Extraction Equilibrium of Hydrochloric Acid at Low Concentrations

Article pubs.acs.org/jced

Extraction Equilibrium of Hydrochloric Acid at Low Concentrations between Water and N235 in Isoamyl Alcohol Solution: Experiments and Simulation Yunzhao Li,† Xingfu Song,*,† Shuying Sun,† Yanxia Xu,† and Jianguo Yu*,†,‡ †

National Engineering Research Center for Integrated Utilization of Salt Lake Resources, East China University of Science and Technology, Shanghai 200237, China ‡ State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, China ABSTRACT: N235 in isoamyl alcohol solution acts as an efficient extraction system for the revovery of hydrochloric acid (HCl) at very low concentrations in a coupled reactive extraction−crystallization process. In this study, the extraction equilibrium of N235 + isoamyl alcohol + HCl + H2O system was investigated systematically. The formation of the extraction complex in the organic phase was determined by using the experimental data and it was confirmed to be (HCl)4(R3N)4(H2O)8. Further, the thermodynamic model was then established by using Pitzer equation to calculate the activities of all the species. The values of the interaction parameters obtained by regression are as follows: βR(org) = 2.8782 and β(org) 4:4:8,4:4:8 = 11.4764. 3N,4:4:8 The extraction equilibrium constant is ln K4:4:8 = 38.0274. The thermodynamic model was demonstrated to be reliable and suitable for the N235 + isoamyl alcohol + HCl + H2O system.

1. INTRODUCTION During the past five years, the global needs for soda have increased from 44 to 53 Mt.1 About 10 m3 of distiller waste is discharged for 1 ton of soda produced in the ammonia−soda process.2 Nowadays, the waste liquids following a simple pretreatment are discharged directly as sewage into the nearest river, lake, or sea in most cases and the residue is usually stacked. The main components in the distiller waste are calcium chloride (CaCl2, 90−120 g L−1) and unreacted sodium chloride (NaCl, 40−50 g L−1), which are responsible for the environmental pollution and a serious waste of resources, and they have become a burning problem to soda industry.3,4 Therefore, the resource of distiller waste has attracted significant attention.5−10 In our previous study, a promising reactive extraction−crystallization coupled process was proposed to solve the above-mentioned problem, in which calcium carbonate (CaCO3) and HCl were produced by the reaction between CaCl2 and CO2.11 An extraction system including N235 and isoamyl alcohol was selected and it was introduced into the reaction system to remove the generated HCl.12 The reaction is as follows:

been extensively investigated. Alguacil et al. described the distribution equilibria of several mineral acids between aqueous solutions and organic solutions of the phosphine oxide Cyanex 923 in toluene or decane.15 Sarangi et al. studied the extraction of HCl at 185.42 g·L−1 (about 5 mol·L−1) using Alamine 336, Aliquat 336, tributylphosphate (TBP), and Cyanex 923 as extractants.16 Lum et al. established the modeling of water and HCl (above 3 mol·L−1) extraction by TBP and deduced various extraction complexes under different extraction conditions.17 Banda et al. investigated the recovery of HCl (about 3 mol·L−1) from chloride leach solution using trioctyl amine (TOA), Alamine 336, Alamine 308, and tri-2-ethylhexyl amine as extractants.18 Obviously, significant attention has been paid to the extraction of mineral acids (in particular, HCl) at high acid concentrations. However, the extraction equilibrium of HCl at low concentrations has rarely been investigated, in particular, in the N235 + isoamyl alcohol system. In this study, HCl at low concentrations was extracted by N235 in isoamyl alcohol solution. First, the extraction complex was determined by liquid−liquid extraction experimental data. The thermodynamic model was then established to predict the extraction equilibrium. Pitzer equation was used to calculate the activities of all the species present in both the phases and the extraction equilibrium constant and the interaction parameters were obtained by regression analysis. Undeniably, this system-

CaCl 2 + CO2 + H 2O + 2S(o) → CaCO3 + 2SHCl(o) (1)

Similarly, based on the above-mentioned concept, formic acid and strontium carbonate were prepared.13,14 Actually, the essence of this reaction is the extraction of HCl at low concentrations, formed by the ionization of carbonic acid. According to the literature, the extraction of mineral acids has © 2015 American Chemical Society

Received: May 11, 2015 Accepted: September 10, 2015 Published: September 16, 2015 3000

DOI: 10.1021/acs.jced.5b00409 J. Chem. Eng. Data 2015, 60, 3000−3008

Journal of Chemical & Engineering Data

Article

Table 1. Experimental Data for the Liquid−Liquid Extraction Equilibrium of N235 + Isoamyl Alcohol + HCl + H2O Systema aqueous phase m(aq) HCl

pH

mol·kg−1 0.00139 0.00139 0.00140 0.00158 0.00183 0.00212 0.191 0.210 0.478 0.568 0.769 0.00145 0.00155 0.00184 0.00198 0.00225 0.00241 0.00268 0.0238 0.291 0.382 0.589 1.53 0.00172 0.00182 0.00226 0.00256 0.00286 0.00325 0.0248 0.102 0.208 0.376 1.36 0.00182 0.00237 0.00257 0.00266 0.00323 0.00358 0.00403 0.0168 0.0479 0.0553 1.07

5.61 5.43 4.87 4.74 4.40 3.18 1.09 1.11 0.73 0.67 0.57 6.05 5.78 5.26 5.16 4.73 4.33 3.05 2.08 0.97 0.84 0.63 0.26 6.12 6.00 5.46 5.31 4.61 4.21 2.08 1.44 1.13 0.83 0.31 6.61 5.92 5.29 5.07 4.77 4.42 4.25 2.25 1.78 1.71 0.37

organic phase m(aq) alcohol

m(org) HCl

ρ(org)

wH(org) 2O

m(org) R3N

mol·kg−1

mol·kg−1

g·cm−3

%

mol·kg−1

0.282 0.280 0.281 0.280 0.280 0.279 0.278 0.279 0.277 0.279 0.280 0.263 0.263 0.262 0.262 0.260 0.261 0.261 0.259 0.263 0.262 0.260 0.261 0.257 0.255 0.253 0.252 0.251 0.253 0.252 0.249 0.251 0.251 0.250 0.240 0.237 0.235 0.236 0.235 0.234 0.233 0.234 0.229 0.231 0.230

0.00490 0.00884 0.0322 0.0516 0.104 0.259 0.273 0.263 0.286 0.298 0.295 0.00543 0.00969 0.0356 0.0574 0.116 0.291 0.602 0.586 0.613 0.626 0.612 0.772 0.00571 0.0106 0.0399 0.0645 0.332 0.687 0.668 1.04 1.03 1.08 1.17 0.00776 0.0134 0.0551 0.0901 0.184 0.463 0.960 0.956 1.59 1.82 2.36

0.815 0.816 0.816 0.816 0.821 0.826 0.821 0.824 0.819 0.823 0.818 0.815 0.813 0.809 0.814 0.815 0.821 0.833 0.830 0.825 0.829 0.830 0.830 0.810 0.810 0.814 0.812 0.819 0.826 0.825 0.830 0.833 0.835 0.833 0.809 0.810 0.811 0.810 0.811 0.815 0.822 0.821 0.833 0.837 0.842

7.17 7.15 7.34 7.41 7.53 8.28 8.38 8.75 8.50 8.41 7.87 5.88 5.92 6.08 6.11 6.28 6.76 7.79 7.86 7.69 7.71 7.60 7.60 4.59 4.60 4.71 4.75 5.35 6.00 6.28 7.03 6.90 6.49 7.39 2.87 2.89 2.94 2.99 3.12 3.59 4.13 4.05 4.79 4.97 5.42

0.293 0.293 0.293 0.293 0.293 0.293 0.293 0.293 0.293 0.293 0.293 0.658 0.658 0.658 0.658 0.658 0.658 0.658 0.658 0.658 0.658 0.658 0.658 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 2.63 2.63 2.63 2.63 2.63 2.63 2.63 2.63 2.63 2.63 2.63

P(HCl) 3.51 6.37 23.04 32.55 56.95 122.34 1.43 1.25 0.60 0.52 0.38 3.75 6.27 19.38 28.98 51.65 120.78 224.58 24.63 2.10 1.64 1.04 0.51 3.31 5.84 17.67 25.18 116.36 211.64 26.94 10.22 4.93 2.88 0.86 4.27 5.68 21.39 33.82 56.78 129.51 238.37 56.88 33.16 32.87 2.20

a

Standard uncertainties are u(pH) = 0.006 and u(ρ) = 1.2 mg/cm3. Relative expanded uncertainties are U(wH(org) ) = 0.17%, U(m(aq) HCl ) = 2.8%, and 2O U(m(aq) ) = 3.3%. alcohol

Shanghai Ling Feng Chemical Reagent Co., Ltd. All the chemicals were used as received without further purification. Deionized water was used in all the experiments. 2.2. Liquid−Liquid Equilibrium Experiments. Equal volumes (25 mL) of hydrochloric acid and solution of N235 in isoamyl alcohol were mixed in a conical flask and stirred at 25 ± 0.1 °C for 4 h in a shaker at a speed of 120 rpm. The molalities of the solutions of N235 in isoamyl alcohol were 0.293 mol· kg−1, 0.658 mol·kg−1, 1.13 mol·kg−1, and 2.63 mol·kg−1,

atic research could provide the theoretical foundation for the reactive extraction−crystallization process.

2. EXPERIMENTAL SECTION 2.1. Materials. Commercial available extractant N235 also as Alamine 336, a mixture of tertiary amines R3N (R: mixture of ∼C8−C10), was purchased from Shanghai Rare-earth Chemical Co., Ltd. Isoamyl alcohol (AR), hydrochloric acid (AR), ethanol (AR), and CaCl2 (AR) were all purchased from 3001



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ionization of water and the protonation of R3N occur in aqueous phase. Ionization of traces of isoamyl alcohol in water can be ignored. The extraction is supposed to occur in the interface of the two phases and then the formed extraction complex is transformed to the organic phase. Isoamyl alcohol acts as physical diluent and does not participate in the chemical extraction. The extraction equilibrium constant of Reaction 2 could be denoted in the form of activity

respectively. The initial concentrations of hydrochloric acid were varied from 0.005 mol·L−1 to 2 mol·L−1. When the equilibrium was attained, both of the phases were separated by centrifugation. The concentration of HCl in aqueous phase was measured by inductive coupled plasma emission spectrometer (ARCOS FHS12, SPECTRO Analytical Instruments GmbH, Germany). Thus, the concentration of HCl in organic phase could be calculated by applying the material balance, ignoring the tiny volume change of both of the phases. The pH of the aqueous phase was determined by using a pH meter (SevenMulti, Mettler Toledo, Switzerland). The content of water in the organic phase was determined by Karl Fischer titration (V20, Mettler Toledo, Switzerland). The concentrations of isoamyl alcohol in aqueous phase were confirmed by gas chromatographic (GC) analysis (6890N, Agilent Technologies Inc., U.S.) using ethanol as an internal standard. In order to calculate the molalities of H2O in organic phase, the density of the organic phase was also determined by using a density instrument (ZMD-1, Shanghai FangRui Instrument Co., Ltd., China).

Kh : j : k =

h (aq) h (org) j (aq) k (a H(aq) + ) (a Cl‐ ) (a R N ) (a H O) 2 3

(3)

where the subscript h:j:k denotes the stoichiometric coefficients of the extraction complex (HCl)h(R3N)j(H2O)k. The P(HCl) value in Figure 2 is the distribution coefficient of HCl between the two phases and defined by the following eq 4 PHCl =

3. RESULTS AND DISCUSSION 3.1. Determination of the Extraction Complex. The molalities of HCl and isoamyl alcohol and pH values in the well-balanced aqueous phase; the molalities of HCl and N235 in organic phase and the content of H2O and density of the organic phase are all listed in Table 1. The components in N235 are all tertiary amines (>98%), including (C8H17)3N, (C8H17)2N(C9H19), (C8H17)2N(C10H21), (C8H17)2N(C7H15), (C8H17)N(C7H15)2, and (C9H19)3N. The contents of these tertiary amines vary from the factories, production process and production time. The N235 used in the experiments was provided by Shanghai Rare-earth Chemical Co. Ltd. and the average molar mass is 387 g/mol. Thus, in this study, N235 was considered as pure R3N in the determination of the complex and the establishment of thermodynamic model. The extraction occurring between the two phases could be assumed as follows: hH+(aq) + hCl−(aq) + j R3N(org) + k H 2O(aq) ⇌ [(HCl)h (R3N)j (H 2O)k ](org)

ah(org) :j:k

(org) mHCl (aq) mHCl

(4)

Figure 2. Relationship between distribution coefficient P and the molality of HCl in aqueous phase. (2)

where h, j, and k denote the stoichiometric coefficient of HCl, R3N, and H2O, respectively. The model of liquid−liquid extraction of HCl between the aqueous and organic phases is shown in Figure 1. HCl is completely dissociated in aqueous phase. Besides, both the

In order to obtain the number of HCl molecules h in the extraction complex, the calculation method reported by Schunk19 was used. The process is as follows. In the organic phase, the molality of HCl could be written as (org) mHCl = hmh(org) :j:k

(5)

Substituting eq 5 into eq 4, lgP(HCl) could be obtained as follows: (aq) lgPHCl = lgh + lgmh(org) : j : k − lgmHCl

(6)

Because the concentrations of the species are low enough, it is assumed that the activity of water and all the activity coefficients are equal to unity. According to eq 3, the molality of the complex could then be expressed in terms of the extraction equilibrium constant as follows: (aq) h (aq) h (org) j mh(org) : j : k = Kh : j : k(m H+ ) (mCl− ) (m R3N )

(7)

Because the protonation of R3N and the ionization of isoamyl alcohol in the aqueous phase are so weak that they

Figure 1. Model of the liquid−liquid equilibrium of N235 + isoamyl alcohol + HCl + H2O system. 3002



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Practically, these interactions exist irrespective of the type of diluents used. Polar diluent could stabilize the polar extraction complex in the organic phase according to the “like dissolves like” theory. High concentration of N235 resulted in more amount of free amine molecules and relatively small amount of isoamyl alcohol. Therefore, it was difficult to stabilize the extraction complex in organic phase. According to Table 1 and Figure 2, the range of the molality of HCl in aqueous phase less than 0.00212 mol/kg, 0.00268 mol/kg, 0.00325 mol/kg, and 0.00403 mol/kg at the N235 concentration of 0.293 mol/kg, 0.658 mol/kg, 1.13 mol/kg, and 2.63 mol/kg, respectively, has been considered in the calculation of h. Thus, the molality of the complex decreased with increasing concentration of N235. An increase in the concentration of HCl in the aqueous phase resulted in a decreased amount of free N235 amine molecules, resulting in good solubility of the polar complex in polar isoamyl alcohol. The slopes of the four rising lines in Figure 2 are found to be approximately 7 and then h is calculated to be 4 according to eq 11, thus indicating the presence of four HCl molecules in the extraction complex (HCl)h(R3N)j(H2O)k. In order to obtain the number of R3N molecules, the complex ratio, that is, the ratio of j to h was then calculated. In general, four methods are used to obtain the complex ratio, namely, slope method, equivalent molarity method, saturation method, and chemical analysis method.21 Figure 2 clearly indicates that at low HCl concentrations, the distribution coefficient decreases with increasing molality of N235 at constant molality of aqueous HCl, thus revealing the unsuitability of the slope method for calculating the complex ratio. Instead, we adopted the saturation method in coupled reactive extraction−crystallization process. The experimental device was the same as that in our previous study.11 Three volume fractions of N235 (10%, 30%, and 50%) and three concentrations of CaCl2 solution (1 mol·L−1, 2 mol· L−1, and 3 mol·L−1) were prepared prior to the coupled extraction, respectively. In the preliminary experiments, it was found that the reaction rate increased with increasing the pressure of CO2 and the product was still the same as that prepared at ambient pressure of CO2. Therefore, CO2 at ambient pressure was used in the saturation method. Following several times of coupled extraction, the organic phase was completely loaded with HCl and its concentration was determined by titration with a calibrated sodium hydroxide (NaOH) solution. Subsequently, the complex ratio n could be calculated and the results are listed in Table 2. The values listed in Table 2 show that the concentration of H+ in the saturated organic phase did not change significantly

could be neglected, the electroneutrality of the aqueous phase can be expressed by using the following equation: (aq) (aq) − + m m H(aq) = mCl OH− O+

(8)

3

−

In the aqueous phase with low pH, the amount of OH can be ignored. Moreover, HCl ionizes completely in the aqueous phase, therefore (aq) (aq) − = m m H(aq) = mCl HCl O+ 3

(9)

Moreover, the concentration of HCl in aqueous phase is negligible compared with the excess N235; therefore, the molality of R3N in the organic phase approximately equals to the initial molality. That is, it could be considered as a constant

m R(org) = const 3N

(10)

Substituting eqs 7, 9, and 10 into eq 6 and differentiating (aq) lgP(HCl) with respect to lgmHCl lead to the following relationship d(lgPHCl) (aq) d(lgmHCl )

= 2h − 1 (11)

Figure 2 displays the relationship between distribution coefficient P and the molality of HCl in the aqueous phase to acquire the parameter h. Figure 2 shows the four curves exhibiting a similar variation tendency. At lower concentrations of HCl, distribution coefficient P increases with increasing concentration of the aqueous HCl. The maximum value of P is 238 corresponding to 2.63 mol·kg−1 molality of N235. Subsequently, P decreases gradually with increasing concentration of HCl. At low concentrations of HCl, the amount of N235 can be considered as excessive, which leads to the extraction of more complexes into the organic phase with increasing concentration of HCl, leading to the rising trend. At high concentrations of HCl, excessive HCl cannot be extracted by N235 or the organic phase has been overloaded, which leads to a decreasing trend. In fact, isoamyl alcohol can also combine with HCl via hydrogen bonds. However, hydrogen bond is significantly weaker than ion−pair formation between tertiary amines and HCl. Figure 2 also exhibits that in the rising curves, the distribution coefficient P decreases with increasing the molality of N235 at constant molality of the aqueous HCl, which is uncommon in the traditional extraction phenomena. In general, the extraction yield increases with increasing concentration of the extractants in a certain range. In N235 + isoamyl alcohol + HCl + H2O system, the formed complex, that is, amine hydrochloride exhibits strong polarity, indicating its good solubility in isoamyl alcohol (strong polarity) and poor solubility in free N235 (weak polarity) according to the “like dissolves like” theory. The results of our previous study indicated that even a third phase could be observed at high concentrations of N235. Schunk et al. reported that the distribution coefficient of mineral acids increased with increasing concentration of extractant using toluene (weak polarity) as diluent19 and decreased with increasing concentration of extractant using methylisobutylketone (strong polarity) as diluent.20 They assumed that during the use of methylisobutylketone as the diluent, the interaction between TOA and complex and the interactions among the complexes should be taken into account from the thermodynamic perspective and then they calculated the interaction parameters.

Table 2. Experimental Data Obtained from Saturation Methoda volume fraction of N235

H+ concentration in organic phase

Complex ratio n = [H+](o)/[R3N](o)

mol·L−1 1 mol·L CaCl2 10% 30% 50% a

3003

0.207 0.619 0.976

−1

2 mol·L−1 CaCl2

3 mol·L−1 CaCl2

0.199 0.625 0.972

0.203 0.630 1.008

0.962 0.988 0.936

Expanded uncertainty is u([H+]) = 0.0005 mol·L−1 DOI: 10.1021/acs.jced.5b00409 J. Chem. Eng. Data 2015, 60, 3000−3008


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the fitted lines are calculated, respectively, and plotted with respect to the volume fraction of isoamyl alcohol as shown in Figure 4.

with the initial concentration of CaCl2 and the complex ratios at three concentrations of N235 were approximately 1, that is, j = h = 4. Neglecting the insignificant change in the volume of both the phases and presence of small amount of isoamyl alcohol in the aqueous phase, the molality of H2O in organic phase could be obtained by using the density and water content of organic phase and the corresponding equation is as follows: m H(org) = 2O

ρ(org)w(H2O)/M(H2O)

(ρ

(alcohol)

)

(1 − V %) /1000

(12)

where mH(org) is the molality of H2O in the organic phase (mol· 2O kg−1), ρ(org) is the density of the organic phase after extraction equilibrium was attained (g·cm−3), w(H2O) is the mass fraction of H2O in the organic phase (%), M(H2O) is molar mass of H2O (18.015 g·mol−1), ρ(alcohol) is the density of isoamyl alcohol at 25 °C (g·cm−3), and V% is the volume fraction of N235 in the organic phase (%).The numerator is the mole number of H2O molecules and the denominator is the mass of the solvent, that is, isoamyl alcohol. The amount of alcohol dissolving in aqueous phase was so low that it was neglected. According to our previous study, excessive HCl and H2O could be extracted by isoamyl alcohol. Therefore, excessive N235 should be taken into consideration in calculating the number of H2O molecules in the extraction complex. Figure 3 shows the relationship between the molalities of H2O and HCl in the organic phase.

Figure 4. Relationship between the intercepts of the four fitted lines and volume fraction of isoamyl alcohol.

The fitted line in Figure 4 exhibits a good linear relativity. Therefore, the molality of H2O in the organic phase can be expressed in terms of the molality of HCl and concentration of N235 as follows: (org) m H(org) = 2mHCl + 3.988(1 − V %) + 1.0211 2O

(13)

The straight line obtained by calculations is shown in Figure 3, which exhibits a high fitting degree with the experimental data. In general, isoamyl alcohol, as a type of protonic polar diluents, can coextract H2O. N235 has weak intersolubility with water. When the molality of HCl is zero, the molality of H2O in organic phase mainly depends on the content of isoamyl alcohol. Therefore, the content of H2O in the organic phase increases with a decrease in the molality of N235. 3.2. Thermodynamic Model for N235 + Isoamyl Alcohol + HCl + H2O System. The thermodynamic model corresponding to the liquid−liquid equilibrium of N235 + isoamyl alcohol + HCl + H2O system is shown in Figure 1. Besides the complete ionization of HCl, three types of equilibrium systems also exist in the aqueous phase, that is, the ionization of H2O, ionization of isoamyl alcohol, and protonation of R3N. The eqs 14 to 16 depict the abovementioned equilibria

Figure 3. Relationship between the molality of H2O and the molality of HCl in organic phase after equilibrium.

2H 2O ⇌ H3O+ + OH−

Figure 3 shows that the molality of H2O is proportional to the molality of HCl in the organic phase and the slopes of the four lines after linear fitting approximate to 2. This indicates that two molecules of H2O were coextracted when one molecule of HCl was extracted by N235. Therefore, k = 2j = 8, thus the formation of extraction complex is (HCl) 4(R 3N) 4(H 2O) 8. Moreover, the molality of H2O increases with decreasing concentration of N235, which indicates the capability of isoamyl alcohol to associate with extra H2O present in the organic phase. The results of our preliminary experiments demonstrated that pure isoamyl alcohol could hardly extract HCl at low HCl concentrations, however, it could combine with H2O by hydrogen bond and the molality of H2O in isoamyl alcohol was kept constant at 5.19 mol·kg−1. It was then used to fit the line. The intercepts of

(14) +

−

C5H12O + H 2O ⇌ H3O + C5H11O

(15)

R3N + H3O+ ⇌ R3NH+ + H 2O

(16)

The values of pH of the aqueous phase after liquid−liquid extraction were measured and listed in Table 1. Figure 5 shows the plot of the pH values vs molality of HCl in the aqueous phase. Obviously, pH decreases with an increase in the molality of HCl. At low HCl concentrations (lgm(aq) HCl < − 2), pH increases with increasing the molality of N235 at constant HCl concentrations. This is attributed to the fact that the tertiary amine N235 dissolved in the aqueous phase shows alkalescence and could combine with H+ ions present in the aqueous phase depicted as eq 16. However, at high HCl concentrations (lgm(aq) HCl > − 2), effect of the molality of N235 on the pH could 3004



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types of model have been established, namely, physical model, local composition model, and chemical model.22 Pitzer model23,24 is a semiempirical physical model and has been successfully used in a variety of electrolyte solutions for its high accuracy and flexibility.25 In the aqueous phase of this system, Pitzer equation was used to calculate the activities of H2O and HCl. The excess Gibbs function was expressed by Pitzer based on the statistical mechanics and it is expressed in terms of eq 22 as follows: Gex 1 = n w f (I ) + RT nw 1 + 2 nw

Figure 5. Relationship between pH of the aqueous phase and the molality of HCl in aqueous phase.

(17)

ϕ−1=

i

(22)

k

(23)

Aφ I (1 + b I )

(0) (1) −2 I e ) + m(βHCl + βHCl

(24)

where I is the ionic strength, Aφ is the Debye−Hückel parameter of H2O (Aφ = 0.392 at 25 °C). b is a size parameter (1) (ϕ) (b = 1.2), β(0) HCl, βHCl, and CHCl are the interaction parameters and their values based on the literature are 0.1775, 0.2945, and 0.00080, respectively.23 Then the activity of H2O could be expressed in terms of eq 25

(19)

where is the chemical potential of solute i in phase k (aqueous or organic phase), which can be expressed by using the equation (20)

a(k) i

where is the activity of i in phase k. The reference state for the solvent (water or isoamyl alcohol) is pure liquid and for all the solutes is 1 M of solute in pure solvent and the solution is infinite dilution. The activity α(k) i of solute i can be expressed as follows: ai(k) = mi(k)γi(k)

j

ϕ + m2C HCl

μ(k) i

μi(k) = μi(k),ref + RT ln ai(k)

i

∂Gex /∂n w RT ∑i mi

=−

(18)

The Gibbs free energy in phase k is the sum of contributions from all the species existing in phase k

∑ ni(k)μi(k)

∑ ∑ ∑ μijk ninjnk + ···

The osmotic coefficient ϕ of water should be calculated first by using eq 24

Following equilibrium, the sum of Gibbs free energy of the aqueous phase and that of the organic phase is the minimum

G(k)(T , ni(k)) =

j

f (I ) = −((4AφI )/b)ln(1 + b I )

4H+(aq) + 4Cl−(aq) + 4R3N(org) + 8H 2O(aq)

Gaq (T , niaq ) + Gorg (T , niorg ) = min

i

where f(I) is a function related to the ionic strength, temperature, and solvent property. It is the energy corresponding to the long-range electrostatic attraction. λij(I) stands for the short-range hard-sphere repulsive energy between two ions. μijk is the interaction among three ions. nw is the mass of H2O in aqueous phase and ni is the mole number of ion i. Pitzer obtained the expression of the function f(I) through theoretical derivation

be ignored compared to the high H+ ions concentration in the aqueous phase. Therefore, pH value plummeted down with increasing molality of HCl. The liquid−liquid extraction occurring in the interface of the two phases is shown in eq 17. Although H2O exists in organic phase in the presence of isoamyl alcohol, the amount of that is much less than that in aqueous phase. Besides, it is not easy to break the combination of H2O and isoamyl alcohol in organic phase. Therefore, H2O in eq 17 was in aqueous phase

⇌ [(HCl)4 (R3N)4 (H 2O)8 ](org)

∑ ∑ λij(I )ninj

ln a w = ln x wfw = − I=

1 2

∑ mizi2 = i

∑i miM w 1000

ϕ

m H+ + mCl− =m 2

(25)

(26)

(21)

(k) where m(k) i is the molality of the solute i in phase k and γi is the activity coefficient of the solute i in phase k. thermodynamic aspects of the N235 + isoamyl alcohol + HCl + H2O system in the aqueous and organic phases were discussed in the following sections, respectively. 3.2.1. Aqueous Phase. Excess Gibbs free energy is commonly applied on the expression of the nonideality of a solution and then the activity coefficient, osmotic coefficient, and other excess functions could be obtained. Basically, three

m H+ = mCl− = m

(27)

mi = ni /n w

(28)

where Mw is the molar mass of H2O and Zi is the charge number of ion i. The mean activity coefficient of HCl in aqueous phase can be obtained based on the above-mentioned equation as shown in eq 29 3005



In the organic Pitzer equation, the reference state for all the solutes is also at infinite dilution and for solvent at pure liquid state. The chemical potential of solute i in reference state of the aqueous phase differs from that in organic phase, that is, μ(aq),ref i ≠ μ(org),ref . However, the chemical potentials of all species have i a relationship after equilibrium expressed as follows:

G ex RT

( )

∂ ln γ±HCl = ln γH+ = ln γCl− =

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∂ni ⎤ ⎡ I 2 = − Aφ ⎢ + ln(1 + b I )⎥ ⎦ ⎣1 + b I b

⎫ ⎧ β (1) ⎪ ⎪ (0) ⎬ ⎨βHCl + 2m⎪ + HCl [1 − (1 + 2 I − 2I )exp( −2 I )]⎪ 4I ⎭ ⎩ 3 2 ϕ + m C HCl 2

(org) (org) 4μH(aq) + 4μCl(aq) + 8μH(aq) = μ4:4:8 − + 4μ + RN O 3

Consequently, the activity of all the species in both the phases could be calculated by using the above-mentioned Pitzer equations. The chemical extraction occurring in the interface of the two phases is shown in eq 17 and the extraction equilibrium constant can be expressed as follows:

(29)

In all the aforementioned Pitzer equations, the reference state for ions is at infinite dilution and for solvent at pure liquid state. 3.2.2. Organic Phase. Several approaches have been used to calculate the activity of the species in organic phase, for instance, the nonrandom two−liquid (NRTL) equation,26−28 the universal quasichemical functional−group activity coefficients (UNIFAC) equation,29,30 Margules equation,31,32 and organic Pitzer equation.19,20 In this study, the organic Pitzer equation was selected to correct the nonideality of the organic phase. The results of our previous study indicated that the conductivity of organic phase at low HCl concentrations was very small. Therefore, herein, it was assumed that there were no ions in organic phase and all ternary interactions could be ignored. The activity coefficient of solute i in organic phase can be expressed by Pitzer equation as follows:

K4:4:8 =

ln

3

3

3

3

3

ln

=

2βR(org) m R(org) 3N 3N,4:4:8

+

(org) (org) 2β4:4:8,4:4:8 m4:4:8

Table 3. Experimental Data for Liquid−Liquid Extraction Equilibrium of N235 + Isoamyl Alcohol + HCl + H2O System and the Simulated Data Calculated by Pitzer Equation at 25 °Ca

(31)

aqueous phase

mol·kg

(32)

γ(±HCl)

i S

S

Ms = [−∑ ∑ β (org)mi(org)m(org) − j 1000 i = 1 j = 1 ij

S org

∑ mi(org)] i=1

(33)

organic phase a(H2O)

−1

0.191 0.210 0.00270 0.0238 0.00320 0.0248 0.0142 0.0376 0.0628 0.00810 0.0479 0.0553

ln as(org) = ln xs(org)f s(org) = −∑ (miMsϕ)/1000 aq

(36)

According to the literature, the solvent has insignificant effect on the interaction parameter between tertiary amines; there33 fore, β(org) The experimental data after R3N,R3N was set as −0.18. extraction equilibrium are listed in Table 3. The extraction

where the subscript 4:4:8 corresponds to the extraction complex (HCl)4(R3N)4(H2O)8. The activity of isoamyl alcohol in organic phase can be expressed as follows:

aq

3

(aq) − 8ln γHCl

m(aq) HCl (org) γ4:4:8

3

(aq) (org) + ln m4:4:8 − 4ln m R(org) − 8ln a H2O − 8ln mHCl 3N

The solutes in organic phase are R3N and the extraction complex. Thus 3

(35)

− 8βR(org) m (org) − 8βR(org) m(org) N,R N R3N N,4:4:8 4:4:8

(30)

ln γR(org) = 2βR(org) m (org) + 2βR(org) m(org) N N,R N R3N N,4:4:8 4:4:8

4 (aq) 4 (org) 4 (aq) 8 (a H(aq) + ) (a Cl‐ ) (a R N ) (a H O) 3 2

(org) (org) ln K4:4:8 = 2βR(org) m (org) + 2β4:4:8,4:4:8 m4:4:8 N,4:4:8 R3N

= 2 ∑ βij(org)m(org) j j=1

(org) a4:4:8

Equation 35 could be written as follows after the logarithm and expansion

S org

γi(org)

(34)

2

m(org) HCl mol·kg

0.7676 0.7646 0.9454 0.8670 0.9406 0.8651 0.8902 0.8446 0.8184 0.9124 0.8323 0.8249

0.9935 0.9929 0.9999 0.9992 0.9999 0.9991 0.9995 0.9987 0.9979 0.9997 0.9984 0.9981

−1

0.2733 0.2625 0.6022 0.5863 0.6872 0.6682 0.8017 1.345 1.499 2.433 1.589 1.818

m(org) N235 mol·kg−1 0.01917 0.03000 0.05591 0.07188 0.4410 0.4600 0.9533 0.4098 0.2560 0.1999 1.677 1.044

a

(org) Relative expanded uncertainties are U(m(aq) HCl ) = 2.8% and U(mHCL ) = 2.8%.

where Sorg is the number of solutes in organic phase and m(org) i is the molality of solute i in organic phase. In the N235 + isoamyl alcohol + HCl + H2O system, isoamyl alcohol acted as a type of protonic polar diluents that did not exhibit any interactions with the solutes; therefore, the binary interaction parameter βi,alcohol was zero. β(org) is the binary interaction ij parameter between solutes i and j. In our system, only three (org) (org) parameters exist, that is, β(org) R3N,R3N, βR3N,4:4:8, and β4:4:8,4:4:8. Ms is the molar mass of isoamyl alcohol.

complex was determined to be (HCl)4(R3N)4(H2O)8 according to the previous study; therefore, m(org) N235 could be calculated by mass balance. Besides, the corresponding activities and activity coefficients of all the species were calculated by using the above-mentioned Pitzer equation and the results are also listed in Table 3. 3006



Article

theoretical foundation for the reactive extraction−crystallization process.

The data listed in Table 3 are used for the regression of the interaction parameters at 25 °C using eq 34. The interaction parameter between the extraction complex and N235 is (org) β4:4:8,R = 2.8782 and the interaction parameter between the 3N (org) = 11.4764. Then the extraction complexes is β4:4:8,4:4:8 equilibrium constant could be obatained by eq 36 and the result is ln K4:4:8 = 38.0273. The experimental and simulated data of P(HCl) were listed in Table 4. The error between the two values is mainly because that the applied N235 is a mixture of tertiary amines and its purity is only 98%.

■

Corresponding Authors

*Phone/Fax: +86-21-64252170. Address: P.O. Box 266, Meilong Road 130, Shanghai 200237, P. R. China. E-mail: [email protected]. *E-mail: [email protected] Notes

The authors declare no competing financial interest.

■

Table 4. Comparison of Experimental and Simulated Data of P(HCl)

ACKNOWLEDGMENTS This study is financially supported by the National High Technology Research and Development Program of China (Grant No. 2011AA06A107)

P(HCl) experimental values

simulated values

1.43 1.25 224.58 24.63 211.64 26.94 56.46 35.78 23.87 301.47 33.16 32.87

1.01 1.38 211.13 22.48 215.39 27.10 52.19 33.45 26.47 289.15 30.89 29.45

AUTHOR INFORMATION

■

REFERENCES

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According to Table 4, the results of the theoretical calculations were in good agreement with the experimental data, indicating that the thermodynamic model established in this study was reliable and suitable for the N235 + isoamyl alcohol + HCl + H2O system.

4. CONCLUSION The extraction equilibrium of the N235 + isoamyl alcohol + HCl + H2O system was investigated. First, the extraction complex was determined by extraction experiments. The number of HCl molecules in the complex was determined by linear fitting of the relationship between the distribution coefficient and the molality of HCl in the aqueous phase. The results indicated that the molality of the complex decreased with increasing concentration of N235 at constant molality of HCl. This was attributed to the fact that the polar isoamyl alcohol could stabilize the polar extraction complex in the organic phase based on the “like dissolves like” theory. The complex ratio was then obtained by saturation method in the coupled reactive extraction−crystallization process and it was proved that the complex ratio was one. The number of H2O molecules in the complex was determined from the relationship between the molalities of H2O and HCl in the organic phase. Thus, following extraction complex was obtained: (HCl)4(R3N)4(H2O)8. Second, the thermodynamic model for the N235 + isoamyl alcohol + HCl + H2O system was established. The activities of all the species in aqueous and organic phases were expressed in terms of the Pitzer equation. The extraction equilibrium constant at 25 °C and the interaction parameters were calculated by regression and the proposed model was proven to be reliable and suitable for the extraction system. Undeniably, this systematic research could provide the 3007



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Extraction Equilibrium of Hydrochloric Acid at Low Concentrations

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