Analyst April 1983 Vol. 108 PP. 443-451 Analytical Use of the Kinetics of Complex Formation: Simultaneous Determination of Iron and Cobalt by Differential Kinetic Methods 443 L. Ballesteros and D. P6rez-Bendito” Department of Analytical Chemistry Faculty of Sciences University of Cdrdoba Cdrdoba Spain The kinetic determination of iron and cobalt mixtures without a prior separa-tion is described. The methods are based on the differential reaction rate between pyridoxal thiosemicarbazone and these metallic ions. Various ratios at the M level of the two ions can be determined photometrically by using either the “logarithmic extrapolation” or the “single-point” methods. These two methods are compared. Keywords Iron and cobalt simultaneous determination ; pyridoxal thio-semicarbazone ; kinetics of complex formation ; differential kinetic methods This paper reports part of a general study of the use of thiosemicarbazones in kinetic analysis.So far we have reported results on catalytic - kinetic analysisl-4 and catalytic titrations.596 We have now extended these studies with the use of thiosemicarbazones in differential kinetic analysis. We describe here the kinetics of the complex formation between pyridoxal thiosemi-carbazone (PT) S II CH=N-NH-C- NHp and iron and cobalt in order to establish procedures for the simultaneous determination of these two ions by means of differential kinetic methods. The methods are based on the fact that the formation of the cobalt - PT complex is rapid whereas the formation of the iron - PT complex is very slow.Several differential rate methods for the analysis of mixtures of metals based on redox rea~tions,~-ll catalysed reactions12-15 and ligand-exchange r e a c t i o n ~ l ~ - ~ ~ has been reported. However only one application of the reactions of complex formation in differential kinetic analysis has been published involving the analysis of mixtures of nickel and cobalt.2s The technique described in this paper for the analysis of iron and cobalt mixtures is very simple and the use of a stopped-flow technique common in the procedures cited above is not necessary. Experimental Apparatus A Perkin-Elmer 575 ultraviolet - visible spectrophotometer with 1 .O-cm glass cells and equipped with an electronic thermostat was used for the kinetic measurements.A Radio-meter PHM 62 pH meter with a combined glass - calomel electrode and a Hewlett-Packard HP-85 computer were also used. Reagents All reagents were of analytical-reagent grade. Pyridoxal thiosemicarbazone was synthesised by the condensation of pyridoxal chloro-hydrate with thiosemicarbazide.27 A 0.1 yo m/V solution of the reagent in “’-dimethyl-formamide was used. * To whom correspondence should be addressed 444 BALLESTEROS AND PI~REZ-BENDITO USE OF KINETICS OF Analyst Vol. 108 Standard solutions of iron(II1) (43.3 pg ml-l) and cobalt(I1) (47.6 pg ml-1) were pre-pared by dilution of iron( 111) nitrate and cobalt nitrate solutions respectively and standardised gravimetrically. Sodium acetate - acetic acid buffer solution [C (total concentration) = 1.70 M and pH = 3.851 was used.Procedure for the Simultaneous Determination of Iron and Cobalt Logarithmic extrapolation method To a 10-ml calibrated flask containing up to 30pg of iron and cobalt in a mixture add 3 ml of 1 M potassium nitrate solution 2 ml of sodium acetate - acetic acid buffer solution (pH 3.85) and an appropriate volume of distilled water so that when 0.5 ml of 0.1% reagent solution is finally added (with great care and last to prevent prior mixing of the solutions), the total volume becomes 1O.Oml. The mixture is warmed in a water-bath at 25 & 0.1 "C for 5 min then shaken (time t = 0) and one portion is transferred into a 1.0-cm cell thermo-stated at 25 5 0.1 "C. The change in absorbance at 425 nm with time is recorded between minute 2 and minute 3.Then the mixture is allowed to stand until development is complete (30 min) and the absorbance is measured (A,). The treatment of the data obtained is indicated later for the mixture analysis. Single-p oint met hod The samples are prepared as described above but the absorbance is measured exactly 1 min after shaking the samples. The mixture is allowed to stand until the reaction is complete (30min) to obtain A,. From a previously plotted calibration graph the molar fraction is obtained together with the amounts of iron and cobalt as indicated later. Results and Discussion Spectrophotometric Characteristics of Iron - PT and Cobalt - PT Complexes In a weakly acidic medium (pH 3.95) PT forms yellow - brown chelates with iron(II1) and cobalt(II) the solutions of which are stable and have maximum absorption at 425 and 440 nm respectively.The absorbance of both complexes at 425 nm is not affected appreci-ably by temperature ionic strength dielectric constant or acetate ion concentration. The molar absorptivities are 1.62 x lo4 and 1.15 x 104 1 mol-l cm-l respectively. The metal to ligand ratio for the iron - PT and cobalt - PT complexes were determined by Job's method at two different wavelengths for each complex (425 and 440 nm for the iron complex and 440 and 470 nm for the cobalt complex). A ratio of 1 3 was found in both instances. The reagent probably behaves as a bidentate ligand forming octahedral complexes. The con-dition stability constants from Job's method data were calculated (logK = 16.4 * 0.2 for the iron complex and logK = 16.9 & 0.5 for the cobalt complex).In order to establish the oxidation state of the metal ions in each complex the effect of oxidising and reducing agents was studied. Whereas the iron - PT complex is formed in the presecce of peroxydisulphate or periodate it is not produced in the presence of ascorbic acid or hydroxylamine and it is concluded that the trivalent iron(II1) ion forms the iron - PT complex. In the presence of the same oxidising and reducing agents the cobalt - PT complex is formed and the oxidation state cannot be determined. On the other hand complex formation does not take place when PT and cobalt(I1) are mixed in an inert atmosphere. However when a current of air is bubbled through the solution rapid formation of the cobalt -PT complex is observed.Therefore the dissolved oxygen oxidises the cobalt(I1) to cobalt(III) which forms the cobalt - PT complex. Kinetic Study of Complex Formation recording of the absorbance - time curves at 425 nm (Fig. 1). after 25-30 min for the iron - PT complex and after 2-3 min for the cobalt - PT complex. The kinetics of the formation of these complexes were followed spectrophotometrically by The reactions are complet April 1983 COMPLEX FORMATION DETERMINATION OF FE AND Co 445 Effect of Reaction Variables Variation of the ionic strength has little influence on the rate constant and the ionic strength was fixed at 0.3 M with potassium nitrate. On the other hand an increase in the NN'-dimethylformarnide concentration decreases the rate constant and a 5% concentration of the organic solvent was chosen for the formation of both complexes.0.8 I 0.6 8 m $ 0.4 u) 2 0.2 0 10 20 30 Time/m in Fig. 1. Absorbance versus time graphs a t 426 nm for (A) iron - PT complex and (B) cobalt - PT complex. CM = 2.60 pg ml-l Fe(II1) or 2.85 pg ml-l Co(I1); CB = 2.08 x 10-4 M; pH = 3.96; T = 26 "C; and p = 0.3 M (KNO,). Efect of temperatwe The effect of temperature on the rate constant for both complexes was studied in the range 2045 "C. The rate constant increased as the temperature increased and in both instances a temperature of 25 "C was selected. From the rate constant values and the Arrhenius equation the activation energies for the two complex formation reactions were calculated and were found to be 17.32 and 2.55 kcal mol-l for the iron - PT and cobalt - PT reactions respectively.As the activation energy for iron - PT complex formation is high temperature control is critical. With the electronic thermostat used a high degree of temperature control is possible as is shown by the small relative error (less than 1%) in the determination of the rate constant for the iron - PT complex. Efect of reagent concentration The effect of the reagent concentration on the rate constants was studied in the range 2 x lo4 - 5 x lo4 M for the iron - PT complex and 1.0 x M for the cobalt - PT complex. These concentration ranges are small because the lower limit is con-ditioned for total completion of complex formation reaction. On the other hand larger amounts of the reagent cannot be used because the complex formation reactions are very rapid especially with the cobalt - PT complex.A 2.08 x 10-4 M concentration of the reagent (0.5 ml of 0.1% solution) was selected. In order to establish the partial orders of reaction with respect to the reagent concentra-tion the logarithm of the rate constant was plotted against the logarithm of the reagent concentration. The reaction rate of complex formation is directly proportional to the square root of the PT concentration for the iron - PT complex and to the square of the PT concentration for the cobalt - PT complex. Therefore the partial orders are 0.5 and 2, respectively. The differences found in the partial orders may be due to the nature of the two reactions being different as is explained in detail later.- 2.5 446 BALLESTEROS AND P~REZ-BENDITO USE OF KINETICS OF Analyst VoZ. 108 Efect of acetate ion The influence of the acetate ion was studied in the range 10-3 - lo- M for both complexes. The rate constant of iron - PT complex formation depends greatly on the sodium acetate concentration. A logarithmic plot showed that the reaction rate is inversely proportional to the acetate ion concentration. In contrast the rate constant for cobalt - PT complex formation is independent of the acetate ion concentration and therefore this reaction is of zero order with respect to acetate ion concentration. The rate constant ratio kc,/kF, increases as the acetate concentration increases and the determination of cobalt and iron mixtures is favoured by high acetate concentrations.An acetate concentration of 0.34 M (2 ml of buffer solution) was chosen because larger amounts of acetate would excessively and disadvantageously delay the iron - PT complex formation. Efect of $H The variation of the rate constants with pH was studied by addition of various amounts of sodium hydroxide to a fixed amount of acetic acid giving a pH range of 3.4-5.3 for the iron - PT complex and 3.04.5 for the cobalt - PT complex. At pH 3.95 the rate constant of iron - PT complex formation attains a minimum value. Therefore we selected a buffer solution of pH 3.85 which yields a final pH of 3.95 probably owing to the effect of the organic solvent added. In this study it is necessary to take into account that as the acetic acid is a weak acid the acetate ion concentration increases as the pH increases.This is not of importance in cobalt - PT complex formation but it is critical in iron - PT complex formation. In the latter instance the rate constant depends on both H+ and the acetate ion when the pH is changed. To prevent this difficulty an attempt was made to obtain partial orders of reaction with respect to H+ and AcO- based on the theoretical calculation of a corrected rate constant obtained by means of a fixed acetate concentration as reference, expressed by From this kcor value a partial order of -1 with respect to the acetate concentration is found. The same partial order with respect to the H+ concentration was also obtained. The same results for orders with respect to H+ and AcO- were found by using a computer program in which pair orders for hydrogen and acetate ions from -2 -2 to 2 2 (half by half units) were employed (i.e.arbitrarily assign a value to the partial order of reaction with respect to H+ and another different value to the partial order of reaction with respect to AcO-) and assuming as optimum orders those which give a smaller relative standard deviation in the values obtained. Rate Equations From this kinetic study the following equations are suggested for the formation of the iron - PT and cobalt - PT complexes in sodium acetate - acetic acid medium at pH 3.95 : The various kinetic dependences indicated above are summarised in Table I. = kFe (PT)t (Fe3+) (AcO-)-l (H+)-l d(Fe - PT) dt = kco (PT) (Co2+) d(C0 - PT) dt where kpe and kco are the conditional rate constants.From these equations we can say that the formation of the iron - PT complex is a reaction of ligand substitution between the reagent and the acetate ion. This is supported by the fact that the acetate ion forms colour-less complexes with iron(II1) and mainly because the rate of iron - PT complex formation decreases as the acetate concentration increases. As the conditional stability constants of the acetate complexes are knownm (log k = 3.4 log k = 6.1 and log k = 8.7) we calcu April 1983 q -1.0 - a A -1.5 COMPLEX FORMATION DETERMINATION OF FE AND Co --447 TABLE I SUMMARY OF KINETIC DATA PARTIAL ORDER OF REACTION Iron - PT complex Cobalt - PT complex A A \ r 1 Concentration Partial Concentration Partial Species range order range order Metal .. 0.3-3.0 pg ml-l 1 0.4-3.0 pg ml-1 1 PT . . . . 2 x 10-4-5 x ~ O - * M 0.6 1 X lO-L2.5 X w 4 M 2 AcO- . . . . 10-2-10-3 M -1 10-*-10-3 M 0 H+ . . 5 x 10-6-4 x 1 0 - 4 ~ -1 3 x 10-5-10-SM 0 lated the molar fractions of the different iron species in the solution (ao = 1.9 x 2.2 x 10-3; cc2 = 0.05; a3 = 0.95). could be written as a = Therefore the over-all reaction of ligand substitution Fe(CH,COO) + 3PT -+ Fe(PT) + SCH,COO-On the other hand we can assume that the reaction between cobalt(I1) and PT involves complex formation as the rate constant depends only on the metal and reagent concentra-tions. Determination of Conditional Rate Constants Under experimental conditions of constant pH and with a large excess of sodium acetate and reagent with respect to the metallic ion concentration the reactions are pseudo-first order with respect to iron(II1) and cobalt(I1) ions.Therefore under these conditions the integrated equation in absorbance terms can be written as Log ( A - A ) = log A - - kM t 2.303 where k is the conditional rate constant and Ao A t and A are the absorbances after a time t = 0 t equal to any time and t equal to a very long time respectively. A graph of log(A - A ) against time (Fig. 2) is a straight line whose slope allows the determination of the conditional rate constant of the complex formation reaction. The average values thus obtained for 11 determinations are k, . PT = 0.248 0.002 min-l and kc PT = 2.6 -j= 0.1 min-1. :'. B I I I I 0 60 120 180 Ti m e/s Fig.2 Graph of log(A,-At) vevssus time for the conditional rate constant calculation for (A) iron -PT complex and (B) cobalt - PT complex. Conditions as in Fig. 1 448 Differential Kinetic Determination of Iron and Cobalt We consider the following pseudo-first-order reactions : BALLESTEROS AND P~REZ-BENDITO USE OF KINETICS OF Analyst VoZ. 108 ka kB A + R - P B + R - P where k and k are the conditional rate constant and k > k,. When these reactions proceed simultaneously and their rate constants are independent of each other (the sum of the concentration of A and B reacting to form a comrnon product P is given) at any time, t we can write where [Ale and [Bl0 are the initial concentrations of A and B; [ A ] [B] and [PIt are the concentrations of A B and P respectively at time t and [PIm is the final concentration of P.Equation (1) is the basis of differential kinetic methods of which we used two for the simultaneous determination of iron and cobalt. Logarithmic Extrapolation Method When the faster reacting component of the mixture A has reacted to completion the term [Ale exp(- kAt) in equation (1) becomes negligible and by taking the logarithm of both sides of the equation we obtain and expressed as a function of the absorbance this equation becomes where eFe is the molar absorptivity of the iron - PT complex and I is the cell path length (1.0 cm). A graph of lo@ - A ) against time (Fig. 3) is a curve ending in a straight line which, when extrapolated to t = 0 allows us to obtain the initial concentration of iron [Fe3+Io.The initial concentration of cobalt [Co2+l0 in the mixture can be obtained by difference from the final absorbance Am. -0.7 -0.8 - 4 cn .-I -0.9 -1.0 I I 0 60 120 180 Ti me/s Fig. 3. Logarithmic extrapolation method ; log(A 00 - A t) as a function of time according to equation (3) for the simultaneous determination of iron and cobalt. CBI = 0.69 pg ml-' Fe(II1) and 0.96 pg ml-' Co(I1); CR = 2.08 x M ; pH = 3.95; T = 25 O C ; and p = 0.3 M (KNO,) April 1983 Single-point Method COMPLEX FORMATION DETERMINATION OF FE AND Co Dividing equation (1) by the total concentration C = A + Bo we obtain 449 where Ct is the total concentration at time t. TABLE I1 EFFECT OF DIVERSE IONS ON THE SIMULTANEOUS DETERMINATION OF 1.04 pg ml-l OF IRON AND 1.43 pg ml-1 OF COBALT Amount toleratedlpg ml-l Ion Be(I1) .. Sr(I1) . . Ba(I1) . . Pb(I1) . . Mn(I1) . . Bi(II1) . . As(II1) . . Cr(II1) . . Cd(I1) . . Zn(I1) . . Cyanide . Phosphate Chloride . Bromide Thiocyanate :4#-;) - - Added as . . Be(NO,), . . Ca(NO,) . . Sr(N03) Ba(NO,) Pb(NO,) Mn(NO,) . . Bi(NO,) Na,AsO . . CrC1 Cd(NO,) Zn(NO,) KCN N%PO . . NaCl KBr NaSCN * . - * Mg(N03)2 r -Logarithmic extrapolation method 26 600 260 600 1000 1000 1000 26 260 2 25 10 6 6 600 600 260 1 Single-point method 26 1000 260 600 1000 1000 1000 10 260 2 26 6 6 6 260 600 100 For a previously fixed time a graph of Ct/Co against the molar fraction of one of the components gives a calibration graph from which the molar fraction of that component in the sample can be calculated.As the final absorbance Am and the molar fractions of both metallic ions are known we can write [A1 0 x A = [A10 + [BIO From these two expressions the initial concentrations [A]. and PI0 can easily be calculated. The optimum time of measurement (topt) is established according to the Lee and Kolthoff expression29 : and is 1 min in this instance. Effect of Diverse Ions A study was made to determine the tolerance limits of various ions that may be present in the simultaneous determination of iron and cobalt using both the logarithmic extra-polation and single-point methods.The cations tested were added as nitrates or chlorides and the anions were added as sodium or potassium salts. Relative errors of less than &5y0 were considered negligible. Similar concentration levels of copper(II) nickel(II) vanadium-(V) silver(1) gold(II1) and palladium(I1) interfere positively owing to complex formatio 450 BALLESTEROS AND P~~REZ-BENDITO USE OF KINETICS OF Artalyst VoZ. 108 TABLE I11 ANALYSIS OF SOME SYNTHETIC MIXTURES BY THE LOGARITHMIC EXTRAPOLATION METHOD Added/pg ml-1 Found/pg ml-l Relative error yo - 7+ - Cobalt Iron Cobalt Iron Cobalt Iron 0.69 0.95 0.68 0.97 - 2.30 2.11 0.69 1.90 0.71 1.87 2.30 -1.68 1.38 0.96 1.36 1.00 -2.31 6.26 1.38 1.90 1.42 1.85 2.89 -2.63 with PT and similar levels of molybdenum(VI) tungsten(VI) antimony(III) tin(II), tartrate oxalate and EDTA interfere negatively by inhibition of the complex formation reactions.The permissible amounts of other ions are shown in Table 11. Determination of Iron and Cobalt in Synthetic Mixtures The logarithmic extrapolation and single-point methods have been applied to the deter-mination of various synthetic mixtures containing different relative proportions of both iron(II1) and cobalt(I1) ions. Tables I11 and IV summarise the results obtained. It can be concluded that when the mixture contains similar concentration levels of both cations the errors are small. On the other hand when the ratio of these concentrations is very large a greater error in the determination of the metallic ion added in the smaller amount is observed.However it should be noted that this disadvantage is common to every additive method for the simultaneous analysis of mixtures. TABLE IV ANALYSIS OF SOME SYNTHETIC MIXTURES BY THE SINGLE-POINT METHOD Added/pg ml-l Found/pg ml-l - Iron Cobalt Iron Cobalt 0.35 0.35 0.35 0.69 0.69 0.69 0.69 1.38 1.38 2.08 0.48 0.96 1.90 0.48 0.95 1.90 2.86 0.95 1.90 0.95 0.36 0.33 0.33 0.67 0.69 0.67 0.71 1.38 1.35 2.10 0.47 0.97 1.93 0.50 0.96 1.94 2.83 0.96 1.96 0.93 Relative error yo Iron 1.99 -4.47 -4.74 -2.52 - 1.00 -3.44 2.71 - 0.43 - 2.68 0.87 Cobalt 1.86 1.27 6.44 1.08 1.85 - 0.97 0.91 2.89 -2.80 -2.13 The single-point method is more advantageous than the logarithmic extrapolation method because in general it gives smaller errors and the relative range of determination of the two ions in mixtures is wider.The accuracy and precision of the two methods applied to a mixture containing 0.87 pg ml-1 of iron(II1) and 0.95pgml-1 of cobalt(I1) are given in Table V. It can be seen that the methods prcposed here are more precise than most of those reported in the literature. TABLE V ACCURACY AND PRECISION OF THE DIFFERENTIAL KINETIC METHODS USED IN THE DETERMINATION OF IRON AND COBALT MIXTURES Relative standard Method Metal Relative error yo deviation yo (n = 11) Logarithmic extrapolation . . . . Fe (0.87 pg ml-l) -0.91 0.64 Co (0.96 pg ml-l) 0.76 0.65 Single-point . . . . Fe (0.87 pg ml-l) -0.94 0.69 Co (0.95 pgml-l) 0.68 1.0 A$ril 1983 COMPLEX FORMATION DETERMINATION OF FE AND Co References 451 1.2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. Perez-Bendito D. ValcArcel M. Ternero M. and Pino F. Anal. Chim. Acta 1977 94 405. Ternero M. Pino F. Perez-Bendito D. and ValcArcel M. Michrochem. J. 1980 25 102. Ferrer J. L. and PBrez-Bendito D. Anal. Chim. Acta 1981 132 157. Moreno A. Silva M. PCrez-Bendito D. and ValcArcel M. Talanta in the press. Ternero M. Pino F. PCrez-Bendito D. and ValcArcel M. Anal. Chim. Acta 1979 109 401. Ternero M. Perez-Bendito D. and ValcArcel M. Microchem. J. 1981 26 61. 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