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About the voltammetric determination of the stability constants for some metal ions complexes with the hydrogen sulfide anion
Talanta 45 (1998) 1031 – 1033
Letter to the editor
About the voltammetric determination of the stability constants for some metal ions complexes with the hydrogen sulfide anion Florinel Gabriel Ba˘nica˘ *, Ana Ion Norwegian Uni6ersity of Science and Technology (NTNU), Department of Chemistry, N-7034, Trondheim, Norway Received 30 May 1997; accepted 13 June 1997
Recently Luther, III et al. used square wave voltammetry on the mercury drop electrode to measure the stability constants of some metal ion-hydrogen sulfide complexes at a very low concentration level [1]. The stability constants are defined as bj =[Mj (HS − )2 j − 1]/[M2 + ] j[HS − ]. It was assumed that the potential of the anodic peak due to mercury oxidation is a function of SH − concentration according to the Nernst equation. It was also presumed that the binding of SH − to a metal ion induces a shift in the peak potential which is dependent on both the combining ratio and the stability of the soluble complexes. Taking into account these postulates, the formalism of DeFord and Hume [2,3] was employed to calculate the stability constants in several metal ionSH − systems. It is noteworthy that this formalism was originally developed for the case of the reversible polarographic reduction of a metal ion in the presence of a high excess of ligand giving a series of successive labile complexes. Under these conditions it is possible to compute the formation constants as the coefficients of a polynomial relating the ligand concentration to the values of the shift in the half-wave potential (Eq. 5 and 6 in * Corresponding author.
[1]). A graphical method was used initially to this end, but dedicated computer programs were subsequently developed [4,5]. The graphical method consists in the sequential determination of the formation constants bj using the extrapolation of non-linear curves. In the commented paper [1] the curves were fitted by empirical interpolation functions and then extrapolated to zero in order to find the values of the formation constants. Apparently this allows a better accuracy as compared with the graphical procedure, although the main drawback of the non-linear extrapolation cannot be completely removed. An example of calculation is provided in Fig. 1 [1] for the nickel ion and also the experimental data used in this case are available (Table 1 in [1]). A summary examination of Fig. 1 in [1] reveals however a high scatter of the points on the third and fourth graphs as well as a marked deviation of the line in the fourth graph from the horizontal, which is at variance with the theory [2,3]. Another reason for scepticism is the discrepancy between the huge values of the reported constants and the minute shift in the peak potential. These findings prompted us to recalculate the values of the formation constants by means of the multiparametric curve fitting procedure. The
0039-9140/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 3 9 - 9 1 4 0 ( 9 7 ) 0 0 1 9 0 - 2
1032
F.G. Ba˘nica˘, A. Ion / Talanta 45 (1998) 1031–1033
sol6er tool of the Microsoft Excel 5 spreadsheet program was used to this end according to the recommendations in [6]. Accordingly, the values of the parameters bj were adjusted as to get the minimum value of the sum of squares of the residuals, S(F0,calc-F0,exp)2, where F0,exp represents the values of the function F0 in Table 1 [1] and F0,calc the values calculated by Eq. 5 in the same reference. This procedure is similar to that previously used by Meites [4]. It was tested with the data of Heath and Hefter [7] and gave results in excellent agreement with that obtained in the quoted paper by the graphical method. The following values of the b constants were found in this way for the Ni2 + – SH − system by means of the experimental data in [1]: b3 = 1.06× 1016; b2 = − 1.15 ×1011; b1 =6.16 ×105; b0 =0.118. It is very important to note that the results obtained by an accurate numerical computation are in conflict with two strong physical restrictions: (i) one of the constant gets a negative value and (ii) b0 strongly differs from 1, the value expected on theoretical ground [2,3]. Since it could be presumed that this failure is due to an inappropriate complexation model the same procedure was applied by assuming that the maximum co-ordination number, n is either 4 or 2 instead of 3 (a linear model with n= 1 is
Fig. 1. Residuals distribution. b values from [1] () or calculated in this paper ().
clearly not appropriate). The results in both these cases shows the same kind of disagreement with the theoretical prerequisite. In addition the residuals obtained with the values in [1] shows a clear deterministic trend and monotonously increase with the rise of Ni2 + concentration reaching anomalously high values whereas the residuals computed with the above given b values are very small and randomly distributed around zero (Fig. 1). However, in view of the inconsistency above mentioned under (i) and (ii) the b values reported in the present paper should be considered only as empirical coefficient of a fitting polynomial without any physico-chemical meaning. It is easy to prove that the theoretical ground of the method in [1] is formally correct. It results therefore that the experimental data in Table 1 [1] do not fulfil the conditions for the application of DeFord and Hume method and any attempt to calculate some stability constant in this way leads to erroneous results. This is not due to some computing errors but to an intrinsic inconsistency of the above procedure with the chemistry of the investigated system. Presumably the actual combination scheme is completely different from that assumed in [1] and the formation of solid phases should also be taken into account. The adsorption of sulfide ion or its metal ion compounds is another source for deviation from the requirements of the DeFord and Hume method. There is still at least one methodological fault in [1] in connection with the prerequisite of a high excess of ligand [2,3]. This condition secures the absence of any significant ligand concentration gradient near the electrode surface. The ligand (in a broader sense) is in [1] the metal ion and the concentration ratio Ni2 + /HS − for the data in Fig. 1 and Table 1 ranges between only about 1 and 5. For comparison, the ligand/ metal ratio in the Cd2 + -Cl − system investigated in [7] extends from about 10 to 2.5× 104. Some uncertainty also arises from the composition of the background electrolyte (half-diluted sea water). The complex ionic composition as well as the presence of natural surface active compounds may contribute to the deviation form the expected behavior. In this connection it is
F.G. Ba˘nica˘, A. Ion / Talanta 45 (1998) 1031–1033
important to point out that any method for the determination of physico-chemical constants in natural water samples should be previously tested using synthetic samples with a well known composition. It results therefore that the stability constants for the species [Nij (HS − )]2 j − 1 reported in [1] are at least dubious. In view of the previous comments it is also questionable how reliable are the stability constants determined in [1] by the same method for other metal ions (Mn2 + , Fe2 + , Co2 + ).
.
1033
References [1] G.W. Luther III, D.T. Rikhard, S. Theberge, A. Olroyd, Environ. Sci. Technol. 30 (1996) 671 – 679. [2] D.D. DeFord, D.N. Hume, J. Am. Chem. Soc. 73 (1951) 5321 – 5322. [3] Z. Galus, Fundamentals of Electrochemical Analysis, Ch. 14, Ellis Horwood, New York, 1994. [4] L. Meites, Talanta 22 (1975) 561 – 572. [5] D.J. Leggett, Talanta (1980) 787 – 793. [6] S. Walsh, D. Diamond, Talanta 42 (1995) 561 – 572. [7] G.A. Heath, G. Hefter, J. Electroanal. Chem. 84 (1977) 295 – 302.
Letter to the editor
About the voltammetric determination of the stability constants for some metal ions complexes with the hydrogen sulfide anion Florinel Gabriel Ba˘nica˘ *, Ana Ion Norwegian Uni6ersity of Science and Technology (NTNU), Department of Chemistry, N-7034, Trondheim, Norway Received 30 May 1997; accepted 13 June 1997
Recently Luther, III et al. used square wave voltammetry on the mercury drop electrode to measure the stability constants of some metal ion-hydrogen sulfide complexes at a very low concentration level [1]. The stability constants are defined as bj =[Mj (HS − )2 j − 1]/[M2 + ] j[HS − ]. It was assumed that the potential of the anodic peak due to mercury oxidation is a function of SH − concentration according to the Nernst equation. It was also presumed that the binding of SH − to a metal ion induces a shift in the peak potential which is dependent on both the combining ratio and the stability of the soluble complexes. Taking into account these postulates, the formalism of DeFord and Hume [2,3] was employed to calculate the stability constants in several metal ionSH − systems. It is noteworthy that this formalism was originally developed for the case of the reversible polarographic reduction of a metal ion in the presence of a high excess of ligand giving a series of successive labile complexes. Under these conditions it is possible to compute the formation constants as the coefficients of a polynomial relating the ligand concentration to the values of the shift in the half-wave potential (Eq. 5 and 6 in * Corresponding author.
[1]). A graphical method was used initially to this end, but dedicated computer programs were subsequently developed [4,5]. The graphical method consists in the sequential determination of the formation constants bj using the extrapolation of non-linear curves. In the commented paper [1] the curves were fitted by empirical interpolation functions and then extrapolated to zero in order to find the values of the formation constants. Apparently this allows a better accuracy as compared with the graphical procedure, although the main drawback of the non-linear extrapolation cannot be completely removed. An example of calculation is provided in Fig. 1 [1] for the nickel ion and also the experimental data used in this case are available (Table 1 in [1]). A summary examination of Fig. 1 in [1] reveals however a high scatter of the points on the third and fourth graphs as well as a marked deviation of the line in the fourth graph from the horizontal, which is at variance with the theory [2,3]. Another reason for scepticism is the discrepancy between the huge values of the reported constants and the minute shift in the peak potential. These findings prompted us to recalculate the values of the formation constants by means of the multiparametric curve fitting procedure. The
0039-9140/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 3 9 - 9 1 4 0 ( 9 7 ) 0 0 1 9 0 - 2
1032
F.G. Ba˘nica˘, A. Ion / Talanta 45 (1998) 1031–1033
sol6er tool of the Microsoft Excel 5 spreadsheet program was used to this end according to the recommendations in [6]. Accordingly, the values of the parameters bj were adjusted as to get the minimum value of the sum of squares of the residuals, S(F0,calc-F0,exp)2, where F0,exp represents the values of the function F0 in Table 1 [1] and F0,calc the values calculated by Eq. 5 in the same reference. This procedure is similar to that previously used by Meites [4]. It was tested with the data of Heath and Hefter [7] and gave results in excellent agreement with that obtained in the quoted paper by the graphical method. The following values of the b constants were found in this way for the Ni2 + – SH − system by means of the experimental data in [1]: b3 = 1.06× 1016; b2 = − 1.15 ×1011; b1 =6.16 ×105; b0 =0.118. It is very important to note that the results obtained by an accurate numerical computation are in conflict with two strong physical restrictions: (i) one of the constant gets a negative value and (ii) b0 strongly differs from 1, the value expected on theoretical ground [2,3]. Since it could be presumed that this failure is due to an inappropriate complexation model the same procedure was applied by assuming that the maximum co-ordination number, n is either 4 or 2 instead of 3 (a linear model with n= 1 is
Fig. 1. Residuals distribution. b values from [1] () or calculated in this paper ().
clearly not appropriate). The results in both these cases shows the same kind of disagreement with the theoretical prerequisite. In addition the residuals obtained with the values in [1] shows a clear deterministic trend and monotonously increase with the rise of Ni2 + concentration reaching anomalously high values whereas the residuals computed with the above given b values are very small and randomly distributed around zero (Fig. 1). However, in view of the inconsistency above mentioned under (i) and (ii) the b values reported in the present paper should be considered only as empirical coefficient of a fitting polynomial without any physico-chemical meaning. It is easy to prove that the theoretical ground of the method in [1] is formally correct. It results therefore that the experimental data in Table 1 [1] do not fulfil the conditions for the application of DeFord and Hume method and any attempt to calculate some stability constant in this way leads to erroneous results. This is not due to some computing errors but to an intrinsic inconsistency of the above procedure with the chemistry of the investigated system. Presumably the actual combination scheme is completely different from that assumed in [1] and the formation of solid phases should also be taken into account. The adsorption of sulfide ion or its metal ion compounds is another source for deviation from the requirements of the DeFord and Hume method. There is still at least one methodological fault in [1] in connection with the prerequisite of a high excess of ligand [2,3]. This condition secures the absence of any significant ligand concentration gradient near the electrode surface. The ligand (in a broader sense) is in [1] the metal ion and the concentration ratio Ni2 + /HS − for the data in Fig. 1 and Table 1 ranges between only about 1 and 5. For comparison, the ligand/ metal ratio in the Cd2 + -Cl − system investigated in [7] extends from about 10 to 2.5× 104. Some uncertainty also arises from the composition of the background electrolyte (half-diluted sea water). The complex ionic composition as well as the presence of natural surface active compounds may contribute to the deviation form the expected behavior. In this connection it is
F.G. Ba˘nica˘, A. Ion / Talanta 45 (1998) 1031–1033
important to point out that any method for the determination of physico-chemical constants in natural water samples should be previously tested using synthetic samples with a well known composition. It results therefore that the stability constants for the species [Nij (HS − )]2 j − 1 reported in [1] are at least dubious. In view of the previous comments it is also questionable how reliable are the stability constants determined in [1] by the same method for other metal ions (Mn2 + , Fe2 + , Co2 + ).
.
1033
References [1] G.W. Luther III, D.T. Rikhard, S. Theberge, A. Olroyd, Environ. Sci. Technol. 30 (1996) 671 – 679. [2] D.D. DeFord, D.N. Hume, J. Am. Chem. Soc. 73 (1951) 5321 – 5322. [3] Z. Galus, Fundamentals of Electrochemical Analysis, Ch. 14, Ellis Horwood, New York, 1994. [4] L. Meites, Talanta 22 (1975) 561 – 572. [5] D.J. Leggett, Talanta (1980) 787 – 793. [6] S. Walsh, D. Diamond, Talanta 42 (1995) 561 – 572. [7] G.A. Heath, G. Hefter, J. Electroanal. Chem. 84 (1977) 295 – 302.