Mixed Electrolyte in Mixed Solvent: Activity Coefficient Measuring and

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Mixed Electrolyte in Mixed Solvent: Activity Coefficient Measuring and Modeling for the HCl + NaCl + Methanol + Water System Zohreh Karimzadeh* and S. A. A. Hosseini*

J. Chem. Eng. Data Downloaded from pubs.acs.org by UNIV OF NEW ENGLAND on 03/22/19. For personal use only.

Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University, Mofatteh Avenue, P.O. Box 15719-14911, Tehran, Iran ABSTRACT: The emf of the cell is measured to investigate the HCl + NaCl + H2O + CH3OH mixed electrolyte systems. The experimental data are obtained over the electrolyte molality ranging from 0.005 mol kg−1 up to about 3.5 mol kg−1, at 298.15 ± 0.01 K, by using a cell containing a pH and a silver chloride electrode in different alcohol mass fractions x(CH3OH) in H2O (where x = 0.10, 0.20, 0.30, 0.40, and 0.50). The mean activity coefficients of HCl in the mixtures are computed. Modeling is implemented by the classical Pitzer (CP) equation and original Pitzer (OP) equation that are included by the additional terms which are arising from interactions of neutral species and finally the modified Pitzer equation by Merida et al. (MP). The different aspects of proper parameter choosing in fitting processes especially for pure and mixed electrolytes in mixed solvent systems are signified in the results.

1. INTRODUCTION

This study intended a systematic consideration of electrolytes in mixed solvent systems together with the nonionic species effects in the Pitzer modeling formalism. In view of these challenges, it becomes important to critically examine the accuracy of correlation results which is implemented by the classical Pitzer (CP) equation and original Pitzer (OP) that includes the additional terms which arose from interactions of neutral species and the modified Pitzer equation by Merida et al. (MP).17 An attempt is made to investigate Pitzer equations in the case of the HCl + NaCl in mixed solvent (MeOH + water) to obtain more accurate regressed parameters. Moreover, it is of interest to see whether the presented models are capable of representing these trends for a single electrolyte in mixed solvent. A survey of literature confirms that the only study for HCl + NaCl + methanol + water was done by Bates and Rosenthal.18 Their emf measurements were performed by hydrogen−silver chloride cells at 298 K in aqueous methanol. The activity coefficient of hydrochloric acid has been determined for molalities from 0.016 to 1.3 in 33.4% methanol. In this work, the potentiometric measurement technique is used to calculate activity coefficients for HCl in HCl + NaCl + methanol + water. Accordingly, the experimental data are obtained over the electrolyte molality ranging from 0.005 mol kg−1 up to about 3.5 mol kg−1, at 298.15 ± 0.05 K, by using a cell containing a pH and a silver chloride electrode in different alcohol mass fractions x(CH3OH) in H2O (where x = 0.10, 0.20, 0.30, 0.40, and 0.50).

Measuring and modeling for electrolyte behavior in aqueous and nonaqueous media is necessary because of the need to investigate the nature of various industrial and environmental processes. Despite the successful achievements of mixed electrolyte studies in aqueous media, investigations in nonaqueous or in mixed solvent media are still very limited.1−14 Among the proposed equations, the Pitzer model and the Harned rule seemed to be the most favored ones among the published works. Typically some of the literature used the Harned rule,1−5 while the others implemented the Pitzer formalism.6−14 The Pitzer formalism, on which our procedure is based, has been extensively applied to represent the thermodynamic properties of various electrolyte systems, but the detailed and systematic study of mixed electrolyte containing nonionic species effects in Pitzer modeling has not been considered up to now. In this line, the short-range effects of neutral species interactions in the Pitzer equation were included explicitly, using the second and third virial coefficient terms which are independent of ionic strength.15 But how should dielectric medium effects be regarded? According to the Pitzer comment, it is necessary to arrange equations for mixed solvent if the solvent composition changes systematically from pure water to pure non aqueous.15 In this regard Gupta16 as the first contribution, investigated 1:1 electrolytes in methanol and water systems as solvent by including mixed solvent dielectric constant. He showed that the nonionic species effects, due to dielectric medium effects, were implicitly included in Pitzer equation. Accordingly the Pitzer parameters variation could be observed in different mass fraction of solvent in regard with dielectric constant changes.15 © XXXX American Chemical Society

Received: November 3, 2018 Accepted: March 12, 2019

A

DOI: 10.1021/acs.jced.8b01033 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

2. EXPERIMENTAL SECTION Electrolyte preparation in mixed solvent systems is performed by bidistilled water with an electrical conductivity of about 1 μS·cm−1. According to Table 1, analytical grade methanol from

γ (0) BMX = 2βMX +

company

mass fraction, purity

sodium chloride hydrochloride methanol

Fluka Fluka Fluka

>99.5% 37% >99.5%

γ CMX

I / m0

(1 + α I /m0

=

(5)

I / m0

(6)

φ (3/2)CMX

(7) (8)

γ±HCl is the molality-scale mean ionic activity coefficient of the electrolyte HCl; γ0±HCl is the molality of electrolyte (kg mol−1) in the absence of neutral species; m is the molality of electrolyte (kg mol−1); mMeOH is the molality of neutral species; I is the ionic strength on a molality scale; β(0) MX (kg· −1 mol−1), β(1) ) and CφMX (kg2·mol −2 are the MX (kg·mol parameters of the Pitzer equation; b = 1.2 (kg1/2·mol−1/2); and α = 2 kg1/2·mol−1/2. Moreover, θHNa (kg·mol−1) and ψHNaCl (kg2·mol−2) represent the mixing ion-interaction parameters for the mixed electrolyte system. Also, the higher-order limiting law14 correction is checked by inserting ÄÅ ÉÑ Å ÑÑ θ (1) Å (0)Å Å θ = θ ÅÅ1 + (0) g (I )ÑÑÑÑ ÅÅ ÑÑ θ (9) ÅÇ ÑÖ where g (I ) = (2/α 2I )[1 − (1 + αI 0.5)exp( −αI 0.5)]

(10)

ξMeOHHCl, ξMeOHNaCl, ηMeOHHNa, and ωMeOHHCl are the interaction parameters of nonelectrolyte−ion−ion and nonelectrolyte−nonelectrolyte−ion. χHClMeOH and ωMeOHHCl in eq 1 involving nonelectrolyte−ion interactions arise from binary and ternary interactions as follows χHClMeOH = υMλMeOHH + υX λMeOHCl ωMeOHHCl =

(11)

3 (υHμMeOHMeOHH + υClμMeOHMeOHCl ) υHCl (12)

The Debye−Hückel coefficient for the osmotic coefficient (Aϕ) is defined as

ln γ±mixture = ln γ±0HCl + χHClMeOH mMeOH HCl

ij e 2 yz 1 zz Aφ = (2πNAρA )1/2 jjj j 4πε0DkT zz 3 k {

2 + ωHClMeOHmMeOH + 0.5mMeOH{mCl ζMeOHHCl

(1)

3/2

(13)

where the constants ε°, k, NA, D, and ρA are vacuum permittivity, Boltzmann constant, Avogadro constant, dielectric constant, and density of the solvent, respectively. When terms involving the interaction between nonelectrolyte and ion are omitted, the OP equation changed to the CP equation. (1) φ β(0) MX, βMX, CMX, ξMeOHMX, χMXMeOH, and ωMeOHMX are the parameters for each related electrolyte in mixed solvent. Moreover, θHNa, ψHNaCl, and ηMeOHHNa represent the mixing ion-interaction parameters for the mixed electrolyte system. The mixing ionic interaction parameters (θΗNa and ψΗNaCl) would be determined according to the Khoo approach.14 This issue is implemented by use of the CP1 and CP2 equations that are proposed for inclusion or exclusion of the higher-order limiting law. 3.2. Modified Pitzer Equation by Merida et al. (MP). Merida et al. modified the original Pitzer (OP) equation to

ln γ±mixture = ln γ±0HCl + χHClMeOH mMeOH HCl 2 + ωHClMeOHmMeOH + 0.5mMeOH{mCl ζMeOHHCl

(2)

where γ ϕ ϕ ln γ±0HCl = f γ + mBHCl + mNaCl (B NaCl − BHCl + θHNa) γ ϕ ϕ + m2C HCl + mmNaCl (C NaCl − C HCl + 0.5ψHNaCl)

+ 0.5mHCl mNaCl ψHNaCl ÄÅ ÑÉÑ ÅÅ Ñ I /m0 2 ÅÅ 0 Ñ γ f = −AφÅÅÅ + ln(1 + b I /m )ÑÑÑÑ 0 ÅÅ 1 + b I /m ÑÑ b ÅÇ ÑÖ

[1 − e − α

m = mHCl + mNaCl

3. MODELING 3.1. Pitzer Equations. As stated by Pitzer15 the following equation is proposed if neutral species are present in the system. In this equation, original Pitzer (OP), the additional terms that have arisen due to binary and ternary interactions because of the presence of neutral species are included which are usually skipped in classical Pitzer (CP) equations. In this regard, for a (1:1) mixture of HCl and NaCl electrolyte in mixed solvent (MeOH + water) and pure electrolyte in mixed solvent, the corresponding OP equation is written as

+ mHζMeOHHCl + mNaCl ζMeOHNaCl + ηMeOHHNa }

0

α (I / m )

φ (0) (1) −α BMX = βMX + βMX e

Fluka (mass fraction >99.5%) is used. Also, HCl (37% GR for analysis) is used for the preparation of different primary concentrated stock solutions in doubly distilled water and methanol mixtures. All primary concentrated stock solutions are, first, prepared by weight using doubly distilled water and then analyzed by potentiometric titration using a standard AgNO3 solution (Merck “Titrizol” standard). The pH (glass membrane) electrode is from Metrohm (model 6.0238.000, Switzerland). The Ag/AgCl electrodes are prepared.19 Data acquisition setup is made using an automated PC. All potential measurements are performed with temperature kept constant at 298.15 ± 0.05 K by employing a doublewall container and thermostated water from a bath (Julabo thermostat MF12, Germany) under stirring conditions. The molality of electrolyte in the cell is changed by a standard addition method and using appropriate Hamilton syringes, with accuracies within ±1% of their nominal volumes and with precisions within 1% (as indicated by the manufacturer).

+ mHζMeOHHCl + mNaCl ζMeOHNaCl + ηMeOHHNa }

2

− (1/2)α 2(I /m0))]

Table 1. Company and Purity of Compounds compound

(1) 2βMX

(3)

(4) B



Article

Table 2. Experimental Mean Activity Coefficients (γ±) of HCl in the (Water + Methanol + HCl + NaCl) Mixture in Different Mass Fractions of CH3OH (x = 0.10, 0.20, 0.30, 0.40, and 0.50) in Water and the Corresponding Potentiometric Responses (ΔE/mV) at 298.15 Ka mHCl 10% γHCl0 = 0.897 0.0071 0.0179 0.0357 0.0536 0.0714 0.0893 0.1071 0.1250 0.1429 0.1607 0.1786 0.1964 0.2143 0.3571 0.5357 0.7143 0.8929 0.0083 0.0208 0.0417 0.0625 0.0833 0.1250 0.1667 0.2083 0.4167 0.6250 0.8333 1.0417 1.2500 1.4583 1.6667

mHCl 40% γHCl0 = 0.868 0.0071 0.0179 0.0357 0.0536 0.0714 0.0893 0.1071 0.1250 0.1429 0.1607 0.1786 0.1964 0.2143 0.3571 0.5357 0.7143 0.8929 0.0083 0.0208

mNaCl

0.0029 0.0071 0.0143 0.0214 0.0286 0.0357 0.0429 0.0500 0.0571 0.0643 0.0714 0.0786 0.0857 0.1429 0.2143 0.2857 0.3571 0.0017 0.0042 0.0083 0.0125 0.0167 0.0250 0.0333 0.0417 0.0833 0.1250 0.1667 0.2083 0.2500 0.2917 0.3333

ΔE

0.0 44.1 78.2 98.0 112.1 122.9 131.0 138.9 144.9 150.2 155.0 160.1 163.9 191.0 208.1 222.2 232.7 0 44.2 74.9 94.1 108 125.1 1382 147.9 183.2 204.1 220 234 246.9 258.1 270.2

mNaCl

0.0029 0.0071 0.0143 0.0214 0.0286 0.0357 0.0429 0.0500 0.0571 0.0643 0.0714 0.0786 0.0857 0.1429 0.2143 0.2857 0.3571 0.0017 0.0042

γHCl

mHCl

0.8970 0.8468 0.8189 0.8056 0.7950 0.7847 0.7656 0.7668 0.7541 0.7388 0.7328 0.7343 0.7276 0.7383 0.6852 0.6749 0.6650 0.8972 0.8449 0.7722 0.7451 0.7339 0.6811 0.6579 0.6394 0.6318 0.6338 0.6490 0.6818 0.7317 0.7769 0.8586

ΔE

3.2 43.2 75.1 94.2 107.3 118.1 126.4 134.1 140.2 147.2 154.3 157.1 161.2 185.2 207.3 222.2 242.2 0.6 43.6

mNaCl

20% γHCl0 = 0.888 0.0071 0.0179 0.0357 0.0536 0.0714 0.1964 0.2143 0.5357 0.7143 0.0083 0.0208 0.0417 0.0625 0.0833 0.1250 0.1667 0.2083 0.4167 0.6250 0.8333 1.0417 1.2500 1.4583 1.6667

0.0029 0.0071 0.0143 0.0214 0.0286 0.0786 0.0857 0.2143 0.2857 0.0017 0.0042 0.0083 0.0125 0.0167 0.0250 0.0333 0.0417 0.0833 0.1250 0.1667 0.2083 0.2500 0.2917 0.3333

ΔE

0.0 44.1 75.9 94.8 109.0 159.1 165.0 209.8 228.0 0.0 45.2 76.9 96.1 110.0 129.8 143.2 154.0 188.0 208.8 225.1 238.0 251.2 260.0 270.1

γHCl

mHCl

0.9237 0.8050 0.7502 0.7239 0.6993 0.6929 0.6747 0.6757 0.6645 0.6769 0.6981 0.6728 0.6667 0.6381 0.6528 0.6555 0.7740 0.8784 0.8290

50% γHCl0 = 0.852 0.0074 0.0371 0.0741 0.1112 0.1483 0.1853 0.0085 0.0212 0.0425 0.0637 0.0850 0.8495 1.0194 1.6990 2.1237 2.3361 0.0092 0.0230 0.0459

C

γHCl

0.8887 0.8366 0.7797 0.7524 0.7410 0.7130 0.7345 0.7054 0.7510 0.8887 0.8536 0.7951 0.7678 0.7561 0.7297 0.7186 0.7121 0.6901 0.6923 0.7089 0.7304 0.7839 0.8005 0.8509

mHCl

mNaCl

ΔE

γHCl

30% γHCl0 = 0.879 0.0071 0.0179 0.0357 0.0536 0.0714 0.0893 0.1071 0.1250 0.1429 0.1607 0.1786 0.1964 0.2143 0.3571 0.5357 0.7143 0.8929 0.0227 0.0455 0.0682 0.0909 0.1364 0.1818 0.2273 0.6818 0.9091 1.1364 1.3636 1.5909 1.8182 2.0455 2.2727 2.7273

0.0029 0.0071 0.0143 0.0214 0.0286 0.0357 0.0429 0.0500 0.0571 0.0643 0.0714 0.0786 0.0857 0.1429 0.2143 0.2857 0.3571 0.0023 0.0045 0.0068 0.0091 0.0136 0.0182 0.0227 0.0682 0.0909 0.1136 0.1364 0.1591 0.1818 0.2045 0.2273 0.2727

0.0 43.0 75.5 94.6 108.1 118.6 127.1 134.4 140.6 146.2 151.1 155.6 159.7 183.7 202.7 216.2 232.7 44.0 80.0 98.0 113.0 133.8 147.5 158.6 209.0 225.0 237.1 247.9 260.0 269.9 278.2 288.0 305.9

0.8787 0.8120 0.7649 0.7386 0.7205 0.7067 0.6957 0.6865 0.6786 0.6718 0.6657 0.6603 0.6553 0.6271 0.6055 0.5907 0.6517 0.8286 0.8346 0.7899 0.7933 0.7927 0.7762 0.7707 0.6851 0.7015 0.7088 0.7303 0.7921 0.8420 0.8746 0.9562 1.1311

mNaCl

0.0026 0.0130 0.0259 0.0389 0.0519 0.0648 0.0015 0.0038 0.0075 0.0113 0.0151 0.1506 0.1807 0.3012 0.3765 0.4142 0.0008 0.0021 0.0041

ΔE

γHCl

0.7 72.8 103.7 121.6 134.7 144.7 0 42.8 78 97 111.1 223 233.1 262.9 282 291.1 0 45.9 79.1

0.8636 0.6993 0.6401 0.6055 0.5847 0.5685 0.8524 0.7892 0.7779 0.7512 0.7393 0.7279 0.6328 0.6542 0.6622 0.7124 0.8528 0.8353 0.7953



Article

Table 2. continued mHCl

mNaCl

γHCl0 = 0.868 0.0417 0.0625 0.0833 0.1250 0.1667 0.2083 0.4167 0.6250 0.8333 1.0417 1.2500 1.4583 1.6667 1.8750 2.0833 2.3333 0.1905 0.2381 0.4762 0.7143 0.9524 1.4286 1.6667 1.9048 2.3810 2.8571 3.3333

0.0083 0.0125 0.0167 0.0250 0.0333 0.0417 0.0833 0.1250 0.1667 0.2083 0.2500 0.2917 0.3333 0.3750 0.4167 0.4667 0.0095 0.0119 0.0238 0.0357 0.0476 0.0714 0.0833 0.0952 0.1190 0.1429 0.1667

ΔE 80.5 94.6 109.5 125.7 140.6 149.6 181.5 203.6 220.7 233.5 243.6 253.6 261.5 270.6 278.7 288.6 142.0 154.1 186.0 207.0 223.1 248.9 258.0 267.2 282.0 304.1 316.0

γHCl 0.8673 0.7645 0.7735 0.7096 0.7180 0.6874 0.6509 0.6731 0.7087 0.7349 0.7477 0.7825 0.8032 0.8544 0.9021 0.9833 0.6884 0.6956 0.6483 0.6504 0.6660 0.7365 0.7521 0.7840 0.8399 1.0739 1.1627

mHCl

mNaCl

ΔE

γHCl

γHCl0 = 0.852 0.0689 0.0919 0.4593 0.9186 1.1024 1.8372 2.2966 2.5262 2.7559 0.0096 0.0479

0.0062 0.0082 0.0410 0.0820 0.0984 0.1640 0.2051 0.2256 0.246063 0.000425 0.002121

99 113.9 189 227.1 237 269.9 285 293.1 300 0 76

0.7819 0.7849 0.6760 0.7081 0.7168 0.8175 0.8757 0.9302 0.9771 0.8530 0.7503

a

The standard uncertainties u are u(T) = 0.01 K, u(ΔE) = 0.1 mV, u(X) = 0.001, and u(γ) = 0.002.

improve the fitting of experimental data containing polar nonelectrolyte. To this aim the dependence of the binary interaction parameters (containing the nonelectrolytes and the ion−nonelectrolyte interactions) on the ionic strength was included.8−11According to the proposed equation, the activity coefficient equations for pure and mixed electrolytes are recommended as17

In eq 13, the ion−nonelectrolyte binary interaction parameter, χHClMeOH, and its derivative χ′HClMeOH are expressed as χHClMeOH = χ (0) +

′ χHClMeOH =

2 α 2I

} (16)

∂χ ∂I

2 = (χ (1,0) + χ (1,1) mMeOH) 2 α I É ÅÄÅ 1 i yÑÑÑ ÅÅ ÅÅ−1 + jjj1 + α I0.5 + α 2I zzzÑÑÑexp( −αI 0.5) ÅÅÇ 2 {ÑÑÖ k

(14)

ij γ mixture yz ′ mMeOHmHCl lnjjjj HClo zzzz = χHClMeOH mMeOH + χHClMeOH j γHCl z k { ′ mMeOHmNaCl + 0.5mMeOH{mCl ζMeOHHCl + χNaClMeOH

(17)

where χ , χ , and χ are considered as adjustable parameters. Similar equations would be represented for χNaClMeOH and its derivative χ′NaClMeOH. In the above equations, I is the ionic strength; b = 1.2 kg1/2· mol−1/2; and m is the molality of the pure electrolyte. The experimental data are fitted by considering α0 = 2.0 kg1/2· mol−1/2 as a fixed value. All named parameters for each electrolyte, χ(0), χ(1,0), χ(1,1), ξ, and ω, are computed by regression using electrolyte activity coefficients (separately for HCl and NaCl). In the case of mixed electrolyte, activity coefficient fitting is implemented to compute ηMeOHHNa.. 3.3. Potentiometric Measurements. The following galvanic cells containing a H+ glass membrane electrode (pH (0)

+ mHζMeOHHCl + mNa ζMeOHNaCl + mNa ηMeOHHNa } 2 + ωHClMeOHmMeOH

(χ (1,0) + χ (1,1) mMeOH)

[1 − (1 + αI 0.5)exp( −αI 0.5)]

ij γ pure yz zz = χ lnjjjj HCl m + mMeOHmHCl ζMeOHHCl o z HClMeOH MeOH z γ HCl k { 2 + ωHClMeOHmMeOH

{

(15)

where γHCl is the mean activity coefficient of HCl in the mixture; γ0HCl is the mean activity coefficient of pure and mixed HCl in the absence of nonelectrolyte; and ζ is the ion−ion interaction parameter arising from the presence of MeOH, respectively. In addition, ξ and ω are the ternary interaction parameters of nonelectrolyte−ion−ion and nonelectrolyte− nonelectrolyte−ion, respectively. In principle, ξ and ω depend on the ionic strength of the solution. D

(1,0)

(1,1)



Article

It is necessary to make corrections in order to eliminate the asymmetry potential of the H+ glass ISE. The corrections are made by computing the activity coefficients of HCl, γHCl0, in ionic strength (mHCl0 + mNaCl0) equal to 0.01 in various mass fractions of methanol in mixed solvent. mR is kept constant equal to 0.01 for each solvent mass fraction to correct the drift over time. Values of γHCl0 is computed by using eq 3. To this aim, the corresponding values of Cφ, β(0), and β(1) in mixed solvent and θHNa and ΨHNaCl, the mixture parameters in water, are used. The corresponding potentials are reported in the absence of asymmetry potential according to eq 22. The calculated γHCl0 for each mass fraction of methanol in mixed solvent using eq 1 are reported in Table 2. The obtained activity coefficient values in all related mass fractions (x) of CH3OH in water, at 298.15 K, are illustrated in Figure 1. This figure shows the related trends of the mean

electrode) and a Ag/AgCl electrode are used for collecting the potentiometric data. The Na+ interfering ion effects on response of pH electrode are negligible. Ag|AgCl|HCl(mHCl ), NaCl(mNaCl ), MeOH(x), H 2O(1 − x)|H+ Glass ISE

(I)

0 0 Ag|AgCl|HCl(mHCl ), NaCl(mNaCl ), MeOH(x),

H 2O(1 − x)|H+ Glass ISE

(II)

For the mixed electrolyte system, the potential of cell (I) can be expressed as Pot E = E′ + k ln(aHCl + KH,Na aNaCl)

(18)

aHCl = γ±m*

(19)

m* =

(20)

mHCl (mHCl + mNaCl )

where E′ represents the cell constant potential; k = (RT/F) is the ideal Nernstian slope; KPot H,Na stands for the potentiometric selectivity coefficient of the H+ ISE toward the Na+ interfering ions; aNaCl is the activity of NaCl; aHCl is the activity of HCl; and γ± is the mean activity coefficient of HCl in the mixture. The most serious practical limitation of the common glass electrode, alkaline error, arose from Na+ competing with H+ for silica sites due to their similar size at pH values above 12 when the Na+ concentration is high. In this study, the investigated system is not affected by this issue because of the HCl concentration confinement. Accordingly, using the negligible interfering effects of Na+ ion on the pH electrode response, the potentiometric response of the pH electrode would be determined by the potential of cell (I) E = E′ + k ln aHCl

(21) Figure 1. Experimental mean activity coefficients of HCl electrolyte versus molality in different mass fractions (x) of CH3OH in water, with x = 0.30 and 0.40. The reported data of Bates and Rosenthal18 at mass fractions of x = 0.34 are also included in this figure.

The asymmetry potential of the glass electrodes appears from the asymmetry of the glass membrane in both sides and is independent of concentration. In lieu of using cell (I), the elimination of asymmetry potential would be achieved by using the combination of potentiometric response of the cells (I) and (II)20 as follows 0 ln γHCl = ln γHCl +

activity coefficients for HCl versus ionic strength. Furthermore, reported HCl activity coefficient values by Bates18 at mass fraction of 33.4% are compared in this figure. Acceptable agreement between reported values and those in the literature18 can be observed over the considered concentration range. This study intended a detailed and systematic modeling of pure and mixed electrolyte in mixed solvent for the HCl + NaCl + methanol + water system, with attention to the nonionic species effects in the Pitzer formalism. In this regard, the OP, CP, and MP equations are used for modeling the mean activity coefficients of HCl in HCl + NaCl + methanol + water in different mass fractions (x) of CH3OH in water. In order to establish a broad systematic investigation to find the best fitting results, modeling is implemented based on two different approaches focused on methanol in computations. First, HCl, NaCl, and methanol are assumed as solute species in water. To this aim, it is necessary to recompute all reported molality and activity coefficient values. All arranged experiments and reported values in Table 2 are achieved by supposing the water and methanol as mixed solvent. Second, methanol is supposed via mixed solvent. We need to carry out least-square analysis of activity coefficients for each electrolyte,

0 0 2 1 jij (mHCl + mNaCl ) zyz ΔE zz + lnjj 2 jk mHCl (mHCl + mNaCl ) z{ 2k

(22)

In the above relation, ΔE is the difference between the emf of the cells (I) and (II), and γHCl is the mean activity coefficient of HCl in the mixture in the presence of the nonelectrolyte (MeOH). mref = m0HCl + m0NaCl is the molality of the reference solution. mHCl and mNaCl are the molality for measuring solutions. γ0HCl is the reference solution mean activity coefficient in various mass fractions of methanol in mixed solvent.

4. RESULT All the potentiometric responses and the corresponding experimental activity coefficient values of HCl electrolyte in the HCl + NaCl + methanol + water system at 298.15 K are reported in Table 2 for different solvent mass fractions (x = 10, 20, 30, 40, and 50%). The experimental ionic strength ranges of the mixed electrolyte are varied from 0.0005 up to 3.0 mol· kg−1. E



Article

Table 3. Values of Pitzer Ion-Interaction Parameters for HCl in the Investigated Binary Electrolyte Systems, Determined According to the CP, OP, and MP Methods, for Various Solvent Mass Fractions (Water + Ethanol), at 298.15 K 10%

20%

30%

40%

50%

CP OP MP CP OP MP CP OP MP CP OP MP CP OP MP

0%

Aϕ

β(0)

β(1)

C(ϕ)

χ

χ(10)

χ(11)

0.4214 0.4214 0.3915 0.4562 0.4562 0.3915 0.4992 0.4992 0.3915 0.5518 0.5518 0.3915 0.6156 0.6156 0.3915 0.3915

0.1822 0.1856 0.1935 0.2012 0.2120 0.2029 0.2160 0.2057 0.2374 0.1899 0.20363

0.3179 0.3487 0.3285 0.3064 0.3712 0.4428 0.4661 0.5623 0.4582 0.1158 0.07853

−0.0011 −0.0126 −0.0023 0.0067 −0.0081 −0.0062 −0.0081 −0.0063 −0.0120 −0.0060 −0.0035

−0.0036 −0.0043 −0.0013 −0.0013 −0.0052 -

−0.0037 0.0830 0.0520 0.0493 0.0388 -

0.0001 −0.0132 −0.0055 −0.0039 −0.0025 -

ζ −0.0025 −0.0052 0.0034 0.0039 −0.0031

σ 0.001 0.051 0.057 0.007 0.001 0.009 0.004 0.0005 0.0090 0.008 0.0005 0.014 0.009 0.0005 0.0100

molality range

refs

0.001−2

21

0.01−4.5

22

0.01−4.5

22

0.001−5.75

22, 23

0.009−3.54

22, 23

Table 4. Values of Pitzer Ion-Interaction Parameters for NaCl in the Investigated Binary Electrolyte Systems, Determined According to the CP, OP, and MP Methods, for Various Solvent Mass Fractions (Water + Ethanol), at 298.15 K 0% 10%

20%

30%

40%

50%

CP OP MP CP OP MP CP OP MP CP OP MP CP OP MP

Aϕ

β(0)

β(1)

C(ϕ)

χ

χ(10)

χ(11)

ζ

σ

0.3915 0.4214 0.4214 0.3915 0.4562 0.4562 0.3915 0.4992 0.4992 0.3915 0.5518 0.5518 0.3915 0.6156 0.6156 0.3915

0.0771 0.0814 0.0801 0.1052 0.0971 0.1139 0.1038 0.1080 0.1015 0.1646 0.1004 -

0.2639 0.2116 0.2194 0.0685 0.1040 0.0289 0.0786 0.0252 0.0681 −0.3299 0.1208 -

0.0011 0.0019 0.0023 −0.0016 0.0013 −0.0006 0.0027 0.0000 0.0010 0.0000 0.0000 -

−0.0003 −0.0005 −0.0006 −0.0005 −0.0037 -

0.1357 0.0407 0.0381 -

−0.0436 −0.0065 −0.0041 -

0.0038 0.0020 0.0034 -

0.0188 0.0342

−0.0015 −0.0022

0.0001 0.0004

0.0001 0.0040 0.0000 0.0070 0.0020 0.0002 0.0070 0.0020 0.0000 0.0090 0.0040 0.0003 0.0050 0.0300 0.0002 0.0018

refs

0−6 0.01−3.29

15 24

0.005−2.32

24

0.01−2.65

24

0.005−1.55

24

0.0076−1.28

24

Single electrolyte parameters are needed, and it must be computed for each electrolyte in the related solvent mass fraction. Equations 2 and 14 are fitted separately by using the values of reported activity coefficients for HCl and NaCl in different mass fraction of methanol + water as mixed solvent. The corresponding parameters are presented in Tables 3 and 4. One may see the related parameters are computed according to each solvent mass fraction. Getting the best results using the minimum number of regressed parameters is the main goal of constructing the computations. To this aim, different ways of keeping parameters are checked, and the results are presented in Tables 3 and 4. Computed parameters for the CP equation are Cφ, β(0), and β(1). The fitting parameters for the OP equation are Cφ, β(0), β(1), χMeOHMX, ζMeOHMX, and ωMeOHMX, and ζMeOHMX and ωMeOHMX are deleted. Finally in the EP equation, all the regressed parameters are χMeOHMX(0), χMeOHMX(10), χMeOHMX(11), ωMeOHMX, and ζMeOHMX and are computable after inserting the corresponding values of Cφ, β(0), and β(1) in water. Only values of χ MeOHMX (10) , χ MeOHMX (11) , and

HCl and NaCl, in solvent. Then the computed Pitzer equation parameters for each single electrolyte are inserted in the corresponding equation of mixed electrolyte. Least-squares analysis of activity coefficients is implemented. The standard deviation values of the fits (σ = RMSD), included in the Tables, are estimated using the following relation 2y ij ∑n (γ jj i = 1 i ,exptl − γi ,calcd) zzz zz σ = jj jj zz n−1 k {

molality range

1/2

(23)

where γi is the objective function and n is the number of experimental data points. The first and second approaches that assumed methanol as solvent or soluble species are tested using all the named equations. The only poor result is obtained by considering methanol as the solute species. Better results can be achieved by including methanol as mixed solvent. Therefore, details of the second approach results are presented in the following section. F



Article

Table 5. Values of Mixture Pitzer Ion-Interaction Parameters for HCl in the Investigated Ternary Electrolyte Systems, Determined According to the CP, OP, and MP Methods, For Various Solvent Mass Fractions (Water + Methanol) at 298.15 K ΨHNaCl 0% 10%

20%

30%

40%

50%

OP MP CP1 CP2 MP MP CP2 CP1 OP MP MP CP1 CP2 MP MP CP1 CP2 MP MP CP1 CP2

−0.0040 0.0088 −0.0024 −0.0062 0.0283 −0.0081 0.0004 −0.0299 −0.0309 −0.0288 −0.0355 0.0162 0.0177 0.0161 0.1447 −0.0824 −0.1445

θ(0)HNa -

θHNa 0.0360 −0.3556 −0.4739

−0.5000

θ(1)HNa

ζMeOHNaCl

ηMeOHHNa

-

−0.5375

−1.9285

0.0596 −0.4927 -

−0.5366

-

0.7724 −2.9351

0.1819 −0.4692 −0.5527

0.3559 −7.7812 0.9164

−0.5662 −0.5120 −0.6595

0.4359 −2.3483 0.0016

0.0407 0.0554 −0.0119

0.2665 24.9757 −32.1206

4.7010 0.3481 −1.1117

5.1480

σ

molality range

0.0606 0.0854 0.0600 0.0600 0.0924 0.0896 0.0608 0.0598 0.0437 0.0491 0.0471 0.0430 0.0435 0.0465 0.0420 0.0402 0.0405 0.0879 0.0471 0.0660 0.0460

max I = 3a 0.01−2

0.01−2

0.01−3

0.01−3.5

0.01−3

a

Values are taken from ref 21.

ξMeOHMXare reported in the tables which show the best optimized results. Tabulated results for NaCl show that the OP equation, by including the additional parameter, χ, gives superior results especially in higher mass fraction of methanol. Moreover, similar results are obtained for HCl using the OP equation except in 10% solvent mass fractions. However, in both of the considered electrolytes, the MP equation produces some rather weaker results when compared to the other equations. The existence of linear dependence between the second virial coefficients in Pitzer the equation (ß(0) or ß(1)) and the solvent dielectric constant was pointed out by Gupta.16 This effect was considered in some works.22,23 However, it may not be possible to perform a similar investigation because of the difference in concentration ranges for each solvent mass fraction that are used in this work. Similar procedures are repeated to correlate activity coefficient values of HCl in HCl + NaCl + methanol + water using CP, OP, and MP equations. The results are depicted in Table 5. The modeling purpose of mixed electrolyte in mixed solvent systems is achieved by inserting the resulting parameters for pure electrolytes in the related eqs (eq 2 and 15). The mixing Pitzer parameters are computed for each percentage of mixed solvents. The regressed parameters for the studied system are ηMeOHHNa, ΨHNaC, and θHNa that represent the mixing ioninteraction parameters for the mixed electrolyte system. The higher-order limiting law16 correction is considered by replacing the θHNa with θ(0)HNa and θ(1)HNa according to eqs 9 and 10. Different possible approaches to investigate the Pitzer equations are discussed in follows. First regression is performed by the CP equation. This issue is implemented by use of the CP1 and CP2 equations that are proposed for

inclusion or exclusion of the higher-order limiting law. One can see better results would be gained using the CP2 equation especially in higher mass fraction of methanol (50%). The next one is the OP equation. The convergence problem is observed for all solvent mass fractions except 30% when the explicit ion + neutral interaction parameter (ηMeOHHNa) is included in the computation. This problem can be removed for 10% solvent mass fraction when ξMeOHNaCl is used in lieu of ηMeOHHNa. The final equation is the MP equation which takes into account χ(0)MeOHHCl, χ(1,0)MeOHHCl, χ(1,1)MeOHHCl, χ(0)MeOHNaCl, χ(1,0)MeOHNaCl, χ(1,1)MeOHNaCl, ξMeOHHCl, ξMeOHNaCl, ηMeOHHNa, and ωMeOHHCl as adjustable parameters. As discussed earlier, computed parameters for a single electrolyte, χ(1,0), χ(1,1), and ζ, which belonged to HCl and NaCl are inserted in eq 15. In fact, χ(0)MeOHNaCl, χ(0)MeOHHCl, ωMeOHHCl, and ωMeOHNaCl are deleted in eq 15. According to the MP equation, θHNa and ΨHNaCl are the mixture parameters in water that must be inserted in eq 15. So the only parameter which must to be fitted against experimental data for each solvent mass fraction is ηMeOHHNa. Another approach that can be checked is considering θHNa and ΨHNaCl as fitting parameters for mixed electrolyte in mixed solvent. One can see acceptable results are obtained by including θHNa and ΨHNaCl in the MP equation as parameters which are not just computed in pure water but that changed by solvent mass fractions. As can be seen this approach gives the best correlation results for 30% and 40%. The negative values of many parameters indicate ionic association in different solvents. Figure 2 shows the difference of experimental and calculated mean molal activity coefficients of HCl versus ionic strength in the HCl + NaCl + water + methanol systems at 298.15 K. Despite the superiority of the OP model over the MP and CP models in regression of pure electrolyte activity coefficient data in mixed solvent, it seems that the presented correlation G



■

Article

AUTHOR INFORMATION

Corresponding Authors

*S.A.A. Hosseini: [email protected]. *Zohreh Karimzadeh: [email protected]. ORCID

Zohreh Karimzadeh: 0000-0001-7140-8239 S. A. A. Hosseini: 0000-0003-3343-545X Funding

The authors gratefully acknowledge the financial support of Kharazmi University. Notes

The authors declare no competing financial interest.

■

Figure 2. Plots of the difference of experimental and calculated mean molal activity coefficients of HCl versus ionic strength in the HCl + NaCl + water + methanol systems at 298.15 K.

REFERENCES

(1) Wang, Q. P.; Lü, X. M.; Sun, X. Li.; Xu, W. G.; Chen, S. S.; Lü, D. Z. Thermodynamic properties of hydrochloric acid in mixed solvents {HCl(mA) + NaCl(mB)} in {(1+ x)H2O + xD-fructose} at T = (278.15 to 318.15) KJ. J. Chem. Thermodyn. 2004, 36, 1089− 1094. (2) Balaban, A.; Kuranov, G.; Smirnova, N. Phase equilibria modeling in aqueous systems containing 2-propanol and calcium chloride or/and magnesium chloride. Fluid Phase Equilib. 2002, 194− 197, 717−728. (3) Dian-Yuan, M.; Zhen, L. D.; Yu, L. C.; Zhen, Y. J. Thermodynamic properties of multicomponent electrolyte solutions in mixed solvents 4. {HCl(mA) + NaCl(mB)} in {(1 − x)H2O + xCH2OHCHOHCH3} at 278.15 to 318.15 K. J. Chem. Thermodyn. 1988, 20, 907−912. (4) Wang, Q. P.; Lü, D. Z.; Sun, X. L.; Zhang, L. Thermodynamic properties of multicomponent electrolyte solutions in mixed solvents {HCl+NaCl-tert-C4H9OH+H2O} at (278.15 to 318.15) K. J. Chem. Thermodyn. 2004, 36, 167−172. (5) Khoo, K. H.; Chan, C. Y.; Lim, T. K. Electromotive-force studies of mixed electrolytes in mixed solvents. HCl+NH4Cl in methanol +water solvents at 25°C. J. Solution Chem. 1978, 7, 349−355. (6) Ghalami-Choobar, B.; Sayyadi-Nodehi, F. Thermodynamic study of electrolyte mixture (KCl+KNO3+water+proline) by potentiometric measurements at T = 298.2 and 303.2K. Fluid Phase Equilib. 2013, 338, 274−281. (7) Ghalami-Choobar, B.; Sayyadi-Nodehi, F. Thermodynamic study of the quaternary electrolyte (NaCl+NaNO3+HCONH2+H2O) system using potentiometric measurements at T = (298.2 and 303.2)K. J. Chem. Thermodyn. 2012, 49, 104−113. (8) Jun, Z.; Shi-Yang, G.; Shu-Ping, X.; Yan, Y. Study of thermodynamic properties of quaternary mixture RbCl+Rb2SO4+CH3OH+H2O by EMF measurement at 298.15K. Fluid Phase Equilib. 2004, 226, 307−312. (9) Farelo, F.; Lopes, V.; Ferra, M. I. A Activity Coefficients of Potassium Chloride and Sodium Chloride in the Quaternary System KCl-NaCl-Water-Ethanol. J. Solution Chem. 2002, 31, 845−860. (10) Chee-Yan, C.; Khoo, K. H. Activity coefficients of hydrochloric acid in mixtures with potassium chloride in methanol + water solvents from electromotive force measurements at 298.15 K. J. Chem. Soc., Faraday Trans. 1 1974, 70, 27−32. (11) Deyhimi, F.; Abedi, M.; Karimzadeh, Z. Modeling of the quaternary NaCl+KCl+CH3OH+H2O mixed electrolyte system: Binary and ternary mixing (ion+ion) and (ion+nonelectrolyte) interaction parameters. J. Chem. Thermodyn. 2015, 88, 15−21. (12) Abedi, M.; Alamdari Shendi, M.; Karimzadeh, Z.; SalamatAhangari, R.; Deyhimi, F. The ternary and quaternary electrolyte systems: Activity coefficient of NaCl measured and modeled for NaCl + C2H5OH + H2O and NaCl + KCl + C2H5OH + H2O systems. Fluid Phase Equilib. 2016, 423, 138−145. (13) Xu, Y.; Li, S.; Zhai, Q.; Jiang, Y.; Hu, M. Investigation on the thermodynamic properties of KCl/CsCl+NaCl+CH3OH+H2O

results of the latter models, MP and CP2 for mixed electrolyte in mixed solvent, are more valid for the considered experimental data especially at higher methanol mass fraction. Modeling of mixed electrolyte activity coefficients in mixed solvent by the MP equation shows that improved fitting results can be obtained by adding θHNa and ΨHNaCl as mixture parameters not only in water but also in mixed solvent. Including the higher-order limiting law as CP2 improves the fitting results especially at higher methanol mass fraction. Also, this effect is checked in the case of ethanol as mixed solvent in our upcoming work, and the ethanol result confirms this idea.

5. CONCLUSION The present investigation reports the measurements regarding the possibilities of determining the activity coefficient of mixed electrolyte (HCl + NaCl) systems in mixed solvent. The experimental data are obtained over the electrolyte molality ranging from 0.005 mol·kg−1 up to about 3.5 mol·kg−1, at 298.15 ± 0.05 K, by using a cell containing a pH and a silver chloride electrode in different alcohol mass fractions x(CH3OH) in H2O (where x = 0.10, 0.20, 0.30, 0.40, and 0.50). The OP, CP, and MP equations are used for modeling the mean activity coefficients of HCl. It can be concluded that, for the case of pure electrolyte activity coefficient data in mixed solvent, the OP equation which takes into account the interaction between nonionic species and involved ions along with additional parameters gives more accurate regression results over the MP and CP models. In the case of mixed electrolyte in mixed solvent, including the higher-order limiting law, by use of the CP2 equation, improves the fitting results especially at higher methanol mass fraction. It will be interesting to compare the ion-interaction treatments for HCl + NaCl + H2O + ROH systems for various alcohol chain lengths. For such cases, one can determine the effect of the alcohol chain length on the electrolyte Pitzer model. It will be addressed in a future article. H



Article

quaternary systems at 298.15K. J. Ind. Eng. Chem. 2014, 20, 2159− 2165. (14) Khoo, K. H.; Fernando, K. R.; Fereday, R. J. Application of the Pitzer Model to a Weakly Associated Uni-univalent Electrolyte in Mixed Solvents: Solubility of Thallium(I) Chloride in the System TlCl + NaCl + Methanol + Water at 25°C. J. Solution Chem. 1999, 28, 747−758. (15) Pitzer, K. S., Ed. Activity Coefficients in Electrolyte Solutions, 2nd ed.; CRC Press: Boca Raton, FL, 1991; pp 90−94. (16) Gupta, A. R. Pitzer’s thermodynamic equations to activity coefficients of 1:1 electrolytes in methanol-water mixtures. J. Phys. Chem. 1979, 83, 2986−2990. (17) Fernandez-Merida, L.; Raposo, R. R.; Garcıa-Garcıa, G. E.; Esteso, M. A. Modification of the Pitzer equations for application to electrolyte + polar non-electrolyte mixtures. J. Electroanal. Chem. 1994, 379, 63−69. (18) Bates, R. G.; Rosenthal, D. Standard Potential of the silver silver chloride electrode and activity coefficients of hydrochloric acid in aqueous methanol (33.4 WT.%) with and without added sodium chloride at 25°. J. Phys. Chem. 1963, 67, 1088−1090. (19) Bates, R.G. Determination of pH: Theory and Practice; John Wiley & Sons: New York, 1964; pp 283−284. (20) Esteso, M. A.; Gonzalez-Diaz, O. M.; Hernandez-Luis, F. F.; Fernandez-Merida, F. Activity coefficients for NaCl in ethanol-water mixtures at 25°C. J. Solution Chem. 1989, 18, 277−288. (21) Harned, H. S.; Owen, B. B. The Physical Chemistry of Electrolytic Solutions, 3rd ed.; Reinhold: New York, 1958; pp 719−720. (22) Deyhimi, F.; Karimzadeh, Z.; Abedi, M. Pitzer and Pitzer− Simonson−Clegg ion-interaction modeling approaches: Ternary HCl +methanol+water electrolyte system. J. Mol. Liq. 2009, 150, 62−67. (23) Koh, D. S. P.; Khoo, K. H.; Chan, C. The application of the pitzer equations to 1−1 electrolytes in mixed solvents. J. Solution Chem. 1985, 14, 635−651. (24) Deyhimi, F.; Abedi, M. NaCl + CH3OH + H2O Mixture: Investigation Using the Pitzer and the Modified Pitzer Approaches To Describe the Binary and Ternary Ion−Nonelectrolyte Interactions. J. Chem. Eng. Data 2012, 57, 324−329.

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Mixed Electrolyte in Mixed Solvent: Activity Coefficient Measuring and

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