simultaneous equations, involving an experimentally determined sensitivity factor for each metal at each voltage, was used. The experimental value for each sensitivity factor was determined on a n aliquot of known concentration of each metal alone. By using 2-min plating times on a 3-MHz crystal, the four sensitivity factors for zinc and cadmium were determined for a concentration of 1.0 X lO-4M metal. Next, synthetic samples containing known concentrations of each metal were prepared, the frequency changes at -0.45 V and -0.90 V were determined, and the concentrations were calculated using two simultaneous equations. The calculated values did not compare well with the known concentrations, differing by 5 % for equal concentrations t o more than 50% when one species was present in tenfold excess. The process was repeated for a 20-min time interval, using 1.0 X 10-jM solutions t o determine the sensitivity factors. The results for a synthetic sample mixture were again in large error. The same procedure was followed for nickel and zinc mixtures, and again the experimentally determined concentrations differed from the known concentrations by more than 50%. The analyses of mixtures of zinc and either cadmium or nickel point out that under these conditions the A j values are not additive and that the individual ions cannot generally be resolved accurately by this method. One of the requirements for the application of this technique to the analysis of mixtures is that the contribution of each species to the total mass change during electrodeposition be independent of the other analytes present. Another way of viewing this stipulation is that only the mass transfer and .-
electron transfer processes must control the plating reactions. Without this limitation on the nature of the control, thermodynamic considerations could possibly make a given site energetically more favorable for the deposition of one metal than for another. Evidently such is the case under these experimental conditions, so that the frequency changes due to electroplating from mixtures are not the simple sums of the frequency changes determined for each metal separately. Jones and Lingane successfully used electrogravimetric separations in the determination of copper, bismuth, lead, and tin ions in a sample (19). Controlled potential deposition was used to plate one metal at a time from 0.25M sodium tartrate onto a platinum working electrode. The weight changes were observed by weighing the electrode periodically. The lowest metal concentration determined was greater than lO-3M because of the limitations of conventional electrodeposition previously discussed. An effort was made in the present investigation to obtain quartz crystals with platinum electrodes so that the experimental conditions of Lingane and Jones (19) could be essentially duplicated in this laboratory and applied to much more dilute mixtures using the new method described herein. However, platinum-surfaced crystals could not be secured at a reasonable cost and the attempt was abandoned. RECEIVED for review October 7, 1968. Accepted December 23, 1968. We thank Phillips Petroleum Co. for a fellowship t o J.P.M. (19) J. J. Lingane and S . L. Jones, ANAL.CHEM.,23, 1798 (1951).
-
A Kinetic and Spectrophotometric Study of the Formation and Reduction of a Phosphorus-Bismuth Dimeric Heteropolymolybdate H. D. Goldman and L. G . Hargisl Department of Chemistry, Louisiana State Uniuersity in New Orleans, New Orleans, La. 70122
A spectrophotometric procedure has been used to determine the composition of a unique, mixed bismuthphosphorus, dimeric heteropolymolybdate. A stoichiometry study indicated that the Mo:P:Bi ratio in the complex was 18:l:l. The complex was more stable in perchloric acid solutions than 12-molybdophosphoric acid but it was reduced considerably more easily to a heteropoly blue. The experimental rate law i s in good agreement with a mechanism involving an equilibrium step forming the heteropoly acid followed by a reduction step. The initial reduction of the complex by ascorbic acid apparently proceeded by a 2-electron, acid independent step. THERE HAVE BEEN several reports in the literature of bismuth affecting the reduction of 12-molybdophosphoric acid t o the corresponding hereropoly blue. The first report arose from some interference studies on a spectrophotometric method for phosphate ( I ) . Campbell and Mellon later developed a spectrophotometric method for bismuth based on an enhancement of the'blue hue produced on reduction of 12-molybdophosphoric acid in the presence of bismuth (2). However, their 'To whom all correspondence should be addressed. ( I ) D. F. Boltz and M. G. Mellon, ANAL.CHEM., 20,749 (1948). (2) R. H. Campbell and M. G. Mellon, ibid., 32, 54 (1960). 490
ANALYTICAL CHEMISTRY
preliminary investigations concerning the nature of the effect were inconclusive and they were unable to determine if the effect was catalytic or the result of complex formation involving bismuth. Recently it was shown for the first time, by means of a spectrophotometric study, that a discrete phosphorus-bismuth heteropolymolybdate can be formed in solution which reduces considerably more rapidly than 12-molybdophosphoric acid (3). This great difference in the rate of reduction, coupled with the fact that it was not previously known that a mixed heteropoly was formed, has contributed t o a false belief that the bismuth may have been acting catalytically in the reduction of 12-molybdophosphoric acid. A quantitative description of the steps leading to the formation of heteropolymolybdates requires knowledge of the principal equilibria of the isopolymolybdates in acid solution. Numerous studies of these equilibria have been made ( 4 4 but general agreement is still lacking, especially for systems at (3) L. G. Hargis, Anal. Lttrs., 1, 799 (1968). (4)I. Lindqvist, Ark. Kemi, 2, 325, 349 (1950). ( 5 ) 1. Lindqvist, Acta Chem. Scand., 5, 568 (1951). (6) Y. Sasaki, I. Lindqvist, and L. G. Sillen, J. Inorg. Nucl. Chem., 9, 93 (1959). (7) P. Souchay, Bull. SOC.Chim. Fr., 1947, 914. (8) F. Chauveau, P. Souchay, and R. Schaal, ibid., 1959, 1190.
higher acidities ; the conditions usually employed when the heteropoly acid is to be reduced. In an equilibrium and kinetic study of the formation and reduction of 12-molybdophosphoric acid (12-MPA), Crouch and Malmstadt (9) shed some light on the nature of these reactions. Their data supported a belief expressed by others ( I O , 11) that Mo(V1) exists largely as a dimer in concentrated acid solution. The experimental rate laws obtained by these investigators for the reduction of 12-MPA acid were in good agreement with a mechanism involving a prior equilibrium to form 12-MPA acid and subsequent reduction of this species to a heteropoly blue. In the present study we determined the stoichiometry of the formation reaction for the phosphorus-bismuth heteropoly in an effort to determine the composition of the complex. The kinetics of the reduction of this complex by ascorbic acid was investigated under conditions suitable for the analysis of bismuth.
0.32
,
,
I
, ,
,
I
EXPERIMENTAL Spectrophotometric Measurements. Spectrophotometric measurements on the formation of 12-molybdophosphoric acid were made on a Beckman DU-2 spectrophotometer. Kinetic measurements were made on either a Beckman DB or Cary 15 recording spectrophotometer. The usual procedure in making kinetic measurements was to prepare the desired solution without reductant in a suitable volumetric flask and equilibrate in a constant temperature water bath at 26.0 0.05 "C. After equilibration, an aliquot was pipetted into the I-cm absorption cell and the reductant was added cia a 100-pl hypodermic syringe. The solution was hand mixed in the absorption cell and then placed in the spectrophotometer. Mixing and placement in the spectrophotometer was accomplished easily in 4-5 seconds and there was no need to go to a more elaborate system. A thermostated cell compartment maintained at 26.0 ~t0.05 "C was used in the Cary 15 spectrophotometer. Measurements on the formation of 12-molybdophosphoric acid and the bismuth-heteropoly acid were made at 350nm. 12-Molybdophosphoric acid is known to conform to the BeerLambert law at this wavelength ( I ) and we found that the bismuth heteropoly also conformed to the law. This wavelength is on a steeply rising portion of the absorption curve and extreme care must be used in setting the wavelength on the instrument. Measurements on the rate of formation of the heteropoly blue were made at 725nm. This wavelength does not correspond to the absorbance maximum which is at 815nm (3) but some compromise was necessary as the recording spectrophotometers used to obtain the rate data could not be used beyond 800nm. The 725nm wavelength offered the best compromise between sensitivity and slit width. Again it was demonstrated that the system conformed to the BeerLambert law at this wavelength, at least over the small concentration ranges used. All measurements were made against distilled water as the reference. Reagent blanks were always prepared and were also measured against distilled water. The blanks were then subtracted arithmetically. This procedure was deemed necessary because the reagent blanks occasionally exhibited somewhat more than minimal absorption and if they were subtracted instrumentally, it would be at the expense of an increased slit width and lower resolution and sensitivity. Acidity Medsurements. With one exception acidities are calculated values ; determined from the analyzed acidity of
*
~-
(9) S. R. Crouch and H. V. Malmstadt, ANAL.~ H E M . , 39, 1084
(1967). (10) Y. Sasaki and L. G. Sillen, Acta Chem. Scand., 18, 1014 (1964). (11) P. Souchay, Pitre Appl. Chem., 6 , 61 (1963).
PH
Figure 1. Effect of pH on absorbance of l&molybdobismuthophosphoric acid and 1Zmolybdophosphoric acid 1. 18-molybdobismuthophosphoricacid: KH,PO, = 40.0pM, Bi(NO,), = 40.0&, Na,MoO, = 2.OOmM 2. 12-molybdophosphoric acid: KH,PO, = 40.0pM, Na,MoO, = 2.00mM
stock acid solutions. The pH values shown in construction of Figure 1 are the only measured values. Reagents. Stock solutions of Mo(V1) were prepared from reagent grade Na2MoO1 2 H 2 0 . Freshly prepared molybdate solutions behave differently from aged solutions in some kinetic experiments (9). Presumably this results from slow polymerization processes occurring in neutral aqueous solutions. In order to ensure that the molybdate aggregates had reached a stable equilibrium, all Mo(V1) solutions were prepared at least 24 hours prior to their first use. Stock bismuth solutions were prepared by dissolving a weighed amount of Bi(NO& 5H20 in the required amount of perchloric acid and diluting with distilled water. The stock solutions were standardized volumetrically using a standard EDTA procedure. Ascorbic acid solutions are not stable for long periods of time at room temperature and so were prepared fresh just prior to use. All other solutions were prepared from reagent grade chemicals. RESULTS Nature of the Bismuth Effect. The formation of the bismuth heteropoly was, like 12-molybdophosphoric acid, very pH dependent. The complex decomposed in both very dilute and very concentrated acid solutions; however, it was stable over a somewhat larger pH range than 12-molybdophosphoric acid as shown by Figure 1. The order of addition of reagents in preparing the solutions had no effect on the final absorbance. Apparently the bismuth complex was more stable than 12-MPA because when bismuth was added to a solution of 12-MPA the bismuth complex formed as indicated by a change in the absorption spectrum (3). The perchloric acid concentration had a large effect on the rate of formation of the heteropoly blue but it did not affect the amount of heteropoly blue produced. When solutions containing the same amount of heteropoly complex at acidities VOL. 41, NO. 3, MARCH 1969
491
a
Table I. Reaction Coefficients for 12-MPA in Perchloric Acid Solutions Varied CKH~PO~,M CMO(VI)t,M CHC104,M KH,P04 4.0 x 10-5-1.0 x 10-4 2.0 x 10-3 0.240 6.0 X 10-4-3.0 x 7.0 x 10-3 0.800 Na,MoO, 8.0 x 10-5 1.6 x 10-3-2.4 x 0.240 1.2 x 10-3 1.0 X 10-2-5.0 X lo-’ 0.800 HC10, 8.0 x 10-5 2.0 x 10-3 0.224-0.264 1.2 x 10-3 5.0 x 10-3 0.500-0.800 Range given is the confidence limits of the regression coefficient at the 95% confidence level. Table 11. Reaction Coefficients for MBiPA in Perchloric Acid Solutions CKH2PO4,M CBII+,M Chlo(VI)i,M CHC~O~,M K H ~ P O ~ 1.0 x 10-5-4.0 x 10-5 4.0 x 1 0 - 5 ~ 2.0 x 10-3 0.272 4.0 x 10-5 1.0 x 10-5-4.0 x Bi(N03)3 2.0 x 10-3 0.272 Na2Mo0, 4.0 x 10-5 4.0 x 10-5 1.6 x 10-3-2.1 x 10-3 0.256 HC10, 4.0 x 10-5 4.0 x 10-5 2.0 x 10-3 0.240-0.336 Varied
ranging from 0.24 to 0.34M in perchloric acid were reduced with ascorbic acid, the absorbance at 725nm was the same for all solutions after 12 hours. In order t o further elucidate the nature of the bismuth complex, experiments were designed t o determine the stoichiometry of the complex using the procedure applied by Crouch and Malmstadt (9) t o the study of the formation of 12-molybdophosphoric acid. These authors worked only with nitric and sulfuric acid solutions but we desired t o work in perchloric acid solutions because it is perhaps the most widely used acid for analyses based on heteropoly acid or heteropoly blue formation and because 12-molybdophosphoric acid appears to be least dissociated in this acid. Because perchloric acid solutions had not been studied and also to serve as a check on our experimental procedures and techniques, we decided to investigate the stoichiometry of 12-molybdophosphoric acid before working with the bismuth complex. Quantitative Description of the Method of Data Treatment. The formation of 12-MPA and of the bismuth complex was virtually instantaneous. The spectrum of each complex was similar to that of acidic molybdate ( I , 3) except being shifted somewhat toward longer wavelengths. When the amount of molybdate was kept sufficiently small, absorbance measurements on the heteropoly complexes could be made a t 350nm with only small blanks due to Mo(V1) and the systems both conformed to the Beer-Lambert law. The method of data treatment will be developed only for the bismuth-heteropoly system although results for both 12molybdophosphoric acid and the bismuth-heteropoly complex will be presented. The reaction between phosphate, bismuth, and molybdate can be written
Rxn. coeff. 0.94 i: 0.05a 0.97 k 0.05 6.06 i-0.26 5.93 2 0.31 6.05 F 0.16 6.15 i: 0.24
Rxn. coeff. 0.96 i: 0.06 1.19 0.17 8.81 f 0.30 8.75 i-0.31
When this equation is solved for A and expressed logarithmically, we obtain log A = log Kyeb
+ alog C H ~ P+Oblog ~ CBI+ clog C M ~ ( V - Id)o~g CH+
(2) Varying the initial concentration of one of the reactantsLe., HoP04-while keeping the others constant allows one to plot log A cs. log C H ~ P O This ~ . should yield a straight line with a slope of a. Similar plots can be prepared for the other reactants. Stoichiometry of the Formation of 12-Molybdophosphoric Acid. The solution acidity proved to be the most valuable tool in adjusting conditions such that the heteropoly acid was formed only in small amounts. The p H dependence illustrated in Figure 1 indicated that the stated concentrations could be used over the p H range of 0.60.8 without danger of forming too much 12-MPA. As a further check on the validity of the results, the same experiment was performed at a second set of conditions different from the first set. The results of the data treated in this manner are presented in Table I. Exactly the same reaction coefficients were obtained when nitric acid was used in place of perchloric acid. The results agree well with those obtained by Crouch and Malmstadt ( 9 ) in all but one case; they obtained a value of nine for the H + dependency as opposed to six in our study. The reasons for this difference are not yet understood but it should be pointed out that we did not duplicate their conditions exactly. The large reaction coefficients for Mo(VI), and H+ prevented the use of a large concentration range for the log A cs. log C plots. Attempts to vary the concentration over a greater range than shown in Table I produced either immeasurably MBiPA dH+ a H 3 P 0 4 bB$+ cMo(VI), small absorbances or too much 12-MPA. Because the comwhere MBiPA refers t o the bismuth-heteropoly complex, position of 12-MPA is well established, the reaction order of Mo(VI), refers to the total amount of unreacted molybdate, six for Mo(VI), is evidence that the principal species in the and a, b, c, and d, refer to the number of moles of each perchloric acid solutions studied was a dimer. Apparently constituent that react with or are formed with one mole of this same species exists in nitric acid solutions (9). MBiPA. Stoichiometry of the Formation of the Mixed BismuthMeasurements were taken under conditions where the Phosphorus Heteropoly. The technique used to determine the heteropoly complexes were highly dissociated (> 95 %) which stoichiometry of the bismuth-heteropoly complex was the made the equilibrium concentrations, [H3P04], [ B P I , etc. same as used for 12-MPA. Again, the solution acidity served very nearly equal to the analytical concentrations, C H ~ P O ~ , as the major factor controlling the extent of complex forCB,, etc. In addition, the absorbance at 350nm was propormation. With the reagent concentrations used in this study, a tional to the concentration of MBiPA ([MBiPA] = A/eb), solution p H of 0.5 to 0.65 was generally required to maintain thus the formation constant for the above reaction can be the sufficient degree of dissociation of the complex. The results expressed as of the data treated in the manner previously described are (A/eb)Cg+ summarized in Table 11. Ki = The data strongly suggest the formation of a mixed heteroC&o4 * C L * C i I O ( V 1 , t (1)
+
492
+
ANALYTICAL CHEMISTRY
+
Table 111. Experimental Reaction Orders for Formation of Reduced 18-MBiPA CKH2PO4,M CB?+>M CX~(VI)& CHCIO~,M CAscorbic,M
Varied 1.0 KH2P04 Bi(N03), Na,Mo04 HClO4 Ascorbic acid a b
x 10-5-6.0 x 4.0 X 4.0 x 10-5 4.0 x 10-5 4.0 X
Rxn. Order
7.6 x 10-3 0.99 k 0.03 0.320 1.0 x 10-3 1.00 f 0.08 0.320 7.6 x 10-3 8.95 i 0.11 0.320 7.6 X -8.78 zk 0.26 to-Oa 0.230-0.336 0.240 1.0 X 10-4-3.0 X lo-* 0.99 i 0.05 to O b
4.0 x 2.0 x 10-3 1.0 x 10-5-4.0 x 10-5 2.0 x 10-3 4.0 x 1.4 x 10-3-1.9 x 4.0 x 10-5 2.0 x 10-3 4.0 x 10-5 2.0 x 10-3
Reaction order was constant at high concentrations of HC10, but varied to almost zero order at low concentrations. Reaction order was constant at low concentrations of ascorbic acid but varied to zero order at high concentrations.
poly acid, molybdobismuthophosphoric acid, in which the ratio of bismuth to phosphorus is 1 : l . Because it now appears well established that in the range of acid concentrations used Mo(V1) exists primarily as a dimer, the molybdenum reaction coefficient of nine indicates that the mixed heteropoly is an 18-molybdobismuthophosphoricacid. Because we experienced a little difficulty in obtaining reliable values for the molybdate dependency and because this value is important in assigning the final composition, we sought to augment the study by checking the molybdate dependency another way. Solution conditions were determined where the heteropoly complex exhibited maximum stability. Under these conditions, varying amounts of molybdate were added t o solutions containing equal amounts of bismuth and phosphate and a fixed amount of perchloric acid. The absorbances were measured at 350nm and, after correction for blank absorbance, plotted against the mole ratio of molybdenum t o bismuth phosphorus. The results of this experiment are shown in Figure 2. Extrapolations of the linear portions of the curve crossed at a molar ratio of 9.2 confirming the validity of our proposed formation of a n 18-molybdobismuthophosphoricacid complex. There are several possible reasons that explain why the one extrapolated line in Figure 2 does not pass through the origin. Recently, it was shown that the formation of 12-MPA involves a n initial reaction between phosphate and Mo(V1) followed by polymerization to form 12-MPA (12). Such a mechanism applied t o the formation of 18-MBiPA could explain the small change in absorbance (concentration of 18-MBiPA) at low Mo(V1) concentrations. Once an initial nonabsorbing complex is more or less completely formed, further polymerization t o the absorbing 18-MBiPA could take place. Thus, initially a small change in absorbance would be obtained followed by a large change and the extrapolated value would still represent the total Mo(V1) dependence. In light of the above data, the stoichiometry of the reaction in perchloric acid can be described by the equation
+--+I-028I
I I
0.24-
+ Bi3+ + 9Mo(VI), e 18-MBiPA + 9H+
A discussion of the rather unique features of this 18-polyacid is presented later in this paper. For the present we shall simply designate the complex as 18-MBiPA or 18-molybdobismuthophosphoric acid. Kinetics of the Reduction of 18-MBiPA. While the formation of the heteropoly complex was very rapid, the reduction by ascorbic acid to form a heteropoly blue was slower, requiring minutes t o days depending on the conditions employed. In order to help clarify the overall reaction scheme, the kinetics of the formation of the heteropoly blue resulting from the reduction of the postulated 18-molybdobismuthophosphoric acid was investigated. (12) A. C. Javier, S. R. Crouch, and H. V. Malmstadt, Abstracts, 156th National Meeting ACS, Atlantic City, N.J., September 1968.
I
020-
+
H3P04
.
0.04 O 0 1
i
Figure 2. Absorbance of 18-MBIPA YS. the molar ratio of total molybdate to phosphorus bismuth
+
Reaction orders were obtained graphically from the slopes of plots of log initial rate cs. log initial concentration. Initial reaction rates were obtained graphically from the initial slopes of the absorbance us. time curves. An induction period preceded the initial linear portion of the absorbance rs. time curves. This induction period was usually quite short, about 5-20 seconds, becoming somewhat longer with slower rates. No more than about 3-4% of the total reaction curve was used in evaluating initial rates. This ensured, in part, that the assumption made in the theoretical treatment, that the solution concentration was the same as the initial concentration, was valid. Relative initial rates were used throughout the study and no rate constants were determined because the exact concentration of the Mo(V1) dimer and the heteropoly blue were not known and could not be easily determined. No attempts were made to adjust the ionic strength to some constant value. The perchloric acid concentration was always constant and much larger than the other reagent concentrations so, in effect, the ionic strength was constant except during the acidity studies. F o r the acidity studies the range of acid conceiitrations used was very small and any ionic strength effect would be very small. VOL. 41, NO. 3, MARCH 1969
493
-log
%SCORBlC
ACID
Figure 4. Determination of reaction order with respect to ascorbic acid Figure 3. Determination of reaction order with respect to perchloric acid
KH,PO, = 40.0pM, Bi(N03), HC104 =0.240M
KH,P04 = 40.0wM, Bi(NO,), = 40.0pM, Na,MoO, = 2.00mM, ascorbic acid = 7.60mM
reduction of 18-MBiPA can be written as
The experimental reaction order data are summarized in Table 111. In 0.16 to 0.32M perchloric acid the reaction was found to be first order in phosphate, first order in bismuth, and ninth order in total Mo(V1). The order of perchloric acid varied from inverse ninth order at high concentrations to almost zero order at low concentrations as shown in Figure 3. It was not possible to actually attain the zero order dependence because further decreases in the acidity resulted in substantial amounts of 18-MBiPA being formed prior to reduction, thus invalidating the assumption that only the perchloric acid concentration was changed. The order of ascorbic acid varied from first order at low concentrations to zero order at high concentrations as shown in Figure 4. This behavior was similar to that observed by Crouch and Malmstadt ( 9 ) for the reduction of 12-molybdophosphoric acid and suggests a rate law given by d[blue]
k [H3P041[BiS+l[Mo(VI),]g
=
40.0rM, Na,MoO,
=
Z.OOmM,
+ Bi3+ + 9Mo(VI), e k i 18-MBiPA + 9H+
H3P04
k-i
and 18-MBiPA
+ Red
kz
Blue
+ Ox
where Red refers to the reductant, ascorbic acid. The reverse of the reduction reaction does not need to be considered here because only initial reaction rates were measured. A standard kinetics derivation using the steady-state treatment (13) produces the final rate equation d[blue] -=-
kl[H3P04 ] [ B P I [Mo(VI),]g
dt
(4)
Thus when the concentration of ascorbic acid is large - , k-1 [H+]9
