Materials Transactions, Vol., No. 5 (003) pp. 957 to 961 #003 The Japan Institute of Metals Chemical Model of the HCl H O Solutions at 5 C Man-Seung Lee 1, Jong-Gwan Ahn ; * and Young-Joo Oh 3 1 Department of Advanced Materials Science and Engineering, Mokpo National University, Chonnam 53-79, Korea Minerals and Materials Processing Division, Korea Institute of Geoscience and Mineral Resources, 30, Daejoen-si, 305-350, Korea 3 Metal Processing Research Center, Korea Institute of Science and Technology, P.O. Box 131, Cheongryang-ri, Seoul, 136-791, Korea A chemical model was developed to calculate the equilibrium concentrations of chemical species in the HCl H O system at 5 C by using chemical equilibria, mass and charge balance equations. The activity coefficients of solutes and the activity of water were calculated with the Bromley equation. The interaction parameters for the individual chemical complexes, which were necessary to calculate the activity coefficients, were obtained from the reported interaction parameters between ions. By applying this model, the distribution of iron species with the electrolyte concentrations was obtained. In the experimental ranges of the ionic strength of solution up to 7.8 m, the experimental ph values were in good agreement with the predicted ph values. (Received December, 00; Accepted March 10, 003) Keywords:, HCl, chemical model, Bromley 1. Introduction Ferric chloride solutions are widely used in the leaching step of concentrates, such as chalcopyrite, galena and tetrahedrite. 1 ) FeCl coexists with the unreacted in the leaching solutions. Many studies have been performed on the solvent extraction of ferric chloride from chloride solutions. 5 7) From these studies, several extractants were found to have selectivity for over FeCl. To regenerate ferric chloride solution from the leaching solution by solvent extraction with these extractants, FeCl must be oxidized to. Since the oxidation reaction depends on the HCl concentration in the solution, 8) the control of HCl concentration is important. To analyze the extraction behavior of iron from chloride solutions and oxidation reaction of FeCl to, the effect of complex formation and activity coefficients of solutes on the ionic equilibria must be considered. Many semi-empirically developed equations, which could explain the nonideality of solutes at high ionic strength, have been proposed. 9,10) However, there are few data on the activity coefficients of in chloride solutions. A chemical model of the HCl H O system at 5 C, which consisted of chemical equilibria, charge and mass balance equations, was developed to analyze the ionic equilibria. The activity coefficients of solutes and the activity of water were calculated by Bromley equation. By applying this model, the distribution of iron species with and HCl concentration was obtained. To test the validity of the model, solution ph was measured at 5 C by varying the concentrations of and HCl and the calculated ph values were compared with the measured values.. Chemical Model Complex formation reactions considered in this study for the HCl H O system and the logarithm of the thermodynamic equilibrium constants of these reactions at zero ionic strength reported in the literature are represented in the following equations. 11) H þ þ OH ¼ H O; log K 1 ¼ 1:00 ð1þ Fe 3þ þ Cl ¼ FeCl þ ; log K ¼ 1:31 ðþ Fe 3þ þ Cl ¼ FeCl þ ; log K 3 ¼ 1:98 ð3þ Fe 3þ þ 3Cl ¼ FeCl 3 ; log K ¼ 1:19 ðþ Fe 3þ þ Cl ¼ FeCl ; log K 5 ¼1:31 ð5þ Fe 3þ þ OH ¼ FeOH þ ; log K 6 ¼ 11:8 ð6þ Fe 3þ þ OH ¼ Fe(OH) þ ; log K 7 ¼ :95 ð7þ Fe 3þ þ OH ¼ Fe (OH) þ ; log K 8 ¼ 5:1 ð8þ Mass balance equations of chloride and iron are given by eqs. (9) and (10). ½ClŠ t ¼ 3½ Š t þ½hclš t ¼½Cl Šþ½FeCl þ Šþ½FeCl þ Šþ3½ Šþ½FeCl Š ð9þ ½FeŠ t ¼½ Š t ¼½Fe 3þ Šþ½FeCl þ Šþ½FeCl þ Šþ½ Šþ½FeCl Šþ½FeOHþ Šþ½Fe(OH) þ Šþ½Fe (OH) þ Š ð10þ In the above equations, subscript t represents the total concentration and the unit of concentration is molality. Charge balance equation is obtained from electroneutrality condition as follows ½H þ Šþ3½Fe 3þ Šþ½FeCl þ Šþ½FeCl þ Šþ½FeOHþ Šþ½Fe(OH) þ Šþ½Fe (OH) þ Š¼½Cl Šþ½FeCl Šþ½OH Š ð11þ The activity coefficients of solutes are calculated by Bromley equation. Bromley ignored any possible cation-cation or anionanion interaction and higher order interactions in developing his equation for the activity coefficients of electrolytes in aqueous solution. The Bromley equation for the activity coefficient of cation, M, is represented by the following equations. 10) *Corresponding author: E-mail: dran@kigam.re.kr
958 M.-S. Lee, J.-G. Ahn and Y.-J. Oh log M ¼ 0:5108ðz MÞ I 0:5 þ F 1 þ I 0:5 M ð1þ In the above equation, F M is defined as F M ¼ _B MX1 ðz MX1 Þ ½X 1 Š þ _B MX ðz MX Þ ½X Šþ _B MX3 ðz MX3 Þ ½X 3 Šþ ð13þ _B MX1 ¼ 0:06 þ 0:6B MX 1 jzm z X1 j 1 þ 1:5 þ B MX1 ð1þ jz M z X1 j I Z MX1 ¼ jz Mjþjz X1 j ð15þ In the above equations, z is ionic charge and I is the ionic strength of solution and B MX is the interaction parameter between cation M and anion X. Substituting eqs. (1) and (15) into eq. (13) gives the following expression for F M. 3 F M ¼ X ð0:06 þ 0:6B MX Þjz M z X j 6 x 1 þ 1:5 þ B MX 7 jz M z X j I 5 ð16þ ð jz Mjþjz X jþ ½XŠ In eq. (16), X extends to all of the anionic species of the solution. The activity of water is also calculated by the Bromley equation. 1) 3. Experimental Procedure Ferric chloride solutions were prepared by dissolving 6H O and HCl (Junsei Chemical Co.) in distilled water. First, known amounts of and HCl were added to 100 g of water and the mixture was stirred for 30 minutes with magnetic stirrer. After the electrolytes were dissolved, the temperature of solutions was controlled to 5 C by immersing the beaker into a water bath. The solution ph was measured by a ph meter (Orion 90A) after the temperature of solution was stable. The electrode was calibrated before each set of measurements by the three-point method, i.e., calibrated by measuring ph buffer and then checked by ph and ph 7 buffers.. Results and Discussion We need twenty three independent equations to calculate the concentrations and the activity coefficients of eleven solutes and the activity of water, i.e., [Cl ], [Fe 3þ ], [FeCl þ ], [FeCl þ ], [ ], [FeCl ], [FeOHþ ], [Fe(OH) þ ], [Fe (OH) þ ], [Hþ ], [OH ], Cl, Fe 3þ, FeCl þ, FeCl þ, FeCl 3, FeCl, FeOH þ, Fe(OH) þ, Fe (OH), þ H þ, OH and a H O. We obtained these equations from eight chemical equilibria, two mass balance equations, charge balance, eleven activity coefficient equations of solutes and the activity equation of water. The chemical equilibria, mass and charge balance equations were simplified into three nonlinear equations containing three key solutes, i.e., Cl,Fe 3þ and H þ by inserting chemical equilibria into mass and charge balance equations. ½ClŠ t ¼ K 5 R 5 ½Fe 3þ Š½Cl Š þ 3K R ½Fe 3þ Š½Cl Š 3 þ K 3 R 3 ½Fe 3þ Š½Cl Š þ 1 þ K R ½Fe 3þ Š ½Cl Š ð17þ ( K 8 R 8 ½FeŠ t ¼ ðk 1 R 1 ½H þ ŠÞ ½Fe3þ Š þ 1 þ K R ½Cl ŠþK 3 R 3 ½Cl Š þ K R ½Cl Š 3 þ K 5 R 5 ½Cl Š þ K 6R 6 K 1 R 1 ½H þ Š ) K 7 R 7 þ ðk 1 R 1 ½H þ ŠÞ ½Fe 3þ Š ð18þ ½H þ Š 3 þ f3½feš t ½ClŠ t g½h þ Š 1 þ K 6R 6 ½Fe 3þ Š ½H þ Š K 7R 7 ½Fe 3þ ŠþK 8 R 8 ½Fe 3þ Š K 1 R 1 ðk 1 R 1 Þ ¼ 0 ð19þ In the above equations, R is the ratio of activity coefficients and defined as follows K ¼ ½FeClþ Š ½Fe 3þ Š½Cl Š FeClþ ¼ ½FeClþ Š Fe 3þ Cl ½Fe 3þ Š½Cl Š 1 ð0þ R In solving the above three nonlinear equations, the values of R are necessary and initial guess for the concentrations of the key solutes ([Cl ], [Fe 3þ ], [H þ ]) are very important. Assuming that the electrolytes dissociated completely, the initial concentrations of these key ions were guessed and the activity coefficients of all solutes as well as the activity of water were set equal to one. The nonlinear equations were solved by Newton-Raphson method and the algorithm is shown in Fig. 1. Bromley proposed that the interaction parameter of strong electrolyte MX could be approximated by eq. (1). B MX ¼ B M þ B X þ M X ð1þ In eq. (1), B and are the interaction parameter and the correction value of individual ions, respectively. In the original work by Bromley, 10) the interaction parameter of was not reported. The interaction parameters between ions in the HCl solutions are obtained from literature 11) and represented in Table 1. From the interaction parameters between ions shown in Table 1, the interaction parameters and the correction values of individual ion are calculated by the following method.
Chemical Model of the HCl H O Solutions at 5 C 959 Table Estimated values for the interaction parameter of ions at 5 C. Species B Fe 3þ 0:0556 0.15 FeCl þ 0:19 0.89 FeCl þ 0:5 0.71 FeOH þ 0:06 0.115 Fe(OH) þ 0.0516 0:09 Fe (OH) þ 0:00369 0.18 FeCl 0:6985 0.0 H þ 0.0875 0.103 Cl 0.063 0:067 OH 0.076 1:0 : reported by Bromley Fig. 1 Flowchart for the calculation of the equilibrium concentrations of solutes. Table 1 5 C. Bromley interaction parameters of Fe(III) complex species at Species Values Species Values B[Fe 3þ,Cl ] 0:0016 B[Fe 3þ, ClO ] 0.0681 B[FeCl þ,cl ] 0:169 B[FeCl þ, ClO ] 0.0381 B[FeCl þ,cl ] 0:58 B[FeCl þ, ClO ] 0.01 B[FeOH þ,cl ] 0.030 B[FeOH þ, ClO ] 0.0667 B[Fe(OH) þ,cl ] 0.1178 B[Fe(OH) þ, ClO ] 0.0306 B[Fe (OH) þ,cl ] 0.060 B[Fe (OH) þ, ClO ] 0.1713 B[H þ, FeCl ] 0:6110 S[, HCl] 0:5779 B½Fe 3þ ; Cl Š¼B Fe 3þ þ B Cl þ Fe 3þ Cl ðþ B½Fe 3þ ; ClO Š¼B Fe þ B 3þ ClO þ Fe 3þ ClO ð3þ Figure shows the distribution of iron species with the concentration in 1.0 m HCl at 5 C. The mole fraction of iron species was defined as the ratio of the concentration of iron species to the total concentration of iron. It is known from Fig. that most of iron exists as FeCl þ and FeClþ in concentration ranges investigated in this study. The mole fraction of FeCl increases with increasing concentration, while the mole fractions of FeCl 3 and ironhydroxide complexes decrease with concentration. Figure 3 shows the distribution of iron species with the HCl concentration when concentration is 1.0 m. It is seen in Fig. 3 that the mole fractions of FeCl þ and FeCl increase with increasing HCl concentration, while those of FeCl þ, Fe 3þ and iron hydroxide complexes decrease with the HCl concentration. The mole fraction of FeCl 3 is constant up to HCl concentration of 3.0 m in 1.0 m at 5 C. From Figs. and 3, it is known that the concentrations of iron-hydroxide complexes, i.e., FeOH þ, Fe(OH) þ and Fe (OH) þ, are negligible in concentrated chloride solutions. This result can be made use of simplifying the ionic equilibria 0 - FeCl Fe 3 FeCl FeCl - Substituting the interaction parameters and the correction values of Cl and ClO into eqs. () and (3) and solving the two equations gave the interaction parameter and the correction value of Fe 3þ. The interaction parameters and the correction values of chemical species calculated by this method are represented in Table. We used Edwards approximation method to obtain the interaction parameters between ion and molecule by eq. (). 13) B ion-molecule ¼ B ion þ B molecule ðþ Log (Mole fraction) - -6-8 -10 o FeOH Fe (OH) Fe(OH) The activity coefficient of FeCl 3 was calculated by eq. (5), in which S[, HCl] represented the salting coefficient in the ionic medium of HCl. 1) log FeCl3 ¼ S½ ; HClŠm HCl ð5þ -1 0.0 0.5 1.0 1.5.0.5 (Molality, mol/kg) Fig. Distribution of iron species with the concentration at 5 C. ([HCl] t = 1.0 m).
960 M.-S. Lee, J.-G. Ahn and Y.-J. Oh Log (Mole fraction) 0 - - -6-8 Fe 3 Fe (OH) FeCl o FeOH FeCl - FeCl Mean Activity Coefficient of 0.7 0.6 0.5 0. 0.3 0. calculated in this study 0.1 m 1.0 m 0.1 m 1.0 m -10 Fe(OH) 0.1-1 0.0 0.5 1.0 1.5.0.5 3.0 HCl (Molality, mol/kg) Fig. 3 Distribution of iron species with the HCl concentration at 5 C. ([ ] t = 1.0 m). 0.0 0 1 3 5 6 HCl (Molality, mol/kg) Fig. Variation of the mean activity coefficients of HCl with the concentration. Table 3 Experimental conditions and calculated values of ph and ionic strength. N [ ] t [HCl] t ph ph c I c 1 0.101 0.0 0.75 0.8 0.61 0.311 0.15 0.38 0.9 1. 3 0.533 0.60 0.1 0.5.1 0.768 0.878 0.09 0.05.78 5 1.017 1.130 0:5 0:13 3.3 6 1.151 1.151 0: 0:16 3.73 7 1.138 1.80 0:35 0:30 3.80 8 1.130 1.696 0: 0:38 3.86 9 1.111. 0:56 0:55.07 10 1.80 1.397 0:3 0:9.07 11 1.07 3.1 0:86 0:80.6 1 1.561 1.681 0:53 0:5.7 13 1.859 1.983 0:66 0:60 5. 1.178.303 0:73 0:75 6.1 15.710.710 0:87 0:95 7.8 subscript (c: calculated) analysis for the HCl H O system at 5 C in concentrated chloride solutions by neglecting the existence of iron hydroxide complexes. Table 3 shows the experimental compositions of HCl H O system and ph values at 5 C. Also ph values and ionic strength calculated in this study are shown in Table 3. From Table 3, it is shown that the experimental ph values are in good agreement with the calculated values in the experimental ranges of the ionic strength of solutions up to 7.8 m. Majima et al. calculated the mean activity coefficients of by the McKay-Perring method using the water activities of the HCl H O system. 1) To test the applicability of Bromley equation, the mean activity coefficients of calculated by eq. (6) in the mixed solutions of and HCl were compared with those reported by Majima. ;FeCl3 ¼f Fe 3þð Cl Þ 3 g 1= ð6þ Figure shows the mean activity coefficient of at 5 C calculated by Bromley equation against those calculated by Majima. It is shown in Fig. that the mean activity coefficients of calculated by Bromley equation in this study agree well with those reported by Majima when the molality is 0.1. However, when the concentration of increases to 1.0 m, the combined effects of and HCl concentration on the ;FeCl3 calculated in this study is contrary to those reported by Majima. In order to elucidate the cause of the discrepancy in the ;FeCl3 values obtained by the two methods, further research on the measurements of activity coefficients of is required. 5. Conclusions By developing a chemical model of HCl H O system at 5 C, the following conclusions were obtained. (1) The equilibrium concentrations of iron species were calculated from the compositions of electrolyte solutions and distribution diagrams of iron species with the and HCl concentration were obtained. () The activity coefficients of chemical species and the activity of water were calculated by using Bromley equation. By applying Bromley s approximation method, the interaction parameters of individual ions, which were necessary in calculating the activity coefficients of individual ions, were calculated from the reported interaction parameters between ions. (3) In the experimental ranges of the ionic strength of solutions up to 7.8 m, the measured and calculated ph values were in good agreement.
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