J. Chem. SOC., Faraday Trans. 1, 1982,78, 7-15 Complex Formation in Molten Salts Association Constants of Lead Halide Complexes in Molten KN0,-Ba(NO,), Eutectic as Solvent BY RAGHUVESH K. GUPTA AND HARISH C. GAUR* Centre of Advanced Study, Department of Chemistry, University of Delhi, Delhi-110 007, India Received 1st July, 1980 Thermodynamic association constants and specific Helmholtz free energies for the formation of the species PbX+, PbX, (X = C1, Br or I) in dilute solutions of Pb(NO,), and KX in molten KN0,-Ba(NO,), (87.6: 12.4 mol%) in the temperature range 568.2-628.2 K are reported. An e.m.f. method involving measurements of activity coefficients of (K,Ba)X and Pb(NO,), using Ag,AgX(s) and Pd-PdO-PbO indicator electrodes, respectively, was employed. Data did not suggest the formation of the dinuclear species.Applicability of the quasi-lattice model equations in predicting temperature coefficients of association constants in the above temperature range has been examined. The near-ideal behaviour of Ag,Ag+ as an indicator electrode in molten alkali and alkaline earth nitrate mixtures as solvents has enabled the potentiometric investigation of silver halide c~rnplexes~-~ in these solvents. Relatively fewer similar studies of complexes of other metal ions, particularly divalent, using indicator electrodes of second kind have been rep0rted.l Although the use of Pd-PdO-CdO as an electrode of a third kind, reversible to Cd2+, was suggested by Inman,8 the applicability of this electrode to other cases does not appear to have been fully exploited.The object of this study was to explore further the possibility of extending the use of the Pd-PdO-MO (M = Pb, Co, Ni, Zn) electrode to potentiometric studies of the halides and other complexes of these metals. In this paper we present a potentiometric study of association equilibria of lead-chloro complexes using the Pd-PdO-PbO indicator electrode, and lead-bromo and iodo complexes using the Ag,AgX(s) (X = Br or I) indicator electrode. EXPERIMENTAL The cell, furnace, method of temperature control and measurement, solvent preparation etc. have been described ear lie^.^ Electrodes were made from silver and palladium wires (1 mm diameter, purity 99.99%, Arora-Matthey) coiled at one end and dipping into a molten-salt solution; the other end of the wire served as the potentiometric lead.Before use, the electrodes were pre-treated in a uniform manner. The palladium wire was polished with an extra fine emery paper moistened with AnalaR acetone and wiped dry. The surface of the wire showed no scratches at x 10 magnification. After a series of measurements the wire had a superficial blue-black surface coating in presence of which the electrode behaviour was sluggish and erratic; it was removed before re-use. The silver wire was pre-treated in the same manner but finally heated in an alcohol flame. The reference half-cell used in the investigation was set up by dipping a coiled silver wire into a solution containing ca. lop3 moles of AgNO, per mole of solvent and an excess of KX (to precipitate AgX), and was isolated in a small portion of the melt contained in a glass tube with a fritted-glass (porosity G-4) bottom dipping in the melt; the rest of the melt in the cell served as the indicator half-cell.7Ag,AgX(s)- KN0,-Ba(NO,), KX(R kx) (4 where n, is the number of moles of species i KN0,-Ba(NO,), PbO, PdO, Pd KX(RKX) (X = C1) Pb(N03)2 (RPb(NOI)2) Agx(s),Ag (X = Br,I) (+I and lZKN03 = 7.06. Y = - nBa(N03)~ At the low solution concentrations (Rd -c lo-,) employed in this study ion molar ratios are not significantly different from the ion fractions. The Ag,AgX(s) (X = Br, I) indicator electrode was set up by the addition of weighed amounts of AgNO, (R,,,,, < lo-, mole fraction) and an equivalent amount of KX. The Pd-PdO-PbO indicator electrode was set up by adding ca.250 mg each of PdO and PbO to the melt. The system was occasionally stirred over 8-10 h to achieve equilibration after which a known amount of KX-Pb(NO,), was added. Complexation was followed by change in e.m.f. of the cell on successive addition of Pb(NO,),-KX. The cell e.m.f. was measured with a L & N (type K-4) potentiometer provided with a L & N (type 9834) direct-current null detector. EVALUATION OF ASSOCIATION CONSTANTS The graphical extrapolation method of Braunstein et aZ.l0 has been employed for analysis of the e.m.f. data; essential details, as needed, are given below. Consider a dilute solution containing both Pb(NO,), and KX in KN0,-Ba(N0,)2 as solvent, and assume that Pb2+ and X- associate to form species of the type PbX+, PbX,, Pb,X3+.. . , the corresponding association constants being Kll, Klz, K,, . . . . In a charge-asymmetric solvent mixture such as this there are different numbers of cations and anions and hence different numbers of sites available to cationic and anionic species; there may thus be ambiguity in assigning Pb-containing species to either the cationic or anionic sites. Instead of using the mixing statistics of charge-asymmetric mixtures, the convention of assigning all Pb-containing species to cationic lattices has been used.ll The total (stoichiometric) concentrations of the solute components* are given by the mass-balance equationsl0? l1 Rpb = Rpb2+ + R p b ~ + RpbXz -I- 2Rpb2x3+ - . . (3) Rx = Rx- +PRp,x+ + 2pRpbx2 +PRpb2~3+ - . . (4) * Subscripts Pb, X and SX refer to the components Pb(NO,),, KX and (K, Ba) X, respectively.R.K. GUPTA AND H. C. GAUR no. of solvent cations = no. of solvent anions y+ 1 where - y + 2' -- We define the activity coefficients of the solutes in the usual form 9 ( 5 ) and RPb l/YPb = - RPb2+ R X VYSX = - RX- and association constants as Kll = RPbX+/RPbZ+ RX- K12 = RPbX2/RPbX+ RX- &i = RPb2X3+/ RPbX+ RPbZ+. (Although the solute is added as KX, its molar ratio, which is < lop3, does not significantly alter the ratio of the two solvent cations and the symbol ysx refers" to the activity coefficients of the pseudo-component Ky12+y Ba112+yX.) Eqn (3) and (4) then take the form '/Yl'b = 1+Kl,RXYSX+KllK12R&Y~X+2KllK21RXRPbYsXYPb+... (6) '/YSX = +PK11RPbYPb+2pK11K12RPbRXYPbYSX+PK11K21 R k b Y h + - .* * (7) Using an iterative procedure on eqn (6) and (7) we get l/?Pb = + Kll R X + K11(2K21 -pKii) RX RPb + Kii K12 R & + - (8) '/?SX = 1 + ~ K l l R P b + ~ K 1 1 ( 2 K 1 2 - K 1 1 ) R X R P b + ~ K ~ ~ K ~ ~ R k b + * . * . (9) * Taking the logarithm of eqn (8), neglecting third- and higher-order terms in the expansion of the individual terms and rearranging, one obtains In ]/?Pb = K1l RX +K11(2K21 -PKii) RX R p t j +K11(K12-~K11) R$ -k . - (10) from which the equations for K,, and K,, using Ag,AgX(s) as indicator electrode are (1 1) s~(o,o) = lim [S,(O>] = lim (T ' ( l ~ ~ ) ) R x = pKll Rx+O Rx-0 and where S,(O) is defined by To evaluate KZl, eqn (9) was re-writtenlO as a function of Rpb in the form (l/ySx- 1) = A R p b + B R k b + . . ..(14) Least-squares fitting was done at several different initial concentrations of Rx. The intercept of the plot of B against Rx on extrapolation to Rx = 0, Bo, enabled the evaluation of K,, lim B = Bo = pKll K21. (15) Rx -*O10 COMPLEX FORMATION IN MOLTEN SALTS Similar equationsll for the Pd-PdO-PbO indicator electrode, based on eqn (lo), are and lim B = B, = K11(~12-4~11) HPb-'O where Spb(0) is defined by The extrapolated limits lead to thermodynamic association constants. RESULTS AND DISCUSSION The liquid-junction potential has been minimised by using the same solvent in both half-cells. The reference half-cell both with Ag,AgX(s), (X = Br, I) and Pd-PdO-PbO, (X = C1) indicator electrodes is the Ag,AgX(s) (X = C1, Br, I) electrode; solubility of silver halide does not interfere with its use as the reference half-cell since the chemical potential of AgNO, in it remains constant owing to its isolation from the indicator half-cell.However, use of Ag,AgCl(s) in the indicator half-cell is excluded owing to the higher solubility12 of AgCl in molten KN0,-Ba(NO,),; the Ag,AgX(s), (X = Br, I) indicator electrode, owing to the lower solubility of AgX in this solvent, has been used successfully. In the absence of Pb(NO,),, the observed Nernst behaviour for the cell with Ag,AgX(s), (X = Br, I) indicator electrode was within k0.2 mV in the concentration range used, indicating that the activity coefficient remains constant and may be defined as unity for an infinitely dilute solution. With the Pd-PdO-PbO electrode (in the absence of KC1) experimental Nernst slopes, Sexpt, were 68.0, 72.0 and 75.0 mV compared with the theoretical values 58.3, 60.3 and 62.3 mV at 588.2, 608.2 and 628.2 K, respectively; the discrepancy in the latter has been ascribede to the possibility of a mixed potential involving oxygen at the palladium electrode. Activity coefficients have been evaluated using eqn (21) where AE,,,, is the change in e.m.f.of the cell on the addition of KX-Pb(NO,),. In the evaluation of the activity coefficient (log ypb) using the Pd-PdO-PbO electrode, Sexpt was employedl37 l4 instead of 2.303 RT/2F. Extrapolation of the Ecell against Rpb2+ plot [before the addition of Pb(NO,),] to Rpb2+ = 0 showed that the concentration due to the dissolution of PbO was no greater than molar ratio; uncertainty of this order in the initial value of R p b would have a negligible effect on the result.Typical data for the variation of YSX/pb as a function of RX/pb were obtained; someR. K. GUPTA AND H. C . GAUR 11 of these data are plotted in fig. l ( a ) and 2(a).* The extrapolated plots are given in fig. l(b) and 2(b). Since the limiting slopes [asB,(o)/aRB,] at all the temperatures employed take near-zero values, it follows from eqn (12) that for lead-bromo association K,, = K11/2. Also the near-zero or negative values of Bo for X = Br or I and the negative slope of (1 +K,,R,,) spb(0) against Rpb plot (not shown) imply the absence of formation of dinuclear species Pb,X3+ (X = C1, Br, I) under the experimental conditions used in this study. 0.2 0.1 :::; 0 1 2 3 4 5 -1.5‘ - 1 :; - 2 0 2 4 6 8 1 104 R~ ab 7 6 1 I 5 t 1 1 I 1 I 0 2 4 6 8 1 1 I 0 4 R~~ FIG.1.-PbCI system. (Temperatures: 0, 588.2; A, 608.2; e, 628.2 K.) (a) Variation of yPb as a function of R,, at different initial values of Rpb ( x lo4): 2.213 (I), 5.524 (II), 5.678 (111). (b) Graphical extrapolation of limiting slopes to evaluate K,, using eqn (16) (0, A, a) and (24) (A). The intercepts give the following values of Spb(O,O): I, 69 2; 11, 73 k 2; 111, 79 f 2. (c) Extrapolation of the coefficient B to evaluate K , , [eqn ( 1911. The plots of (l/ySBr) against R,, are straight lines [fig. 2(a)] at low R,, over the concentration range of lead nitrate employed; the data thus correspond, within experimental error, to eqn (22) [cf. eqn (9)] lim l/ySX = +PK1lRPb).R x -0 Following Braunstein et al. l4 and from the thermodynamic relation * Detailed data (at nine temperatures and 100 initial values of R,,,, with 1112 data points) may be obtained from H. C. G. on request.12 COMPLEX FORMATION I N MOLTEN SALTS 104 R~ 2 .4 2.2 2 .o - ' 1.8 i2 + 1.6 1.4 1.2 1 .o 103 R~,, 104 R~ FIG. 2.-PbX system [X = Br (I, 11, III), X = I (IV, V, VI)]. Temperatures: 0,568.2; 0,588.2; A, 608.2 K. (a) Variation of ysx as a function of Rpb at different initial values of Rx ( x lo4): 12.239 (I), 10.817 (II), 6.121 (111), 5.777 (IV), 9.484 (V), 11.588 (VI). (b) Graphical extrapolation of limiting slopes to evaluate K , , and K,, [eqn (11) and (12)]. The intercepts give the following values of S(0,O): I, Sf;O) = 150::; 11, S$;O) = 135f 1; 111, Sf;') = 1225:; IV, Sio,O) = 2120+:!,; V, S:Ovo) = 2580f80; VI, Sio,O) = 3280+,6:.TABLE 1 .-ASSOCIATION CONSTANTS K,, AND K,, AND SPECFIC HELMHOLTZ FREE ENERGIES - AAll AND - AA,, FOR THE ASSOCIATION OF LEAD AND HALIDE IONS IN MOLTEN KN0,-Ba(NO,), EUTECTIC MIXTURES ~~ temp./K K1lU K1zU - AAllb - A A , , ~ 588.2 608.2 628.2 568.2 558.2 608.2 568.2 588.2 608.2 79+2 73+2 69+2 169:; 152+ 1 1372; 3687';; 2900 +_ 90 2383f!!, 33+ 1 26:; 212; 84f 1 76f 1 69+ 1 14701g 98 1 ?:: 81 1::: PbCl 13.80 & 0.12 13.89 +O. 13 13.38':::; 14.08 k 0.14 12.86'::;: 13.89 k 0.14 PbBr 16.772:::; 17.752:::: 16.86 k 0.03 17.89 f 0.06 Values of Ki, are in (moles per mole of solvent)-'. Values of AAij have been given for 2 = 5 only and are in kJ mol-l.R. K . GUPTA AND H. C.GAUR 13 Thus PKll spb(o) = 1 +pKll R,, by virtue of eqn (20), (22) and (23). This equation, valid at low solute concentrations and in tile absence of inuclear species, can enable evaluation of Kll even from a single set of data. Values of K,, (PbCI+) evaluated using eqn (24) [fig. 1 (b)], are close to the extrapolated values. Values of the association constants are given in table 1. Temperature variation in the values TABLE 2.-sPECIFIC HELMHOLTZ FREE ENERGIES FOR THE ASSOCIATION OF Pb2+ WITH x- (X = C1, Br, I) IN DIFFERENT NITRATE SOLVENTS nitrate solvents (mole %) - AAIla ( Z = 5 ) Li Na K Ba temp./K /kJ rnol-' ref. 50 - 50 - 87.6 - 25 75 50 50 53 47 75 25 50 87.6 100 - - - - - 50 - - - - - 87.6 - x = c1 - 433-473 12.4 568-628 X = Br - 553-573 - 5 13-573 - 528-592 553-573 - 433-473 12.4 568-608 - 51 3-573 X = I 12.4 568-608 - 14.40 13.92 17.07 16.86 16.30 16.63 18.90 16.86 17.21b 31.17 22 this work 24 24 25 24 22 this work this work a Average values in the indicated temperature range have been taken for comparison.* By extrapolation of values in ref. (24). of the Kii was used to evaluate the specific bond free energies the energy required for the formation of associated species PbiXYi-i)+, (X = C1, Br, I) using the following equations for the gener alised quasi-lat tice model' 5-1 Kll = Z(P11- 1) (25) K12 = T [ / ? 1 2 - 2- 1 1 P11- 1 where Pii = exp ( - Acii/RT) and Z is the quasi-lattice coordination number. Since the value of 2 is not known a priori, calculations were made for 2 = 4, 5 and 6 (a reasonable range of values of this parameter).18 Constancy of Acij (table 1) for different values of 2 indicated that the specific entropy of association was negligible and thus Aeij could also be c o n ~ i d e r e d l ~ ~ ~ ~ - ~ ~ as the specific Helmholtz free energies AAij so that the temperature coefficient of Kij was predictable within the temperature range investigated. AAll in this study has also been compared (table 2) with values in other single and binary molten nitrates as solvents.The effect of the presence of Ba2+ ions in the solvent mixture KN0,-Ba(NO,), on the association energy (available from data14 COMPLEX FORMATION I N MOLTEN SALTS for lead-bromo association) has been examined in terms of the reciprocal coulombic effe~f.~l-~, Considering AA,,, (in mixed solvent) to vary according to the equation (27) (where Y is the mole fraction of KNO,) calculations predicted a ‘destabilisation’ to the extent of 3.38 kJ mol-1 in the KN0,-Ba(NO,), eutectic mixture when compared AAmix = YAA,,,3+(l - Y)AABa(No3), 3.01 Ba _c - 1 \ L i with KNO,; the experimental results give 0.35 kJ mol-l.The discrepancy is probably due in part to the neglect of long-range coulombic forces,24 the dispersion and polarisation energiesl89 23 and also the difficulty in assigning21 an ‘effective ionic radius ’ to the nitrate ion. For a given solvent composition the magnitude of destabilisation is in the order Ba2+ > Na+, while stabilisation due to the presence of Li+ is observed (fig. 3). The authors are indebted to the University Grants Commission, New Delhi (India) for a teacher-fellowship at the C.A.S., Department of Chemistry, University of Delhi to R.K.G.* Y. Marcus, Molten Salt Mixtures in Introduction to Liquid State Chemistry (Wiley Interscience, New York, 1977), p. 255. * H. C. Gaur and R. S. Sethi, Trans. Faraday Soc., 1968, 64,445. H. C. Gaur and N. P. Bansal, Indian J. Chem., 1971,9, 1273. H. C. Gaur and N. P. Bansal, J. Chem. Soc., Faraday Trans. I, 1972, 68, 1368. A. K. Adya, K. W. D. Verma, R. S. Sethi, S. K. Jain and H. C. Gaur, Electrochim. Acta, 1979, 24, 267. A. K. Adya, K. W. D. Verma and H. C. Gaur, Indian J. Chem., 1979, 17A, 232. K. W. D. Verma, R. K. Gupta and H. C. Gaur, Trans. Soc. Adv. Electrochem. Sci. Technol., 1980, 15, 1 . H. C. Gaur and W. K. Behl, Electrochim. Acta, 1963, 8, 107. * D. Inman, Nature (London), 1962, 194, 279, lo J. Braunstein, M. Blander and R. M. Lindgren, J . Am. Chem. Soc., 1962, 84, 1529.R. K. GUPTA AND H. C. GAUR 15 l1 H. Braunstein, J. Braunstein, A. S. Minano and R. E. Hagman, Znorg. Chem., 1973, 12, 1407. l2 H. C. Gaur and R. S. Sethi, Electrochim. Actu, 1968, 13, 1737. l3 D. Inman, Electrochim. Actu, 1965, 10, 11. l4 H. Braunstein, J. Braunstein and D. Inman, J. Phys. Chem., 1966,70, 2726. l5 M. Blander, J. Chem. Phys., 1961, 34, 432; J. Phys. Chem., 1959, 63, 1262. l6 M. Blander and J. Braunstein, Ann. N.Y. Acad. Sci., 1960, 79, 838. l7 D. G. Hill, J. Braunstein and M. Blander, J. Phys. Chem., 1960, 64, 1038. M. Blander, Molten Salt Chemistry (Wiley-Interscience, New York, 1964), p. 127. l9 S. H. White, D. Inman and B. Jones, Trans. Furaduy Soc., 1968, 64, 2841. 2o A. Alvarez Funes, J. Braunstein and M. Blander, J. Am. Chem. Soc., 1962,84, 1538. J. Braunstein and J. D. Brill, J. Phys. Chem., 1966, 70, 1261. 22 J. Braunstein and A. S. Minano, Znorg. Chem., 1964, 3, 218. 23 D. L. Manning, R. C. Bansal, J. Braunstein and M. Blander, J. Am. Chem. Soc., 1962, 84, 2028. 24 D. L. Manning, M. Blander and J. Braunstein, Inorg. Chem., 1963, 2, 345. 25 M. Bonneymay and R. Pineaux, C.R. Acad. Sci., 1955, 240, 1774. (PAPER O/ 1027)