaged as:
I
OY
I
*fX
q[/. ~y
(~o~
Ao,
MX6
1. The negative charge on the electrode will increase the ligand field of those ligands directly approaching the electrode surface, i.e. Ao will be effectively increased. 2. Increase of negative potential of the electrode gives rise to two interrelated effects: (i) electrons are made
MZ6
Further evidence for a constant reduction mechanism throughout the series is provided by the correlation of the Q~In data with the kinetic data of Baxendale for reaction with hydrated electrons. Little else can be coneluded from this observation since while the former
Correlations of polarographic and spectroscopic parameters of metal ions of the first transition series relate to heterogeneous reactions at an electrode/solution interface the latter apply to homogeneous processes. However, the correlation of Baxendale's data for rate constants of the diffusion-controlled reactions with our data for the diffusion activation energies would suggest the essential correctness of the latter. REFERENCES
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867
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