Diffusion coefficients of lead (II) nitrate in nitric acid aqueous solutions at 298 K

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1 Journl of Moleculr Liuids 111 (004) 8 Diffusion coefficients of led (II) nitrte in nitric cid ueous solutions t 98 K, b Artur J.M. Vlente, An C.F. Ribeiro, Victor M.M. Lobo *, A. Jimenez Deprtment of Chemistry, University of Coimbr, Coimbr, Portugl b Deprtment of Anlyticl Chemistry, University of Alicnte, P.O. Box 99, 0080 Alicnte, Spin Received 10 Mrch 00; ccepted 9 June 00 Abstrct y5 Interdiffusion coefficients of led (II) nitrte in wter nd in nitric cid (10 10 M) mixtures t K, nd t concentrtions from to 0.1 M, hve been mesured using conductimetric cell nd n utomtic pprtus to follow diffusion. The cell uses n open-ended cpillry method nd conductimetric techniue is used to follow the diffusion process by mesuring the resistnce of solution inside the cpillries, t recorded times. The diffusion of led (II) nitrte is clerly ffected by the presence of HNO s well s by the led (II) hydrolysis. At the highest HNO concentrtion (0.01 M) the effect of the hydrogen ions on the whole diffusion process hs n importnt nd min role, whilst t the highest Pb(II) concentrtion the presence of HNO s well s the hydrolysis cn be neglected. These vlues re supported by UV-spectroscopy s well s by ph mesurements. The experimentl interdiffusion coefficients re discussed on the bsis of the Onsger Fuoss model. 00 Elsevier B.V. All rights reserved. Keywords: Mutul diffusion coefficients; Interdiffusion coefficients; Led; Hevy metls 1. Introduction Hevy metls, with mny useful pplictions in our life, re very hrmful if dischrged into nturl wter resources. Led is n exmple of hevy metl clssified s priority pollutnt by the US Environmentl Protection Agency Metls w1x. Mny industril pplictions, e.g. surfce tretment, still use led in their components; it cn lso be bsorbed by living beings; one interesting cse is tht cork used for mny pplictions (s for exmple, seling wine bottles nd conseuent diffusion of such metls to wine) cn crry some mounts of led bsorbed by Quercus Suber L. In the lst few yers much work hs been done in heterogeneous systems to remove led from different environments w,x. Fundmentl studies on Pb(II) solutions hve been done often involving determintion of self-diffusion coefficients by electrochemicl techniues w4 8x. However, s fr s *Corresponding uthor. Tel.: ; fx: E-mil ddresses: vlobo@ci.uc.pt (V.M.M. Lobo), lfjimenez@u.es (A. Jimenez). the uthors know, no dt on the mutul differentil diffusion coefficients of Pb(II) slts re published w9x. Led (II) nitrte ueous solutions re slightly cidic if unbuffered. The generl hydrolysis eution of Pb(II) my be ( xyy) xpb yøho Pb x(oh) y yho (1) nd the most prominent hydrolysed species re 4 4 Pb 4(OH) 4 nd Pb 6(OH) 8 w10x. The formtion of number of complex species cretes difficulties in the mesurements, nd my justify the scrcity of diffusion dt for led (II) ueous solutions. In this study mutul diffusion coefficients, D, (interdiffusion coefficients) re reported for ueous solutions of led (II) nitrte in concentrtion rnge to 0.10 M, t different nitric cid conditions (0, y5 y 1.00=10, 1.00=10, 1.00=10 M). The open- ended conductimetric cpillry cell w11,1x ws used. These dt fulfil gp in the literture for hevy metl ions nd will help the understnding of the mechnism of sorption nd relese kinetics of these ions in polymeric systems /04/$ - see front mtter 00 Elsevier B.V. All rights reserved. doi: /j.molli

2 4 A.J. Vlente et l. / Journl of Moleculr Liuids 111 (004) 8. Experimentl.1. Regents Led (II) nitrte, Pb(NO ) nd nitric cid (HNO ) were obtined from Riedel-de-Hen, pro nlysis grde. Pb(NO ) solutions were prepred from the solid slt, dried t 10 8C; distilled nd degssed wter, with n y4 y1 y1 ionic conductivity lower thn 1.0=10 V m, ws used... Open-ended conductimetric cpillry cell An open-ended cpillry cell, used to obtin mutul diffusion coefficients of lrge mount of electrolytes w1x, is described in gret detil in previous ppers w14 16x. Bsiclly, it consists of two verticl cpillries, ech closed t one end by pltinum electrode nd positioned one bove the other with the open ends seprted by distnce of pproximtely 14 mm. The upper nd lower tubes, initilly filled with solutions of concentrtions 0.75c nd 1.5c, respectively, re surrounded with solution of concentrtion c. This mbient solution is contined in glss tnk 00=140=60 mm immersed in thermostt t 5 8C. Perspex sheets divide the tnk internlly nd glss stirrer cretes slow lterl flow of mbient solution cross the open ends of the cpillries. Experimentl conditions re such tht the concentrtion t ech of the open ends is eul to the mbient solution vlue c, i.e. the physicl length of the cpillry tube coincides with the diffusion pth. In other words, the reuired boundry conditions described in the literture w1x to solve Fick s second lw of diffusion re pplicble. Therefore the so-clled Dl effect w11,1x is reduced to negligible proportions. In mnully operted pprtus, diffusion is followed by mesuring the rtio wsrtyrb of resistnces Rt nd Rb of the upper nd lower tubes by n lternting current trnsformer bridge. In n utomtic pprtus, w is mesured by Solrtron digitl voltmeter (DVM) 7061 with 6.5 digits. A power source (Brdley Electronic Model ) supplies 0-V sinusoidl signl t 4 khz (stble to within 0.1 mv) to potentil divider tht pplies 50 mv signl to the pltinum electrodes t the top nd bottom cpillries. By mesuring the voltges V9 nd V99 from top nd bottom electrodes to centrl electrode t ground potentil, in frction of second, the DVM clcultes w. In order to mesure the differentil diffusion coefficient D t given concentrtion c, the bulk solution of concentrtion c is prepred by mixing 1 l of top solution with 1 l of bottom solution, mesured ccurtely. The glss tnk nd the two cpillries re filled with c solution, immersed in the thermostt, nd llowed to come to therml euilibrium. The resistnce rtio ws w mesured under these conditions (with solutions in ` both cpillries t concentrtion c) ccurtely gives the 4 untity t`s10 y(1w `). The cpillries re filled with the top nd bottom solutions, which re then llowed to diffuse into the bulk solution. Resistnce rtio redings re tken t recorded times, beginning 1000 min fter the strt of 4 the experiment, to determine the untity ts10 y(1 w) s t pproches t `. The diffusion coefficient is evluted using liner lest-sures procedure to fit the dt nd, finlly, n itertive process using 0 terms of the expnsion series of Fick s second lw for the present boundry conditions. The theory developed for the cell hs been described erlier w11x... Instruments ph mesurements were crried with ph meter PHM 40 from Rdiometer, with ph conjugted electrode Ingold U457-K7; the electrode ws clibrted immeditely before ech experimentl set of solutions. From ph meter clibrtion results zero ph of 6.897"0.00 nd sensitivity higher thn 98.7%. ph ws mesured in fresh solutions nd the buffers used were IUPAC-type of 4 nd 7 ph. UV-spectr were obtined using spectrophotometer Jsco V-50; the spectr were obtined between 45 nd 65 nm with bndwidth of 1.0 nm.. Results Mutul diffusion coefficients of Pb(NO ) in ueous solutions, D v0, nd in HO HNO mixtures, D v, re shown in Tbles 1 4, respectively. Dv is the men diffusion coefficient, clculted on the bsis of, t lest, three independent mesurements. Tble 1 lso shows the diffusion coefficients of Pb(NO ) nd HNO estimted by the Onsger Fuoss eution E. (), D w17x. The following polynomil in c dt by lest sures procedure 1 of ws fitted to the 1 Ds01c cc 4c () where the coefficients,,, nd re djustble prmeters. Tble 5 shows the coefficients to of 0 4 E. (). They my be used to clculte the vlues of diffusion coefficients t specified concentrtions within the rnge of the experimentl dt shown in Tbles 1 4. The goodness of the fit (obtined with confidence intervl of 98%) cn be ssessed by the correltion coefficient, R. 4. Discussion Tbles 1 4 show tht, decresing the ph, the diffusion coefficients of led(ii) nitrte chnge to higher vlues (positive devition in (D yd )yd ). Such devitions v0 0

3 A.J. Vlente et l. / Journl of Moleculr Liuids 111 (004) 8 5 Tble 1 Interdiffusion coefficients of led (II) nitrte in ueous solutions, D v0, nd those clculted from Onsger Fuoss eution (E. ()), D of, t5 8C cym Dv0y S Dv0 y DofPb(NO ))y D of(hno )y b D v0 b S Dv0 is the men diffusion coefficient of three experiments. is the stndrd devition of tht men. Tble Interdiffusion coefficients of led (II) nitrte in nitric cid (10-5 M) ueous solutions, D, t 5 8C Dvy S Dv y Dvv0 yd =100 y% See Tble 1. v D v0 Tble Interdiffusion coefficients of led (II) nitrte in nitric cid (10 y M) ueous solutions, D, t 5 8C Dv y S Dv Dvv0 yd =100 y% See Tble 1. v D v0 Tble 4 Interdiffusion coefficients of led (II) nitrte in nitric cid (10 M) ueous solutions, D,t 5 8C Dv y S Dv Dvv0 yd =100 y% See Tble 1. v D v0

4 6 A.J. Vlente et l. / Journl of Moleculr Liuids 111 (004) 8 cn be neglected only t 0.1 M concentrtions, probbly due to other phenomen such s, for exmple, ion-pir formtion w18 0x. Those devitions cn be minly due to two different fctors: () ltertion of free Pb (II) concentrtion with decrese of hydrolysis products; ndyor (b) effect of the free hydrogen ion concentrtion in solution. To understnd the trnsport process of this electrolyte in the bove systems, it is necessry to know the behviour of Pb(NO ) in ueous solutions. For tht the experimentl interdiffusion coefficients were compred, s first pproch, with those estimted by the Onsger Fuoss eution (E. ()) M B lny E " Ds000 RT C1c F () c D c G where c ) z1) nl 1 c c M ll DM9 DM0 s1.0741=10 (4) In E. (4), the first- nd second-order electrophoretic terms re given by 0 0 ) z ) l y) z ) l y19 DM =10 cyt s = 0 1 c ) ) h ET 1k nd Ž. zz 1 L Ž. 0Ž. Ž. 0 0 Ž zl1yz1l. y1 DM0 9.04=10 c s = 1 f(k) 0 c Ž L. h0ž ET. where ts8cz i i is the ionic concentrtion, h 0 is the viscosity of the solvent, k is the reciprocl verge rdius of ionic tmosphere (e.g. w1x), is the men distnce of pproch of ions, f(k)s k ) e E(k)y(1k) i ) hs been tbulted by Hrned nd Owen w1x, nd the other letters represent well-known untities w1x. In this eution, phenomen such s ion ssocition nd hydrolysis re not tken into considertion. Compring the estimted diffusion coefficients of Pb(NO ), D, with the relted experimentl vlues of (Tble 1), n increse in the experimentl D vlues is Tble 6 Estimted percentge of hydrogen ions,, resulting from the hydrolysis of Pb in ueous solutions of led (II) nitrte t K, using Es. (5) nd (6) wpb(no ) xy(m) y% For this concentrtion we cn consider s non-relevnt. found in led(ii) nitrte concentrtions below 0.05 M. This cn be explined not only by the initil Pb(NO ) grdient, but lso by further HO flux, ccording to E. (1). Conseuently, s HO diffuses more rpidly y thn NO or Pb, the led(ii) nitrte grdient gener- tes its own HNO flux. Thus, the Pb(NO ) ywter mixture should be considered ternry system. However, in the present experimentl conditions we my consider the system s pseudo-binry, minly for cg0.01 M. For c-0.01 M, we cn estimte the concentrtion of HO produced by hydrolysis of Pb(II) using Es. (5) nd (6) ssuming tht: () the fluxes of the species, HNO nd Pb(NO ), re independent; (b) the vlues of the diffusion coefficients, D of, come from E. (). The percentges of HO (or the mount of cid tht would be necessry to dd to one solution of Pb(NO ) in the bsence of hydrolysis, resulting in this wy simultion of more rel system) re estimted from the following eutions D (HNO )b D (Pb(NO ))sd (5) of of v bs1 (6) where =100 nd b=100 re the percentges of nitric cid nd led nitrte, respectively. From Tble 6 we cn conclude tht, for cg0.01 M, becomes very low, suggesting tht either the hydrolysis effect or the contribution of D (HNO ) to the whole diffusion process, of cn be neglected. Another limit sitution occurs in the HNO (0.01 M) Pb(NO ) systems (Tble 4). At M Pb(NO ) the experimentl interdiffusion coefficient is pproximtely the sme s the diffusion coefficient of nitric cid in ueous solution of 0.01 M concentrtion (Ds.01=10 m s ); however, t 0.1 M Tble 5 Coefficients to of E. () for interdiffusion coefficients of Pb(NO ) t H O HNO mixtures, t 5 8C 0 4 whno xym R 0.=10 y9.14=10 y8 1.61=10 y7 y5.6=10 y7 7.=10 y =10 y5.=10 y9 y1.=10 y8 4.77=10 y8.1=10 y =10 y.4=10 y9 y1.5=10 y8 5.5=10 y8 y7.47=10 y =10.49=10 y9 y8.97=10 y9 y8.45=10 y8 5.61=10 y7 y8.79=10 y7 0.98

5 A.J. Vlente et l. / Journl of Moleculr Liuids 111 (004) 8 7 Pb(NO ), Dvis very close to the interdiffusion coefficient of led(ii) nitrte in ueous solution, for the sme concentrtion (see Tble 1). While in the first cse the nitric cid is the species tht controls the diffusion process, in the ltter is the led (II) nitrte. Hving in mind these considertions, we cn lso use Es. (5) nd (6) to estimte the percentges of nitric cid nd led nitrte, which re, in ech concentrtion rnge, controlling the diffusion process (Tble 7). For tht, we took the experimentl vlues of diffusion coefficients of led nitrte in ueous solutions (Tble 1) due to limittions of the Onsger Fuoss theory for c)0.01 M w18,1x. From Tbles 6 nd 7, we my conclude tht for wpb(no ) xf0.01 M the percentge of nitric cid responsible for contribution of the diffusion of led nitrte in ueous solutions t 0.01 M nitric cid, re the result of the sum of two contributions: the hydrolysis of led nitrte nd the dded HNO. For the other vlues of HNO mixtures (0.001 M nd M) the contribution of the percentge of nitric cid is very smll nd in some cses cn even be neglected. For wpb(no ) x)0.01 M the percentge of nitric cid direct- ly results from HNO (see Tble 8), being more relevnt to 0.01 M. From the estimted vlues of nd b shown in Tbles 6 nd 7, we my conclude tht the pplicbility of Es. (5) nd (6) is only relible t M- wpb(no ) x-0.1 M. Those estimtions re in good greement with other experimentl results. UV-spectr of Pb(NO ) M solutions t different nitric cid concentrtions were obtined. The normlised bsorbnce, A, of Pb(II), t 00 nm, in solution of HNO 0.01 M, is pproximtely five times higher (As0.089) thn tht found for Pb(II) Tble 8 ph vlues of Pb(NO ) ueous solutions with different concentrtions of HNO t 5 8C whnoxym 0 1=10 y5 1=10 y 1= y5 solution without nd with HNO 1=10 M (As 0.018). When the nitric cid concentrtion increses to y4 y 1=10 M nd 1=10 M only slight bsorbnce increse is found, 0.01 nd 0.06, respectively. This shows tht only in HNO =10 M mixture the concen- trtion of Pb(II) is closer to the initil concentrtion of Pb(NO ), nd on these conditions the mesured diffusion coefficient becomes close to the interdiffusion coefficient of led(ii) nitrte (without hydrolysis products). However, compring the fitting eutions (Tble 5) of the experimentl results to the Pb(NO ) HNO 0 (10 M) system, the limiting diffusion coefficient, D, obtined by extrpoltion of the mentioned fitting eution is significntly higher (.7=10 m s ) thn 0 the D of Pb(NO ), which is 1.407=10 m s. The Nernst limiting diffusion coefficient ws computed from 0 0 y D (Pb )s0.95=10 m s nd D (NO )s 1.90=10 m s w18x. Although the hydrolysis cn be neglected t such conditions, this cnnot explin such Dv vlues. However, t the lowest Pb(II) concentrtions nd HNO 0.01 M, Dv vlues pproch the diffusion coefficients of nitric cid in ueous solution. This suggests tht in these conditions, the hydrogen ions will hve n importnt contribution to the mesured diffusion coefficient. The nlysis of the ph vlues in led(ii) nitrte fresh ueous solutions, with different HNO concentrtions (Tble 8), shows tht the hydrogen ions chnge with Pb(II) concentrtion ccording to the following fitting eutions: who xs5.58=10 y5 6.81=10 ln wpb(ii)x (R s0.988), who xs y5 y5 4.1=10 4.1=10 ln wpb(ii)x (R s0.98), y y5 who xs1.414=10 9.9=10 lnwpb(ii)x (R s y 0.989), who xs1.45= =10 lnwpb(ii)x (R s0.989), to mixtures of Pb(II) nd y5 y HNO t concentrtions 0, 10, 10 nd 10 M, respectively. Tble 7 Estimted percentge of nitric cid,, responsible for further contribution to the diffusion of led nitrte in ueous solutions t different HNO concentrtions, using Es. (5) nd (6) y% whnoxs0.01 M whnoxs0.001 M whnoxs M ; ;0.0 ;0.0 ;0.0

6 8 A.J. Vlente et l. / Journl of Moleculr Liuids 111 (004) 8 From the experimentl fitting eutions (of who x s function of initil concentrtion of Pb(II)) described bove, nd from the open-ended conductimetric initil conditions, it is possible to conclude tht in HNO =10 M mixtures, the hydrogen ions bulk con- centrtion, t wpb(no ) xs10 M, is pproximtely y 6.6=10 M, whilst t wpb(no ) x eul to 0.01 M nd 0.1 M tht concentrtion increses to 9.10=10 y nd 1.18=10 M, respectively. However, it is cler tht the ionic strength t the Pb(NO ) lowest concentrtion is controlled by the cid w18x. In the unbuffered Pb(NO ) solutions the hydrolysis cn lso be noted by the nlysis of the ph vlues, but the contribution of the HO for the whole diffusion process is not so significnt s before: the hydrogen ion concentrtion chnges from 6.9=10 (wpb(no ) xs y M) to.78=10 M (wpb(no ) xs0.1 M). Although, in this cse, only trcer HO concentrtion grdients occur (1.9=10 to wpb(no ) xs0.001 M nd.=10 M to wpb(no ) xs0.1 M), they cn be neglected in the Pb(NO ) highest concentrtions, but justify the increse of Dv0 when the Pb(NO ) concen- trtion increses. Acknowledgments Finncil support from POCTIyQUIy nd Projecto Luso-Espnhol (E-y0) is grtefully cknowledged. References w1x L.H. Keith, W.A. Tellird, Environ. Sci. Technol. 1 (1979) wx J.C. Aguilr, M. Snchez-Cstellnos, E.R. de Sn Miguel, J. de Gyves, J. Memb. Sci. 190 (001) wx K. Kesenci, R. Sy, A. Denizli, Eur. Polym. J. 8 (00) w4x C.A. Allen, D.T. Irelnd, W.J. Fredericks, J. Chem. Phys. 46 (1967) w5x G.A. Motorny, E.Y. Ben ysh, Russ. J. Phys. Chem. 47 (197) w6x V. Dnel, V. Plichon, Electrochim. Act 7 (198) w7x T. Store, G.M. Hrbeg, R. Tunold, J. Appl. Electrochem. 0 (000) w8x R. Mills, V.M.M. Lobo, Self-diffusion in Electrolyte Solutions, Elsevier, Amsterdm, w9x V.M.M. Lobo, Hndbook of Electrolyte Solutions, Elsevier, Amsterdm, w10x C.F. Bes Jr, R.E. Mesmer, The Hydrolysis of Ctions, John Wiley nd Sons, New York, 1976, pp w11x V.M.M. Lobo, Ph.D. Thesis, Cmbridge, w1x J.N. Agr, V.M.M. Lobo, J. Chem. Soc., Frdy Trns. I71 (1975) w1x V.M.M. Lobo, Pure Appl. Chem. 65 (199) w14x V.M.M. Lobo, A.C.F. Ribeiro, M.P.V.erıssimo Luıs, Ber. Buns. Phys. Chem. 98 (1994) w15x V.M.M. Lobo, A.C.F. Ribeiro, L.M.P. Verıssimo, J. Chem. Eng. Dt 9 (1994) w16x V.M.M. Lobo, A.C.F. Ribeiro, S.G.C.S. Andrde, Ber. Buns. Phys. Chem. 99 (1995) w17x V.M.M. Lobo, A.C.F. Ribeiro, S.G.C.S. Andrde, Port. Electrochim. Act 14 (1996) w18x R.A. Robinson, R.H. Stokes, Electrolyte Solutions, nd ed, Butterworths, London, w19x V.M.M. Lobo, A.C.F. Ribeiro, Port. Electrochim. Act 1 (1994) w0x V.M.M. Lobo, A.C.F. Ribeiro, L.M.P. Verıssimo, J. Chem. Eng. Dt 9 (1994) w1x H.S. Hrned, B.B. Owen, The Physicl Chemistry of Electrolytic Solutions, rd ed, Reinhold Pub. Corp, New York, 1964.