F r a n k l i n A. S c h u l t z Flor~daAtlantlc Unwers~ty Boca Raton. Flor~da33431
Stoichiometry and Formation Constant Determination by Linear Sweep Voltammetry
A number of routine determinations m a y b e used as a basis for demonstrating modern electroanalytical techniques in t h e undergraduate laboratory. However, i n developing experim e n t s for a n integrated laboratory program at t h e advanced undergraduate level o u r faculty also sought to illustrate imp o r t a n t chemical concepts via t h e experimental results. A descriptive m a n n e r of presenting soiution equilibria is t o d e m o n s t r a t e how the distribution of molecular species in a m e t a l ion-ligand system d e p e n d s o n t h e stoichioinetry a n d formation constants of the m e t a l complex(es) and the concentration of t h e lieand. I n this oaDer a n e x ~ e r i m e n it s d e scribed i n which the equilihriumco&tants necessary for determinine the c o m ~ o s i t i o nand distribution of lead(I1)-oxalate . . species m a y b e measured by linear sweep voltammetry.
of oxslate concentration can he expressed by the mass balance condition
Description A traditional procedure for determining the formula and formation constant of a metal complex is to measure the shift in polamgraphic or voltammetric half-wave potential (AEIl2) for reduction of the metallic species as a function of the logarithm of ligand concentration ( I ) . However, if more than one complex exists in solution, this approach frequently leads t o incorrect or ambiguous results. For example, in the lead(l1)-oxalate system a conventional plot of Ellz versus log [CzOr2-] is linear and has a slope corresponding to a ligand number of approximately 2, which suggests the presence of only a single complex, Ph(Cs0r)z2-, with aformation constant of -5 X 10V2-4). DeFord and Hume (5) presented a more rigorous approach for analyzing E I R - C P ~ ~data , , ~ for possible successive complex formation, and Jain et al. ( 6 )used this method to demonstrate the existence of two complex species, Pb(C204)0and Ph(C20d)2Z-.The DeFord-Hume method requires calculation of the antilog of the measured half-wave potential shift and therefore is very sensitive to small errors (-0.5 mV or greater) in this quantity (7). We have found that undergraduate students encounterine electroanalvtical techniaues for the first time
Experimental Procedures Solid lead oxalate is prepared by mixing equimolar quantities of lead nitrate and sodium oxalate. The solid is washed thoroughly with water and ethanol and dried a t llO°C. A series of solutions is prepared with K z C ~ O concentration ~ varying between 0 and 0.050 M. The ionic streneth of eaeh solution is adiusted ~ ~ toaeonstant value (between 0.15and 1.j0) with KNOB.Solid PhC204. 100-200 mg, is equilibrated with occasional mixing with 100-ml portions of each solution for approximately 5 da in a water bath thermostated a t 25°C. After equilibration, a portion of each solution is carefully withdrawn and analyzed by linear sweep voltammetry. A calibration curve is constructed aver a concentration range of roughly 1X 10-5 to 2 X 10WM PhZ+in KN03 supporting electrolyte of the same total ionic strength as the oxalate solutions. The calibration curve is most easily prepared by making standard additions of a more concentrated Pb(NOs)2stock solution in KN03 to the base potassium nitrate electrolyte. This eliminates the need of frequent solution changes and lengthy deaeration procedures in the eleetrochemical cell duringpreparation of the standard curve. The lead nitrate stock solution can be standardized by titration with EDTA
Cpb = [Ph2+] t [Pb(C20d0) + [ P h ( C s 0 J ~ ~ - l Substitution of eqns. (1)-(3) into (4) yields
(4)
Cpb is determined by measuring the voltammetric peak current (i,) for Pb(I1) reduction a t different concentrations of C 2 0 F and comparing to a standard curve. The data are fitted to eon. (5) to obtain K,,,&, and Pp. Since voltammetric peak currents can be measured with greater accuracy than AE112values,this procedure isa more reliable way of determining the composition and formation constants of lead-oxalate complexes.
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(9).
oxalate complex formation. The necessary equilibrium constants can be ohtained from solubility studiesprouided the metal ion forms an insolublesalt and soluble complexes with the same ligand. Fortunately, such is the case for the Ph(l1)-oxalate system. Klatt (8) used this approach to establish the correct nature of the metallic species formed in this system by measuring the solubility of Ph(l1) in ovalate solutions polarographically. This experimental approach is readily adapted to linear sweep voltammetry with the advantage that data can he acquired more easily and rapidly by the voltammetric technique. While our experimental we discovresults are in excellent agreement with thoseof Klatt (8), ered that the soluhility data had been analyzed incorrectly in that work. The correct procedure for treating the solubility data is described in this paper. In solutions containing Ph(l1) and oxalate ion the pertinent equilibria are
K,, is the solubility product uf solid lead uxalatr.JI 13the formation constant of the uncharged 1:I wmplex, and s. is ihr overall hrmntron cunitant of the 1.2comldrx. I t solid lead urdlatr isequililrrated w t h solutions of increasing oxalate concentration, lead solubility first decreases due t o equilibrium (1)then increases due to equilibrium (3). The total concentration of Ph(I1) in solution, Cpb as afunction 62 1 Journal of Chemical Education
Voltammetric measurements are carried out with a Heath Model EUW-401 polarography module operated a t a scan rate of 0.5,1, or 2 V min-'. The i-ECurve is recorded on either an x-y or strip chart recorder. Solutions are contained in a Brinkmann Model E615 cell thermwtated a t 25%. Three electrode circuitry is used. A Brinkmann Model E410 microburet is used as a hanging mercury drop working electrode. The electrode area is typically 0.022 em2, and the drop is renewed prior to each trial. Three to five replicates are run on eaeh solution. A P t coil auxiliary electrode and commercial saturated calomel reference electrode complete the circuitry. Pure nitrogen gas is passed through the solution far -15 min prior to each experiment and over the solution during the measurement. Results a n d Discussion One set of experimental results is presented in Table 1. The voltammetric peak currents are converted to total Ph(I1) concentration and plotted against oxalate concentration as the solid line in Figure 1.One normally would think to obtain K,, by squaring the measured value of Cpb for the solution containing no added oxalate. Then, since the solubility curve is linear a t large oxalate concentrations, division of the intercept and slope of this line by K,, would yield 0, and 82, respectively (see eqn. (5)). Experimental results calculated in this manner by an entire class are compared with those from reference (8) in the upper two sections of Table 2. Both sets of results were caleulated by the same procedure and are in excellent agreement with one another. The above approach is incorrect, however, in that it fails to account for the intrinsicsolubility of lead oxalate in theOM oxalatesolutions. This contribution to solubility is frequently neglected, as has been pointed out on a number of occasions (I(t13). The intrinsic solubility
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(10) is defined as the concentration of the uncharged 1:l complex in a saturated solution of the salt
The concentration of Ph(C20A0 is equal to K,& and is independent of oxalate concentration. Contributions of the various Ph(I1I s ~ e c i e s i u Figure I, and tt cnn he to ('I.,,arr reprcirntrd i ~ ythe d ~ t t w hnrs l seen that PI,!('.04i ' makes .t < ~ o n ~ l ' ~ cmtrlhutivn mnt tro total .olw i,dtry;rr rrn~w.rr..st.~~Iate l'he(.t>nrentraI!c,nuf free 1 4 i r m in this solution is correctly expressed as
Results are plotted in Figure 2 at II = 1.00 using the corrected values in Table 2 for the calculations. It is interesting to note that the predominant lead species changes from Ph" to Pb(C204)0t o Pb(C204IiL)-over the range of oxalate concentrations studied. Also of significanre is the behavior of the uncharged 1:l complex, Pb(C20do, whose irnptrrtance in solubility equilibria is frequently overlouked. This species contributes suhstantially t o total lead solubility a t all oxalate concentrations examined, and in fact is the predominant Pb(l1) species between -3 X 10Wand 1 0 P M C ? O F .
Literature Cited Ill M c ~ ~ PI.I .."Pt,law~raphic'Perhniquer."?nd . Ed.. Wiley-ln&rscienceN e w York, 1961,
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