J . Chem. Soc., Faraday Trans. I , 1982, 78, 3447-3460 Rates of Extraction of Zinc into Organic Single Drops Containing Dithizone BY MICHAEL A. HUGHES* Schools of Chemical Engineering, University of Bradford, Bradford, West Yorkshire BD7 1DP AND Hou SUNGSHOU General Research Institute of Non-Ferrous Metals, Ministry of Metallurgical Industry, Peking, China Received 16th November, 1981 The rate of extraction of zinc from an aqueous phase, pH 4.0-5.2, by single drops of chloroform containing dithizone is reported. Rates for both drop travel and drop formation are given. The rates are compared with those of previous workers, but in this study the interfacial area is controlled and measured. Arguments are presented to demonstrate that the locale of the reaction is at the liquid-liquid interface and not in the hydrodynamic layer or bulk phase on the aqueous side of the interface as reported by previous workers.Criteria are presented which can be used to test for the locale of the general reaction between any extractant and metal in liquid-liquid contacting. The present rate data may be accounted for by Chapman’s model of chemical reaction at the interface coupled with diffusional transfer of all the species taking part in the overall reaction. Dithizone systems have served as the main model systems from which the basic ideas of the kinetic extraction mechanism of metal chelateslt have been developed. Irving et aL3 have suggested that the extraction rate is determined by the chemical reaction Zn2+(aq) + R-(aq) -+ ZnR+(aq) in which R- is the dithizone anion.The extraction rate increases almost in proportion to the equilibrium concentration of dithizone in the aqueous phase, the partition coefficient varying with diluent type. In almost all metal dithizone systems examined by F r e i ~ e r ~ - ~ a first-order rate of reaction with respect to metal and extractant concentrations was observed, together with a reciprocal first-order rate of reaction with respect to the hydrogen-ion concentration which corresponds to the equation above and an assumed aqueous-phase reaction. The rates for different metals follow the rates of substitution of the coordinated water. For the particular concentration conditions of the system of extraction used by Freiser we conclude that the formation of the 1 : 1 complex is a rate-limiting step.Fomin’s7 general approach to this problem allows for either 1 : 1 and 1 : 2 complex formation steps to be rate-limiting. Freiser contacted the two phrases at high intensity and found that increasing the rate of mixing did not increase the extraction rate. This was considered as proof of the homogeneous character of the limiting step. The unreliability of such a method of demonstrating the homogeneous character of a limiting step has been remarked upon several times in the literature. Probably the most important defect in Freiser’s work is the lack of interfacial area data, which makes the interpretation of the extraction mechanism difficult. 34473448 EXTRACTION OF ZINC Nitsch et al.sl rejected the homogeneous aqueous-phase mechanism of reaction, suggesting that reaction with zinc takes place at the interface.Extensive research involving various chelates and metals has been carried out by Kletenic et a1.1°-12 The heterogeneous character of the chemical reaction was demonstrated by the fact that the extraction rate is in proportion to the interfacial area and this proportionality is preserved on changing the interfacial area by more than 1000 times. However, Fomin7 considered that the surface reaction mechanism for the extraction with dithizone was not proved. These facts caused us to re-examine the extraction process of zinc by dithizone but using a technique where interfacial area is measured. We now include the generalised approach of mass transfer with chemical reaction coupled with a consideration of the solubility of the extractant in the aqueous phase.EXPERIMENTAL APPARATUS The falling-single-drop apparatus was standard has been previously described by Hanson et in an investigation to study the extraction of copper by chelating hydroxyoximes. The data were treated as in ref. (14) so as to remove the end effects due to mass transfer during drop formation. Four different column lengths were used in each run. The temperature of the experiments was 25 & 0.5 O C . CHEMICALS Dithizone was of A.R. grade (> 99% pure from B.D.H. Ltd). This extractant was also purified by the method used by Kletenic and Vinokurova,lo but in any case no significant difference was observed between the behaviour of the A.R. grade specimen and the purified form.The organic phase was prepared just before starting an experiment. Zinc solutions were made from zinc oxide (A.R.) dissolved in hydrochloric acid, evaporated to near dryness and then redissolved in the required amount of perchloric acid and then mixed with acetic acid and sodium acetate to the required ionic strength and pH. The diluent, chloroform, was of special high purity (A.R. grade) and described as ‘suitable for dithizone analysis’. All other chemicals were of A.R. grade, and water distilled from glass was used in all experiments. TECHNIQUE Ca. 80 drops per minute of the appropriate organic phase were made to fall through the appropriate aqueous phase. The drop size is ca. 2 mm in diameter when formed at the tip of a 33 gauge stainless-steel needle. The first 1 cm3 of organic loaded phase was discarded and then the next cubic centimetre(s) was retained for zinc analysis. The zinc in the solvent was analysed by a spectroscopic method13 at wavelengths 535 and 524 nm; a Pye Unicam SP800 spectrophotometer was used.The pH of the aqueous phase was kept constant by an acetate buffer. Before extraction the aqueous phase was saturated with chloroform and the organic phase was saturated with the aqueous phase but without zinc present. The ionic strength of the aqueous phase was kept constant (p = 0.25). Interfacial tensions were measured by use of the drop-volume method and viscosities were measured using an Ubbelohde viscometer.M. A. HUGHES A N D H. SUNGSHOU 3449 RESULTS PROOF THAT THE REACTION CONTROL STEP IS NOT I N THE AQUEOUS HOMOGENEOUS BULK PHASE OR A N AQUEOUS ZONE The rates of extraction per unit area during drop travel are calculated from a least-squares treatment of the mass-transfer data from the different column lengths after ref.(14). The value of the intercept obtained from the plot of mass transfer against time was considered to be the amount of metal extracted during drop formation per unit interfacial area. A typical treatment of results is given in table 1. In all these experiments the HR concentration is always higher than the Zn concentration in the bulk phases. The rate of mass transfer, D, = 3.833 x loA7 rnol m-2 s-l, was calculated from the plot of mass $ransfer against time from table 1. The amount of metal extracted during the drop formation is 5.35 x mol mP2, calculated from the intercept.TABLE 1 .-TYPICAL RESULTS C,,, organic phase = 1 x loF3 mol dmP3, pH 4.25, Czn, aqueous phase = 1 x mol dmP3, ionic strength = 0.25, temperature = 25 "C. column v, s, length time volume of surface of (s/v) [Zn],/105 mass transfer/106 /cm / s drop/cm3 drop/cm2 /cm-l mol dm-3 rnol m-2 45 3.0 0.003 85 0.1187 30.83 2.0 6.48 75 5.1 0.003 77 0.1170 31.08 2.3 7.41 125 8.7 0.003 67 0.1149 31.31 2.6 8.30 180 12.73 0.003 38 0.1087 32.19 3.3 10.25 TABLE 2.-sUMMARY OF RATES OF EXTRACTION UNDER VARIOUS CONDITIONS results of experiments rate of during drop during experimental conditions mass transfer extraction [H+l [HWO [Zn2+] formation drop falling pH /mol dmP3 / 1 OP3 rnol dmP3 / 1 0-4 mol dm-3 / 1 0-9 rnol cm-2 /mol cmP2 s-' 4.75 5.157 4.154 4.701 5.099 4.186 4.47 5.090 4.52 4.52 5.099 5.14 1.78 x 6.79 x 7.01 x 10-5 1.99 x 10-5 6.51 x 10-5 3.39 x 10-5 3.0 x 10-5 3 .o ~ 10-5 7.96 x lop6 8.02 x 01-6 7.96 x lop6 7.69 x 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 0.496 1.829 0.496 1.829 1 .o 1 .o 2.5 2.5 2.5 5.0 5.0 5.0 2.5 2.5 2.5 2.5 1.246 0.826 0.73 0.86 1.02 1.01 1.04 1.14 0.56 1.31 0.54 1.33 7.0 x lo-" 1.06 x 10-lo 5.1 x lo-" 1.01 x 10-'O 1.09 x 10-lo 7.5 x 10-1' 9.55 x lo-" 1.29 x 10-lo 3.30 x 10-l' 1.20 x 10-10 5.40 x lo-" 2.19 x3450 EXTRACTION OF ZINC TABLE 3.-INTERFACIAL TENSIONS AT 25 & 0.1 OC IN mN Ill-' aqueous zinc solution, pH 4.66, zinc solution, pH 5.1, [Zn] = 2.5 x mol dm-, [Zn] = 2.5 x mol dm-, chloroform 23.0 - 0.496 x lo-, mol dm-, - 22.29 1.06 x lop3 mol dm-, - 23.40 1.829 x lop3 mol dm-, - 22.68 dithizone in CHC1, dithizone in CHC1, dithizone in CHC1, - 23.27 22.26 6(av) = 22.78 mN m-'.TABLE VI VISCOSITIES AT 25 & 0.1 OC IN mPa s ~~ ~ ~ ~~ sample viscosity CHCI, 0.536 1.06 x lo-, mol dm-, HDz in CHCl, 0.5814 1.829 x lop3 mol dmp3 HDz in CHCl, 0.5852 H2O 0.895 Zn aqueous solution 0.91 11 TABLE 5.-DENSITIES AT 25 f 0.1 OC IN gCmP3 sample density CHC1, 1.4753 1.06 mol dm-, HDz in CHC1, 0.496 mol dm-, HDz in CHCl, 1.4766 1.4757 1.829 mol dm-, HDz in CHC1, I .4752 Zn aqueous solution 1.0056 TABLE 6.-DIFFUSIVITIES IN Cm2 S-' (CALCULATED USING THE WILKE-CHANG AND REII~SHERWOOD EQUATIONS) sample diffusivity dithizone in CHCl, Zn(C10,), in H,O ZnDz, in CHCl, Zn2+ in CHCl, H+ in H,O dithizone in H20 1.39 x 1.072 x 9.19 x lop6 9.79 x 10-6 5.08 x 9.31 x 10-5M.A. HUGHES AND H. SUNGSHOU 345 1 More extensive runs were carried out, and in table 2 we report the rates of extraction per unit area for different conditions of pH, CHR(o) and C,,!,,. The interfacial tensions, viscosities and densities required for the model are given in tables 3-5, respectively. The diffusivities of different species were calculated using the Wilke-Chang and the Reid-Sherwood equations and are listed in table 6. organic phase DISCUSSION I film, thickness A/ . I I 1 I I I LOCALE OF THE CHEMICAL REACTION According to the conventional mechanism of metal extraction by chelating extractants, the process involves : (i) partition of the extractants between the organic phase and the aqueous phase; (ii) dissociation of the extractants in the aqueous phase; (iii) chelation and formation of metal complexes in the aqueous phase; (iv) partition of the metal complex so formed between the aqueous phase and the organic phase.The necessary requirement for the bulk aqueous-phase reaction is that the chemical reaction rate is slow and the solubility of extractant in the aqueous bulk phase is sufficiently large, as described by Astarita15 under ‘the slow reaction regime ’. This process involves the mass transfer of the extractant from the bulk organic phase to the interface and then from the interface to the bulk aqueous phase; it should also involve the mass transfer of all other species. An ‘aqueous film’ exists which is part of the aqueous phase adjacent to the interface and is usually 10-3-10-4 cm thick, see fig.1 . The concentration of extractants in this film, like the concentration in the bulk aqueous phase FIG. 1.-Concentration profiles in the aqueous film adjacent to the interface. aqueous phase, has to be related to the concentration in the organic phase via the partition coefficient. In terms of film theory, the mass transfer of any species in this film is governed by molecular diff~si0n.l~ The treatment in this payer is based on the mass transfer of the extractant HR rather than the mass transfer of the metal. PROOF THAT THE REACTION IS NOT IN THE BULK AQUEOUS PHASE Consider the mass transfer of extractant, HR, from the interface to the bulk aqueous phase. For a quasi-stationary state the rate of chemical reaction is equal to the rate of mass transfer:3452 EXTRACTION OF Z I N C where r is the rate of extraction in mol cm2 s-l, koHR, is the mass-transfer coefficient of the extractant in the aqueous phase and CI-IR(a)i is the concentration of extractant on the aqueous side of the interface.CHR(a)i = C H R ( o ) / P H R assuming that there is no resistance to the mass transfer of HR in the organic phase. CWR(a) is the concentration of extractant in the bulk aqueous phase; CHR(o) is the concentration of extractant in the bulk organic phase (here CHR(o) = 1.06 x lop3 mol dmp3), PHR is the partition coefficient of extractant between the two phases (for dithizone PHR = 7.94 x lo5), k is the reaction rate constant if the concentrations of metal and the pH in the aqueous phase are considered to be constants and CHS!eq) is the equilibrium concentration of extractant.Here we assume CHR(eq) = 0. Finally v is the volume of the reaction zone in the aqueous phase and s is the interfacial area. Let us assume that CHR(a) = 0, i.e. the rate of extraction is controlled by a mass-transfer process involving a diffusion layer where only molecular diffusion exists. According to the film theory where DHR(&) is the diffusion coefficient of extractant HR in the aqueous phase (0.508 x cm2 s-l, see table 6), 3, is the thickness of the diffusion zone, r = 0.38 x 10-lo mol cm2 s-l, 1.00 x 10-3 7.94 x 105 mol dm-3 = I .26 x 1 0-l2 mol ~ m - ~ CHR(a)i = and a is the specific interfacial area in cm-l. Thus kgR = 60.84 cm s-l (which is an unlikely high value) and 3, = 1.23 x lopR cm.The calculated value of R is ca. ten times less that the diameter of dithizone molecule (ca. 1 x lo-’ cm) calculated from the value of the molecular volume of dithizone and assuming a sphere. If the assumed model is correct then in order to maintain the supply of the extractant to match the rate of consumption in the chemical reacion the mass transfer coefficient k& has to be as big as 60 cm s-l and the diffusion film becomes ten times less than the diameter of a dithizone molecule. Note that in this calculation we have assumed that CHR(a) = 0 and also the equilibrium concentration CHR(eq) = 0, but if the rate is controlled by the chemical reaction in the bulk aqueous phase, as suggested by Freiser, implying that (CHR(a)i - CHR(a)) 6 (CHR(a) - CHR(eq)), then k& should be > 120 cm s-l and 2 should be -= 0.62 x cm.Such values of k& and 3, are unlikely to be true even in a shake-out or stirring apparatus. In other words, the model involving the reaction in the bulk phase does not account for the observed rate. PROOF T H A T THE REACTION IS NOT I N THE AQUEOUS FILM The chemical reaction could take place in the aqueous film because according to Astarita’s ‘fast reaction regime’ theory15 the chemical reaction is so fast that all the species are at equilibrium in the bulk aqueous phase; the reaction zone coincides with the diffusion zone in the aqueous film. Rewriting Astarita’s expression for a first-order reaction in which the rate of zinc reaction, Y , is expressed in terms of CHR(a), we obtainM.A. HUGHES AND H. SUNGSHOU 3453 When the equilibrium concentration CHR(eq) in the aqueous phase is assumed to be equal to zero and the experimental values of extraction rate are substituted for r in eqn (3) then k = 7.16 x lo8 s-l. Two reaction schemes might be considered, namely and kf &'+(a) + HR(a) -+ ZnR+(a) + H+ Znz+(a) + R- -+ ZnR+. k" and in which Ka is the dissociation constant of dithizone in the aqueous phase (Freiser gives K, = 5.0 x Czn(a) is the concentration of Zn2+ in the aqueous phase and C, is the concentration of hydrogen ion in the aqueous phase. = 7.16 x 10l2 s-l mol-1 dm3 k f = ~ Czn(a) (6) k It follows that and (7) Thus the calculated value of k" is 6 orders of magnitude higher than the value reported by Freiser (6.1 x lo6 dm3 mol-1 s-l) and 5 orders of magnitude higher than the v.alue of the rate constant for water replacement around the Zn ion (5.0 x lo7 dm3 mol-1 s-l).Therefore the locale of the reaction cannot be in the aqueous film. GENERAL CRITERION FOR LOCALE OF THE CHEMICAL REACTION The following criteria for the location of the site of the chemical reaction in the liquid-liquid extraction of metals exist. CRITERION 1 Examination of eqn (2) shows that if then a bulk aqueous-phase locale is impossible. vary between taken as 1 cm s-l, then eqn (8) becomes The value of k t R varies according to the contacting experiment: typically it may and lop2 cm s-l.15 For a single-drop experiment the maximum is 1 Examination of eqn (3) shows that if (10) 1 rPHR 9 2 (D€iR k)' CHR(o) then an aqueous-film locale is impossible.The partition coefficient enters into the left-hand side of eqn ( 9 ) and (10) and is especially important. 112 F A R 13454 EXTRACTION OF ZINC The low partitioning of the dithizone extractant into the aqueous phase is a very important reason for the interfacial location of the chemical reaction. This partitioning phenomenon was neglected in the argument put forward by Kletenic. MODELLING THE RATE BASED O N A CHEMICAL REACTION AT THE INTERFACE COUPLED WITH DIFFUSION OF HR ONLY From the experimental results of table 2 the following dependence of the zinc extraction rate on the concentrations of the extractant, the metal and the hydrogen ions was observed: where n = 0.25, rn = 1.0 and p = 0.35. Such a dependence is quite different from that reported by Freiser and Kletenic, although these workers used a more acid range of pH and a different contacting technique.Since the extraction rate is proportional to the concentration of extractant and is much less dependent on the concentrations of hydrogen and metals ions, a one- dimensional mathematical model describing the diffusion of the extractant from the bulk organic phase to the interface where the chemical reaction then takes place is tenable. The rate of chemical reaction at the interface was assumed to be a function of the interfacial concentration of the extractant, HR, only. For this work, the differential equation is The initial and the boundary conditions are CER(o) = CHRo(o) = constant, t = 0 (13) CHR(o) = CHRo(o) = constant, x = 00.(15) Note that for eqn (15) the change in CHR(o) during extraction is considered to be negligible. Also k , = kiii C,,/C, = constantlo for each experiment, kiii = 1.05 x cm s-l, and C&R(o) is the initial concentration of HR in organic phase; DHR(o) is the diffusivity of HR in the organic phase and is equal to 1.39 x Here the concentrations of Zn2+ and H+ in the continuous bulk of the aqueous phase are considered to be constant and equal to the concentrations at the interface. Then an analytical solution of these differential equations can be obtained:16? l9 cm2 s-l (see table 6).M. A. HUGHES AND H. SUNGSHOU 3455 r = r(av) = M/t (19) where t is the time at moment t, rt the instantaneous rate of extraction at time t, M the mass transfer per unit area during the period from t = 0 to t = t and r(av) the average extraction rate during the period from t = 0 to t = t .in which rint is the interfacial reaction rate. In other words, the rate is then controlled by chemical reaction at the interface. then and the rate of extraction is controlled by a diffusion process. The results calculated from eqn (18) and (19) are listed in table 7 together with experimental results and the values of extraction rate based on interfacial reaction only The results in table 7 demonstrate a fairly good agreement between the experimental and calculated rates, especially for those cases where the interfacial chemical reaction rates are low, i.e. where the pH or the concentrations of Zn2+ and the extractant are low. Also the differences between the values calculated from eqn (18) and (19) and values calculated from eqn (21) are smaller.In this range of experimental conditions the extraction rate is controlled by chemical reaction at the interface. But at higher pH and Zn concentrations the difference between the calculated and experimental rates is quite obvious; we then have a mixed regime of mass transfer with chemical reaction. The pH values in Kletenic's experiments were varied from 3 to 4; in this region the reaction takes place at the interface so the value of constant kiii suggested by himlo has been confirmed in a general way by our experiments. However, this value is probably only some kind of empirical constant valid only for a certain step of the process and for certain experimental conditions. These chemical rate constants are in fact physicochemical constants and they are quite different from such parameters as mass-transfer coefficients because the latter will vary with the differing hydrodynamic conditions.If the constant kiii was a constant having some physical meaning then it should be valid during drop formation as well as drop travel. That is to say during drop formation the extraction rate should not go beyond the limits allowed by the interfacial chemical reaction the rate constant of which is kiii. It is known that in the single-drop experiments appreciable extraction occurs during drop formation (we assume here that mass transfer during coalescence is negligible in comparison). The experimental values of the amount of mass transfer during drop formation may be compared with those calculated by assuming that the process is controlled by chemical reaction only during drop formation (see table 8).The Heertjes modell8* l9 was used to calculate the total amount extracted during drop formation per unit interfacial area, Mf,19 and gives [eqn (21)l. kiii = 1.05 x lop5 cm s-l. A difference of about two orders of magnitude was found between the calculated and experimental values of Mf. Such a difference cannot be due to experimental error or to errors in the coefficients of the chosen model. On the other hand, the big 112-2TABLE 7.---THEORETICAL VALUES OF EXTRACTION RATE CALCULATED USING A ONE-DIMENSIONAL DIFFERENTIAL-EQUATION METHOD experimental conditions extraction rate/mol cm-2 s-' [H+l [HWO [Znl no.pH / 1 0-5 mol dm-3 / 1 0-6 mol dm-3 / 1 OV4 mol dm-3 calculated, eqn (18) and (19) interfacial reaction, eqn (21) experimental 1 2 3 4 5 6 7 8 9 10 11 12 4.75 5.157 4. I54 4.701 5.099 4.186 4.47 5.096 4.52 4.52 5.099 5.14 1.78 0.697 7.01 1.99 0.796 6.5 1 3.39 0.802 3.00 3 .OO 0.796 0.769 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 0.496 1.829 0.496 1.829 1 .o 1 .o 2.5 2.5 2.5 5.0 5.0 5.0 2.5 2.5 2.5 2.5 5 . 6 0 ~ 1 * 10 x 10-10 3.80 x lo-" 1.20 x 10-lO 2.51 x 7.81 x 1.38 x 3.81 x 3.94 x lo-" 1.45 x 10-lo 4.33 x lO-'O 1.175 x 6.25 x lo-" 1.60 x 10-lo 3.97 x lo-" 1.40 x 10-lo 3 . 5 0 ~ 8.55 x lo-" 1 . 6 4 ~ 6.94 x 4.34 x 10-11 I .60 x loplo 1.64 x 6.03 x 10-lo 7.0 x 10-l' 1.06 x loplo 5.1 x lo-" 1.01 x 10-10 1.09 x 7.50 x 10-l' 0.955 x 1.29 x 3.30 x lo-" 1.20 x 10-'O 5.4 x lo-" 2 91 x 10-loM.A. HUGHES AND H. SUNGSHOU 3457 difference between the amount of mass transfer during drop formation and drop travel (see table 2) implies that the whole process involving drop formation and drop travel involves a very significant contribution from mass-transfer mechanisms. Thus the chemical rate constant suggested by Kletenic seems to be an average value valid only for certain experimental conditions related to the pH range of his experiments. A new approach must be made based on the mass transfer of all species involved in the extraction system. MODELLING THE RATE BASED ON THE MASS TRANSFER OF ALL SPECIES2' The interfacial reaction is assumed to be very fast and the concentrations of all species involved in the extraction process at the interface are assumed to be at equilibrium, i.e.(25) cZnR2i (cHi)2 Czn(a)i (CHrt(o)i)2 Kex = where Kex is a mass-action equilibrium constant, Cii is the concentration of species j at the interface, CZnRZi and CHR(,,)i are the concentrations of ZnR, and HR on the organic side of the interface, and Czn(a)i and CHi are the concentrations of Zn2+ and H+ on the aqueous side of the interface. The rate will be decided by the mass transfer of all the species between the bulk and the interface. The analysis of the problem is based upon the transfer of the extractant HR rather than Zn and related to the transfer of other species. We therefore rewrite Chapman's equation for the expression of Kex in terms of the fluxes, NHRi, as follows : or where k: is an individual film mass-transfer coefficient of species j , NNRi is the flux of species HR across the interface and Ci is the concentration of speciesj in the bulk Eqn (28) is a cubic equation for N , in terms of the bulk concentrations, individual film mass-transfer coefficients and the equilibrium constant.Thus the rate of extraction r can be calculated through the calculated value of N , since - NHRi = 2r. As in Chapman's equation the mass-transfer coefficient ratios (kRR/k&), (k&/k&) and (k&/kg) are assumed to be in proportion to the square roots of the individual species diffusivities. The equilibrium constant Kex was chosen to be 2.0 x according to ref (1 7). Calculation in this way shows that the contribution of the mass transfer of metal to the extraction rate is too high.It is true in a falling-drop experiment that the phase ratio of the continuous phase3458 EXTRACTION OF ZINC to the dispersed phase tends to infinity; this will probably cause a decrease in the value of the ratio (kgR/kgn). On the other hand, the counter-current flux of Zn2+ and H+ at the interface also causes an increase in the value of kin (for the hydrogen ion the value of diffusivity is some ten times larger than that of Zn2+). Therefore (k'&/kin) must be calculated in another way. The Handlos-Baron equation21 (for fully circulating drops) is used for the calculation of kgn and the equation from the Kronig-Brink modeI2l for the calculation Of kLR; then -- - 20. kOZn kOHR The values of the other ratios k&/k; eqn (28) were taken as before in proportion to roots of the individual species' diffusivities.From the calculated values of N,, the average value of kGR(av) was obtained, then the calculated values of Nzni(calc), ( Z J ( ~ ~ ~ ~ ) ) , were obtained through the k&R(av). In TABLE 8.-AMOUNT OF METAL EXTRACTED DURING DROP FORMATION Mf (calculated) (experimental) no. /mol cm-2 /mol cmP2 1 2 3 4 5 6 7 8 9 10 11 12 2.345 x lo-" 5.99 x 10-11 1.49 x 10-l' 5.24 x 10-l' 1.31 x 10-lo 3.20 x 6.16 x 2.60 x 10-lo 1.65 x lo-" 5.81 x 6.13 x lo-" 2.34 x 1.24 x 10-9 0.73 x 10-9 0.86 x 10-9 1.02 x 10-9 1.01 x 10-9 1.04 x 10-9 i . i 4 x 10-9 0.56 x 10-9 1.31 x 10-9 0.55 x 10-9 0.826 x lov9 1.33 x TABLE 9.-cOMPARISON OF EXTRACTION RATES BETWEEN THE EXPERIMENTAL VALUES AND THOSE CALCULATED USING CHAPMAN'S MODEL 1 2 3 4 5 6 7 8 9 10 11 12 -0.1867 - 0.2045 - 0.2000 -0.2579 - 0.2701 - 0.2629 -0.2974 - 0.3273 -0.2675 -0.2193 -0.3219 - 0.2362 6.914 6.84 x 10-lo 7.0 x 7.50 x lo-" 1.06 x 7.33 x lo-" 9.45 x 10-1' 9.90 x 10-l' 9.63 x lo-" 1.09 x 0.955 x 1.20 x 10-lo 4.59 x lo-" 1.39 x 10-lo 1.20 x 5.52 x lo-" 1.89 x 2.19 x 0.51 x 10-lo 1.01 x 10-10 1.09 x 10-lo 7.50 x 10-l' 1.29 x 10-lo 3.30 x lo-" 5.40 x lo-"M.A. HUGHES AND H. SUNGSHOU 3459 all cases eqn (28) exhibited only one real root, Values of Nzni(calc) were compared with the values of NZni(expt), taking rexpt as the experimental value of extraction rate. It is seen from table 9 and fig. 2 that a better agreement was obtained between theoretical and observed rates than was obtained in table 7.Thus the mass-transfer model suggested by Chapman fits, in general, our falling-drop experiments except at the data points no. 3, 6 and 9, where the differences between the experimental and calculated values amount to ca. 30%. This disagreement can be explained by the lower pH or lower extractant concentration when the species at the interface are probably not at equilibrium. So the process of extraction in this region shows more chemical- control character. A’z,,;+/l O-’O mol cm-2 s-l (calculated) FIG. 2.-Comparison of the values of experimental extraction rates and the theoretical rates based on Chapman’s It might be noted that in the range 5 < kgR/k&, < 20 the results of calculation are almost the same; in this range the calculation is not sensitive to the value of this ratio.Now we should return to the problem which was discussed before, i.e. does Chapman’s model of mass transfer also fit the experimental data observed during drop formation? At the first moment of drop formation the concentrations of the various species at the interface should be equal to zero, since CZnRi I- 0. Thus the concentration of HR at the interface, CHRi is also zero. Then according to the model of Heertjes and Newman the mass transfer of metal at the interface during drop formation, Mf,19 becomes : 1 4 Mf = 7 (DHR lf/.)’ CHR(o) (29) where t, is the time for drop formation (0.755 s in our experiments) and CHR(o) is the concentration of HR in bulk organic phase. The calculated values of M, are 2.2 x mol cm-2 at CgR(o) = 1.829 x lop6 mol cmP3, 1.29 x mol cmL2 at CgR(o) = 1.06 x 10+ mol cm-3 and 6.02 x mol cm-2 at CHR(o) = 0.496 x 10+ mol cmP3.These calculated values of Mf are in the range of the experimental data (see table 8). A more quantitative calculation of M, under different experimental conditions is not possible by this last method unless the changing value of the difference between the bulk and interfacial value of HR during drop formation is taken into account. In the comparison of the experimental rates with the rates calculated by this last mass-transfer model, better agreement is obtained than when eqn (18) and (19) are3460 EXTRACTION OF ZINC used. Also the agreement with the Chapman model covers both the drop-travel and drop-formation experiments. CONCLUSIONS The solvent-extraction process of Zn2+ by dithizone occurs by means of an interfacial reaction. The locale of chemical reaction cannot be in the bulk aqueous phase nor in the aqueous film, because of the large value of the partition coefficient of the extractant.The process of extraction under most experimental conditions studied here can be explained by Chapman’s mass-transfer model. In the lower ranges of pH extractant concentration the species at the interface are not at equilibrium, and the process then shows more chemical-control character. 1 P. R. Danesi and R. Chiarizia, Critical Reviews in Analytical Chemistry, ed. B. Campbell (C.R.C. 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