Distributions of Hydrochloric Acid between Water and Organic

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Distributions of Hydrochloric Acid between Water and Organic Solutions of Tri-n-octylphosphine Oxide: Thermodynamic Modeling Houpeng Wang, Wei Qin, Yi-gui Li, and Weiyang Fei Ind. Eng. Chem. Res., Just Accepted Manuscript • Publication Date (Web): 11 Jul 2014 Downloaded from http://pubs.acs.org on July 12, 2014

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Industrial & Engineering Chemistry Research

Distributions of Hydrochloric Acid between Water and Organic Solutions of Tri-n-octylphosphine Oxide: Thermodynamic Modeling Houpeng Wang, Wei Qin,* Yi-Gui Li, and Weiyang Fei State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China

1

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Abstract: Tri-n-octylphosphine oxide (TOPO) is a widely used extractant because of its high extractive ability. However, there is no systematic research on the thermodynamics of TOPO/n-dodecane in the separation of hydrochloric acid (HCl) from aqueous solution. In this study, the liquid–liquid equilibrium (LLE) system (water + n-dodecane + TOPO + HCl) was investigated. Both the equimolar series and slope methods were used to determine the composition of the complex formed in the equilibrated organic phase. The form of the water molecules in the equilibrated organic phase was firstly investigated by thermodynamic method. The thermodynamic model was established with Pitzer equation for aqueous phase and both Margules and organic Pitzer equations for organic phase. Two chemical equilibrium constants and their corresponding interaction parameters were regressed from experimental LLE data. The correlated results were in good agreement with the experimental data. Furthermore, this model can also be used to predict the organic phase composition for this system. This confirmed that the thermodynamic model chosen was suitable for the extraction system.

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1. INTRODUCTION

Organophosphorus compounds containing the phosphoryl (P=O) functional group1-6 are widely used in separation processes, 1-4 the production of nanoparticles, 5 and as surfactants in chemical reactions. 6 Among these materials, tri-n-octylphosphine oxide (TOPO) (C8H17)3PO) is one of the most commonly used extractant because of its remarkable extraction ability. Studies using TOPO have included the separation of rare earth metals (lanthanides4,7-9), actinides,10-12 transition metals, 13-17 inorganic acids, 18,19 and carboxylic acids. 20-22 The recovery and treatment of hydrochloric acid (HCl) has received much attention in the chemical separation process. The neutralization process that is traditionally used for the treatment of the acid always increases the difficulty of purification,23 because more cations/anions are added into the system. And these cations/anions may have an effect on the further treatment of the solution.24 Electrodialysis25,26 and membrane distillation23,27 have been suggested for the recovery of HCl. These two methods have shown the benefits arise from recycling of the acid and avoiding the neutralization process, with a good perspective to recovery HCl from the solutions. However, for the membrane distillation process, the porous hydrophobic membrane and the temperature gradient is essential.28 For the electrodialysis process, the maximum reconcentration level of the acid may hinder the recovery of HCl. 29 From an economical point of view, energy consumption of these two technologies should be considered. Recently, liquid–liquid extractions have become a common method for the recovery of acids from aqueous solution. 24,30-35 There are some advantages for the liquid-liquid extraction:31 (I) Liquid-liquid extraction can be operated in large-scale industrial separation processes in the inorganic, organic, pharmaceutical and biochemical industries, especially in the dilute polar 3



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solution; (II) On the basis of the high selectivity of the extractant, the special molecules can be obtained while others are retained in the solutions; (III) The valuable material is obtained without other hazardous by-product produced. Recently, Schunk and Maurer

30,32

investigated the single

mineral acid (nitric, hydrochloric or sulphuric acid) extraction using a liquid-liquid equilibrium of systems mineral acid + water + tri-n-octylamine (TnOA) and highly enhanced extraction was achieved. Moyer et al.33 studied the water and nitric acid extraction by di-2-ethylhexyl sulfoxide in dodecane. Schunk and Maurer

34

had a research on the influence of some inorganic salts on the

citric acid extraction with TnOA in toluene. Sarangi et al.24 studied solvent extraction of hydrochloric acid from solutions with Alamine 336, Aliquat 336, Tri-butylphosphate (TBP) and Cyanex 923. Apelblat 35 investigated the hydrochloric acid and sulphuric acid extraction with TBP as extractant in carbon tetrachloride, benzene, and chloroform. And these reports indicate that liquid–liquid extraction is effective for the recovery of HCl. However, studies concerning the extraction of HCl using TOPO extractant from aqueous solution are scanty. To date, there has been no systematic research on the thermodynamic analysis of TOPO/n-dodecane in the separation of HCl from aqueous solution. Considering the importance of thermodynamic modeling and the related prediction of the system, we have attempted to develop the TOPO/n-dodecane system to separate HCl and determine the composition of the complex in equilibrated organic phase. In this work, the experimental data for the equilibrium system (water + n-dodecane + TOPO + HCl) was investigated, and thermodynamic modeling was chosen to determine the chemical equilibrium constant. In this model, non-ideality of both the organic and aqueous phases was considered. For the aqueous phase, the Pitzer equation was used to calculate the activity of both the solute and solvent species with wellknown Pitzer interaction parameters. 4


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For the organic phase, the organic Pitzer and Margules equations were used to regress the interaction parameters in order to calculate the activity of the solute species, respectively. After the chemical equilibrium constants and interaction parameters were obtained, the thermodynamic model was tested by experimental LLE data.

2. EXPERIMENTAL SECTION

2.1. Materials. Hydrochloric acid (HCl, 36 wt%, AR) and sodium hydroxide (NaOH, AR) were purchased from Beijing Modern Eastern Fine Chemical Co. (Beijing, China). Tri-n-octylphosphine oxide (TOPO, minimum99%, (C8H17)3PO, CAS: 78-50-2) was purchased from J&K Scientific Ltd. (Beijing, China). n-Dodecane (minimum 99%, AR) was purchased from Kermel Tianjin Chemical Reagent Co., Ltd. (Tianjin, China) and was used as the diluent for TOPO. Potassium acid phthalate (minimum 99.99%, C8H5KO4, GR, CAS: 877-24-7) was purchased from Acros Organics (NJ, USA). These chemicals were used without further purification. Deionized water was used in all experiments. 2.2. Liquid–Liquid Phase Equilibrium Experiments. All of the experiments were carried out at room temperature and atmospheric pressure. The procedure for the distribution measurements of HCl in the two phases was as follows: Equal volumes (15 mL) of an aqueous solution containing HCl and a solution of TOPO in n-dodecane were mixed in glass Erlenmeyer flasks. The system was then swayed for 9 h in a homothermal oscillator at 25±0.1 °C with a constant frequency (200 round/min). Equilibrium was determined to have been reached when the concentrations of the distributing components in both phases were unchanged after 2 h. After equilibration, both phases were separated into glass bottles. And the compositions in the organic and aqueous phases were measured, which will be explained in the following paragraphs. The concentrations of HCl in the aqueous and organic solutions were measured by an automatic potentiometric titrator (T50 series, Mettler-Toledo, Greisensee, Switzerland) with the equivalence point method. During this process, a certain concentration of NaOH solution was used 5



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as titrant, with the relative concentration of the NaOH solution standardized by potassium acid phthalate solution before the titrations. The concentration of water in the organic solutions was measured using a Karl Fischer titrator (Mettler-Toledo) with a relative uncertainty of ±0.2%. In brief, the sample was weighed prior to use and injected drop by drop into an anodic electrolyte. Then, the mixed solution was stirred with a magnetic rotor for 60 s. The content of water was obtained when the reaction between the water and iodine finished. The densities of the aqueous and organic solutions were determined with the pycnometer method using a high precision balance with an uncertainty of ±0.0001 g and a pipette gun (1–5 mL) with high precision. Each equilibrium experiment was repeated at least three times to ensure the accuracy of the data. In addition to the molality of the HCl in the two phases, the molality of TOPO and H2O in the equilibrated organic phase was also calculated (The detailed equations about the calculation can be found in the Supporting Information). Also the partition coefficient of the acid between the two phases was calculated.

3. THERMODYNAMIC MODELING 3.1. Chemical Reaction and Gibbs Free Energy Change. The reaction of the liquid–liquid equilibrium in the reactive extraction when HCl is partitioned from the aqueous solution to the organic solution is given by ℎ HCl + TOPO + H O ⇌ (TOPO) ∙ (HCl) ∙ (H O)

(1)

It is assumed that HCl was completely dissociated in the aqueous solution. The solubility and the form of water in the organic phase should be considered. The reaction that induces the formation 6


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of the complex(TOPO) ∙ (HCl) ∙ (H O) occurs upon interaction of the two phases. The complex is assumed to be soluble only in the organic phase. In principle, there might be several complexes in the organic phase with different stoichiometry, which will be discussed later. For the chemical reaction, the Gibbs free energy change depends on the Gibbs free energies of formation of the reactants and products: ∆ = ∑ ∆ (products) − ∑ ∆ (reactants)

(2)

For the hypothetical reaction%A + 'B → *C + +D, the Gibbs free energy change can be expressed as ∆ == *μ. + +μ/ − %μ0 − 'μ1

(3)

where μ2 is the chemical potential of the solute species i. The chemical potential μ2 is (without any influence of pressure) μ2 = μ32 + 45ln62

(4)

where 62 is the activity of the species i. μ32 is the chemical potential of the species i in the standard state. The activity of the solute species i can be expressed as α2 = 82 92

(5)

α2 = :2 ;2

(6)

or

where 82 and 92 are the molality and the activity coefficient of the solute species i, and :2 and ;2 are the mole fraction and its activity coefficient of species i, respectively. Substituting eq 4 into eq 3 gives ∆ = ∆ 3 + 45ln

(6.< 6/= ) @ > ? (60 61 )

(7)

where ∆ 3 is the standard Gibbs free energy change of the reaction. The definition of standard 7



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state is at α= 1 (mole fraction x= 1 and fugacity f = 1), or m = 1mol/kg (or 1mol/L) and 9 =1 in liquid phase. For gas phase, it is at p = 1atm and fugacity f = 1 (at any T) (it means in ideal gas). When the chemical reaction reaches the equilibrium state, that is, the sum of the Gibbs free energies of the products equals the sum of Gibbs free energies of the reactants, the Gibbs free energy change is zero: ∆ = ∆ 3 + 45ln

Therefore,

∆ 3 = −45ln

(6.< 6/= ) @ > ? =0 (60 61 )

(8)

(6.< 6/= ) @ > ? (60 61 )

= −45lnB

(9)

where H

I B = ∏2JK [62 ]FG

(10)

the subscript R denotes reaction. SR is the number of components of the reaction. F2 is the stoichiometric coefficient of species i in the reaction, which is positive for the products and negative for the reactants. 3.2. Activity Coefficients of Compositions in Aqueous and Organic Phases. For the organic and aqueous phases of the equilibrium system, the non-ideality of the solution should be taken into account. In the present work, Pitzer theory36,37 was used to correct the non-ideality of the aqueous solution. The organic Pitzer30,32 and Margules38,39 equations were used for the correlation of the organic phase. These theories will be discussed later. 3.2.1. Expression for Activity Coefficient of Composition in Aqueous Solution. Based on the statistical mechanics and the expression of the excess Gibbs free energy (Gex), Pitzer deduced the expressions of activity coefficients both for solvent (water) and solute (ionic) species in single and 8


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mixed electrolyte aqueous solutions. 36,37 The main equations are as follows:

LM 1 1 = NO ;(P) + R R S2 (P)N2 N + R R R U2 N2 N N (11) 45 NO NT 2

2

Here f (I) represents the long-range electrostatic attractive energy and S2 (P) represents the short-range hard-sphere repulsive energy between two ions. U2 is the interaction among three ions. NO is the mass of water (kg) in aqueous solution and N2 is the mole number for ionic species i. In this work, only single electrolyte HCl-H2O system was studied. In order to calculate the activity of water (6O ) in aqueous phase, the osmotic coefficient ∅ should be deduced beforehand. Therefore, the osmotic coefficient ∅ can be expressed as: ∅ − 1 =

YZ PK/ ∂ LM / ∂NO (b) (K) c>\ d e.g ∅ =− ^ + 8 h`.a (12) \ + 8 [_`.a + _`.a e 45 ∑2 82 [1 + 'P ] ^ ln6O = ln:O ;O = −

∑k jk lm Kbbb

∅=−

∑k jk

nn.nbo

∅

(13)

where 1 m`r + m.as P = R 82 p2 = = m （m`r = m.as = m) (14) 2 2 2

and 82 =

N2 uNT (mol/kg)

(15)

Here, I is ionic strength, where YZ is the Debye–Hückel parameter of water (YZ (25 °C) = 0.391), b is a size parameter (b=1.2) and Mw is the molecular mass of water. The parameters (b）

(K）

|

_`.a , _`.a , and h`.a have the values 0.1775, 0.2945 and 0.00080, respectively. 36 From the above equations, deduction from thermodynamics shows that the mean activity coefficient (9±`.a ) can be expressed as ln9±`.a = ln9`r = ln9.as = (\)

d

(

)

k

= −YZ \

\

d]

\ K?d]

\

(b）

+ ? ln [1 + 'P ] ^ + 28{_`.a + \

∅ [1 − [1 + 2P ] − 2P^ exp [−2P ] ^]} + 8 h`.a

9


(16)


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(9±`.a) = 9`r × 9.as

where

(17)

%`r × %.as = 8`r × 8.as × 9`r × 9.as = m 9±`.a

(18)

If the equilibrium molarity of HCl (mol/kg H2O) in aqueous solution was measured, the activity of water can be calculated by eqs 12 and 13, and the activity of HCl (%`r %.as ) can be calculated by eqs 16 and 18. The definition of the reference state is only at f = 1 or γ = 1. In Pitzer equation, the reference state for ionic species is at infinite dilute and the solvent (water) is at pure liquid state. 3.2.2. Expression for Activity Coefficient of Composition in Organic Solution. For the organic phase, there are a variety of methods to calculate the activity coefficients of the components, such as the Margules equation,38,39 the nonrandom two-liquid(NRTL) equation,40,41 the universal quasi chemical functional-group activity coefficients (UNIFAC) equation,42 the organic Pitzer equation, 30,32

and the Scatchard–Hildebrand equation.43 In this present work, the organic Pitzer and

Margules equations were used to calculate the activity coefficients of the components. 3.2.2.1. Organic Pitzer Equation. In the organic phase, there are no ionic species and all ternary interactions are ignored. Therefore, the expressions for the activity coefficient of a solute species i and the activity of n-dodecane in the organic phase by the Pitzer equation are () ln92

H

(）

= 2 R _2 JK

(）

8

(19) ()

ln6

() () ;

= ln:

=−

H H

∑2 82 ∅u 1000

H

() () () () = [− R R _2 82 8 − R 82 ] 1000 2JK JK

2JK

(20) 10


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()

where Sorg is the number of solute species in the organic phase. 82

is the molality of species i

per kg n-dodecane. The subscript s represents the solvent n-dodecane. It is assumed that the solvent molecules act as inert medium and have no influence on the other solute species in the system. Thus, the parameters _2, ¡¢ for binary interactions between solute species i and the solvent are 0. _2, is the parameter for binary interactions between solute species i and j. Ms is the ()

molecular mass of the n-dodecane solvent. 6

is the activity of the n-dodecane solvent.

In organic Pitzer equation, the reference state for neutral solute species is also at infinite dilute while for diluent as solvent species it is also at pure liquid state. 3.2.2.2. Margules Equation. For the quaternary system, if the interactions between two types of molecules are only considered, the excess Gibbs energy can be determined from the thermodynamics in the following way: LM = (NK + N + N + N)(YK :K : + YK :K : + YK :K : + Y : : + Y : : 45 + Y : : )

(21) It is assumed that there is no interaction between the diluent (expressed as 4) and the solute molecules (expressed as 1, 2 and 3). The parameters YK , Y , and Y are zero. Therefore, eq 21 can be simplified as LM = (NK + N + N + N )(YK :K : + YK :K : + Y : : ) RT (YK NKN + YK NK N + Y N N ) = (NK + N + N + N ) (22) From the thermodynamics, the activity coefficient of the component in the organic phase can be determined as 11



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∵ln;K = =

¤(

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¥¦ ） I§

¤\

(NK + N + N + N )(YK N + YK N ) − (YK NK N + YK NK N + Y N N )

（NK + N + N + N ）

=YK : (1 − :K ) + YK : (1 − :K ) − Y : : (23) ln; =

lnf =

¤(

¥¦ ） I§

¤]

=YK :K (1 − : ) + Y : (1 − : ) − YK :K :

¥¦ ) I§

(24)

¤(

¤©

=YK :K (1 − : ) + Y : (1 − : ) − YK :K :

(25)

where Gex is the excess Gibbs energy of the organic phase, N2 is the moles of species i, xi is the mole fraction of the species in the organic phase, ;2 is the activity coefficient of the component i in the organic phase, and Y2 is the parameter for binary interactions between species i and j. In Margules equation, the reference states for all the solute and solvent species are at pure liquid states (:2 = 1, ;2 = 1). If the equilibrium molality of solute species (mol/kg n-dodecane) in organic phase was measured, the activity coefficients of these solute species cannot be obtained by eqs 19 or 23, ()

because the _2

and Y2 parameters are all unknown. So these parameters should be regressed

from our experimental LLE data. For the species i distributing in the two phases: aqueous solution and organic phase, if the reference state or concentration units are different, the chemical potential in the reference state is also different ( μaq,ref ≠ μG G

org,ref

¬,L

the values of μ2

). So during the process of the calculation of a phase equilibrium,

,L

and μ2

should be expressed. However, due to the chemical potential of

the species i in the two phases equal when the reaction reaches equilibrium state, the difference 12


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¬,L

(μ2

,L

− μ2

) could be replaced by the following equation, which is induced from the eq 4: ¬,L

(μ2

,L

− μ2

) = −RT ln

¬

62

@ 62

(26)

To determine the equilibrium constant of HCl partitioned in the two phase system (n-dodecane, TOPO, water, and HCl), some conditions are required: (I) the parameters (b,¬)

(K,¬)

|

()

_`.a ，_`.a ，h`.a , Y2

()

, and _2

for the interactions between the solute species in

aqueous solution (superscript: aq) and organic phase (superscript: org); and (II) the formation of the complex (TOPO) ∙ (HCl) ∙ (H O) with the related stoichiometry (j:h:k), which is the key feature that determines the equilibrium constant in this work. This also means that the forms of HCl and water in the organic phase have an important effect on the equilibrium. (b,¬)

(K，¬)

In the present work, the parameters _`.a , _`.a

|

, and h`.a of the Pitzer equation for ()

the aqueous phase were taken from literature,36 whereas the parameters Y2 ()

equation and _2

for the Margules

for the organic Pitzer equation of the organic phase were determined from

regression based on the experimental phase equilibrium data. The formation of the complex(TOPO) ∙ (HCl) ∙ (H O) with the related stoichiometry (j:h:k) is explicitly discussed. 4. RESULTS AND DISCUSSION The following section will firstly investigate the ratio of TOPO to HCl in the complex. Then, the form of molecular H O will be discussed. 4.1. Equimolar Series Method for Determination of Composition of Complex. To determine the ratio of TOPO to HCl in the complex (TOPO) ∙ (HCl) ∙ (H O) in the liquid–liquid equilibrium of n-dodecane +TOPO + water + HCl system, the equimolar series method was used. In this way, for each set of experimental data, the initial concentration of the

13



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TOPO in n-dodecane and HCl in aqueous solution was regulated as the sum of the concentration and kept constant at a value of 0.226 mol/L. The initial concentration of TOPO and HCl is summarized in Table 1. After the system reached equilibration, the equilibrium concentrations of HCl in the organic phase were measured. Figure1 shows the concentration of HCl in the organic phase versus the initial mole ratio of the extractant TOPO to the sum of TOPO and HCl. From Figure 1, when the initial mole ratio of TOPO/(TOPO+HCl) increased from 0 to 0.5, the concentration of HCl in the organic phase also dramatically increased. This change could contribute to the increasing concentration of TOPO in the organic phase. However, when continuously increasing the ratio of TOPO/(TOPO+HCl), the concentration of HCl in the organic phase dramatically decreased. For these 14 experimental points, the maximum HCl concentration occurred at point A (Figure 1) with a TOPO/(TOPO+HCl) ratio of 0.5. To further test if the maximum of the HCl concentration in the organic phase corresponded with the ratio of TOPO/(TOPO+HCl), the experimental data in Figure1 was fitted with a polynomial curve. The result are shown in Figure 1 (red curve), and the peak of the curve (point B), with the related ratio of TOPO/(TOPO+HCl) = 0.5. According to the equimolar series method, j=h for the complex(TOPO) ∙ (HCl) ∙ (H O) . Therefore, the expression of the complex formula should be (TOPO) ∙ (HCl) ∙ (H O) . This result will be further investigated in Section 4.2. 4.2. Relationship between Partition Coefficient PHCl and Parameter h. To determine the number of HCl molecules in the complex(TOPO) ∙ (HCl) ∙ (H O) , we used the method previously reported for the relationship between the partition coefficient of inorganic acid in the liquid–liquid equilibrium system PHX and the parameter h in the molecular formula of the complex.30 The partition coefficient of HCl in the two phases is defined as the ratio of the 14


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stoichiometric molality of HCl in the organic phase to that in the aqueous phase: ¯ j

°±²

®`.a = j¯ ³´

(27)

The relationship between the partition coefficient ®`.a and the parameter h is

¯ `.a = ℎ × 8 ¯ :: 8

(28)

¯ :: is the stoichiometric molality of the complex(TOPO) ∙ (HCl) ∙ (H O) . where 8 From eqs 27 and 28, it can be concluded that

¬

¯ :: − ln8 ¯ `.a ln ®`.a = lnℎ + ln8

(29)

The molality of the complex(TOPO) ∙ (HCl) ∙ (H O) can be replaced with the chemical equilibrium constant for the complex B:: , where the activity coefficients of all the species is equal to one:

¬

¬

¯ :: = B:: × (8`r ) × ¶8.as · (8¸¹º¹ ) 8

(30)

In a low pH aqueous solution, the molality of OH c ions is much smaller than that of H , so it can be concluded that ¬

¬

¬

¯ `.a )» (8`r ) = ¶8.as · = (8

(31)

Furthermore, at low aqueous phase acid concentrations, the molality of TOPO in the organic phase ¬

¯ `.a, so it can be replaced by a constant: does not significantly change with 8

8¸¹º¹ = constant

(32)

Substituting eqs 30–32 into eq 29 gives ¬

¯ `.a + ln(8¸¹º¹ ) (33) ln ®`.a = lnℎ + lnB:: + (2ℎ − 1)ln8 Therefore, at low aqueous phase acid concentrations, the final result gives the slopes and the intercept: d(ln ®`.a ) = 2ℎ − 1 (34) ¬ ¯ `.a ) d(ln8 15



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Intercept = lnℎ + lnB:: + ln(8¸¹º¹ )

(35)

d(Intercept)/d(ln(8¸¹º¹ )) = j

(36)

where h and j are the numbers of HCl and TOPO molecules in the complex (TOPO) ∙ (HCl) ∙ (H O) . To investigate the relationship between the partition coefficient PHCl and the parameter h in the liquid–liquid equilibrium system, new experiments were designed: the initial concentration of

¯ ¸¹º¹= 0.068, 0.104, 0.140 mol/kg) and HCl in the TOPO in n-dodecane was kept constant (8 aqueous solution was varied between 0.015 and 1.5 mol/L. Table S1 (SI Table S1) and Figure 2 ¬

¯ `.a

Distributions of Hydrochloric Acid between Water and Organic

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