Ability of the Ion-Selective Electrode in the Thermodynamic Modeling

Jul 31, 2014 - Ability of the Ion-Selective Electrode in the Thermodynamic Modeling of the Mixed Electrolyte System: The Case of the Ternary NH4Cl + K...
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Ability of the Ion-Selective Electrode in the Thermodynamic Modeling of the Mixed Electrolyte System: The Case of the Ternary NH4Cl + KCl + H2O Mixed Electrolyte Systems Farzad Deyhimi,# Maryam Abedi, and Zohreh Karimzadeh* Department of Chemistry, Shahid Beheshti University, G.C., Evin-Tehran, 1983963113, Iran ABSTRACT: With the recent development and apparition of new sensors and selective membranes, ion-selective electrodes (ISEs) have become an attractive alternative method to the more usual vapor pressure or solvent activity methods for the investigation of thermodynamic properties of electrolyte systems. In this context, it seemed interesting to explore the ability of the ion-selective electrode in the thermodynamic modeling of mixed electrolyte systems. For this purpose, the mixed 1:1 electrolyte system with a common anion, namely the ternary NH4Cl + KCl + H2O electrolyte system was selected, in which the corresponding NH4+ and K+ cations are considered mutually as severe interfering ions for K+ ISE and NH4+ ISEs, respectively. In addition, Pitzer ion-interaction theory for mixed salts was applied for modeling the behavior of ternary electrolyte systems in concentrations ranging from 0.01 mol/kg up to 5 mol/kg, at 298.15 K. The reported results show, effectively, how the magnitude of the potentiometric selectivity coefficient (Kpot 12 ) of these ISEs, could play as limiting factors on the investigation of these systems.

■

For NH4+ ISE, K+ is a strong interfering ion, while NH4+ is mutually a strong interfering ion for K+ ISE. For each of these studied ternary electrolyte systems, different series of mixed electrolyte systems, at similar ionic strengths, by a defined molal ratio (r = m1/m2), were used at 298.15 K for the activity coefficient modeling. The limiting impact of their selectivity on the resulting potentiometric data used for modeling the concentrated mixed binary electrolyte system was investigated using a large value of r. The selected NH4+ and K+ ion-selective electrodes are of solvent polymeric membrane types, but the involved aspects are also valid for other type of ion-selective membranes (e.g., glass, crystal, etc.).

INTRODUCTION The knowledge of the thermodynamic properties (particularly activity coefficients) of aqueous mixed electrolyte solutions is required to investigate the nature of various ionic interactions in many industrial and environmental processes, such as desalination, chemical separation, marine chemistry, geology, and environmental aerosol sciences.1−3 The usual experimental techniques used for these purposes are vapor pressure or solvent activity methods and potentiometric measurements. However, the more recent development of the ion-selective electrodes (ISEs) offers more attractive alternatives for the determination of the activity coefficients of electrolyte systems. We have used pH-glass membrane4 and solvent polymeric membrane ISE for the determination of mean activity coefficients of NH4Cl in mixed (ROH + H2O) solvents and in several mixed electrolyte systems (refs 5 and 6 and refs therein). However, it is well-known that in a mixed electrolyte system the response of ISEs could be more or less affected by the presence of an interfering ion, as expressed by the potentiometric selectivity coefficient (Kij) of the ISE.7,8 In view of the usefulness of this device, it seemed particularly interesting to explore the limit of applicability of a typical ISE for the study of the activity coefficient of mixed electrolyte systems. For this purpose, the ternary electrolyte system (NH4Cl + KCl + H2O), and related galvanic cells containing the solvent polymeric (PVC) NH4+ ISE and Ag/AgCl and also K+ ISE and Ag/AgCl electrodes, were utilized to calculate the mean molal activity coefficients for NH4Cl and KCl, respectively, in these electrolyte systems. © 2014 American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Reagents, Ion-Selective Electrodes, and Potentiometric Setup. NH4+ and K+ ion-selective membranes were prepared from selectophore grade reagents (Fluka, Switzerland) and evaluated (refs 5 and 6 and refs therein). NH4+ ion-selective membranes were prepared from the following compounds: high molecular poly(vinyl chloride) (PVC), mixture of nonactin (72%) and monactin (28%) as ionophore, and bis(2ethylhexyl)sebacate. Also, the following ingredients were used for the preparation of solvent polymeric K+ ISE: valinomycin ionophore, potassium tetrakis(4-chlorophenyl)borate, bis(1-butylpentyl) decane-1,10diyl diglutarate, and PVC. The NH4+ and K+ electrodes were each time backfilled with NH4Cl or KCl internal filling solutions, Received: February 8, 2014 Accepted: July 24, 2014 Published: July 31, 2014 2428

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on a molality scale; β(0) (kg mol−1), β(1) (kg mol−1), and Cϕ(kg mol−1)1/2 are the parameters of the Pitzer equations; b = 1.2 kg1/2·mol−1/2, and α = 2 kg1/2·mol−1/2. In addition, θMN and ψMNCl represent the ionic interaction parameters for the mixed salt system. The Debye−Hückel coefficient for the osmotic coefficient (Aϕ) is defined as

respectively, and an Ag/AgCl wire was used as internal reference electrodes. The Ag/AgCl wire electrodes were made by electrolysis.10 Different concentrations of internal electrolyte filling solution were utilized to find the best case. The best results were those obtained with 0.1 M NH4Cl or KCl electrolyte. All primary stock solutions (NH4Cl and KCl) were, first, prepared by weight using doubly distilled water and their concentration were determined by potentiometric titration using AgNO3 standard solution. All used salts (NH4Cl and KCl salts (with mass % > 99.5, and > 99, respectively)) from Fluka, were dried overnight in an oven (at 130 °C). A PC automated potentiometric data acquisition setup and a Metrohm ion-meter (model 619) with high input impedance (>1 TΩ) recorded the experimental cell potential data. The circulation of thermostated water from a bath (the variance interval of the circulating thermostatic water is 11 L per minute) was performed as explained elsewhere (refs 5 and 6 and refs therein). The standard addition method was used to prepare the studied electrolyte solutions in the galvanic cell as explained elsewhere (refs 5 and 6 and refs therein). Hamilton syringes, with accuracies within ± 1 % of nominal volumes, and with precisions within 1 % (as indicated by the manufacturer) were used to implement the standard addition steps.

⎛ e2 ⎞3/2 1 (2πNAρA )1/2 ⎜ ⎟ 3 ⎝ 4πε DkT ⎠ (7) ° where the constants ε°, k, NA, D, and ρA are vacuum permittivity, Boltzmann constant, Avogadro constant, dielectric constant, and density of the mixed solvent, respectively. For water, its value is 0.39145 (kg mol−1)1/2 at 298.15 K. 3.2. Potentiometric Measurements Principle. The potentiometric data were measured on the basis of the following three galvanic cells. Each galvanic cell contains a solvent polymeric PVC M+ (NH4+ and K+)ISE, and an Ag/AgCl electrode: Aϕ =

Ag | AgCl | MCl(m1), H 2O | M+ ISE

(A)

Ag | AgCl | NCl(m2), H 2O | M+ ISE

(B) +

Ag | AgCl | MCl(m1), NCl(m2), H 2O | M ISE

3. METHOD 3.1. Ion-Interaction Model. The semiempirical Pitzer ioninteraction theory was successfully applied to investigate the various high-concentrated pure and mixed electrolyte systems.3,9−11 In this theory, the nonideal behavior of the electrolyte system was considered by the excess Gibbs free energies. For a single Mν+Xν−electrolyte (e.g., M = NH4, N = K, and X = Cl), and for a (1:1) mixture of MCl and NCl electrolyte, the corresponding Pitzer equations are written respectively as12

Measurement of the slope (s) and the cell constant potential (E′) was performed by cell (A). For the NH4+ ISE, the resulting regressed slope and intercept values with their and standard deviations (for 3 replicates) were s = 57.3 ± 0.29 mV/(per decade molal change and E″ = 107.99 ± 0.53 mV (R2 = 0.9994, N = 3 replicates), respectively. The slope and intercept of the K+ ISE versus the reference electrode were measured to be s = 53.39 ± 0.16 mV/(per decade molal change) and E′ = 108.99 ± 0.55 mV (R2 = 0.9994, N = 3 replicates), respectively. + The potentiometric selectivity coefficient (Kpot 12 ) of the M ISE toward the N+ interfering ions was obtained by cell (B). The determination of the mean activity coefficients for MCl in the aqueous mixed (MCl + NCl) electrolyte (at 298.15 K) was performed by the galvanic cell (C). Effectively, for this mixed electrolyte system, the cell potential can be expressed by

⎛ 2(υ υ )3/2 ⎞ ⎛ 2υ υ ⎞ ⎟⎟C γ ln γ± = |z+z −|f γ + m⎜ + − ⎟Bγ + m2⎜⎜ + − ⎝ υ ⎠ υ ⎝ ⎠ (1) γ ϕ ϕ ln γ±MCl = f γ + I {BMCl + y2 (B NCl − BMCl + θMN)}

ψ ⎧⎛ 3 ϕ ⎞ ⎛ ϕ ⎞ ϕ ⎟ + y ⎜C + I 2⎨⎜ CMCl − CMCl + MNCl ⎟ 2 ⎝ NCl ⎠ ⎩⎝ 2 2 ⎠ ψ ⎫ + y2 (1 − y2 ) MNCl ⎬ 2 ⎭ (2)

where ⎡ ⎤ I /m0 2 + ln(1 + b I /m0 )⎥ f γ = −Aϕ⎢ ⎢⎣ 1 + b I /m0 ⎥⎦ b

− (1/2)α 2(I /m0))] γ

C = (3/2)C

φ

Biϕ = βi(0) + βi(1) exp( −αI 0.5)

E(C) = E′ + s log[a1 + K12pota 2)]

(8)

a1 = m1(m1 + m2)γ±2,1

(9)

a 2 = m2(m1 + m2)γ±2,2

(10)

where E′ represents the cell constant potential, s is the Nernstian slope, Kpot 12 represents the potentiometric selectivity coefficient of the M+ ISE (e.g., M+ = NH4+ or K+) toward the N+ interfering ions (e.g., N+ = K+or NH4+) and γ±,1, γ±,2 are the activity coefficients. It is first necessary to evaluate the value of the potentiometric selectivity coefficient (Kpot 12 ) to determine the experimental mean activity coefficient values in mixed salt solutions. First in pure solution of interfering NCl(m2) salt, the potentiometric response of the galvanic cell (B) could be rearranged as

(3)

0 1/2 2β (1) [1 − e−α(I / m ) (1 + α I /m0 2 0 α (I / m )

Bγ = 2β (0) +

(C)

(4) (5)

⎛1⎞ K12pot = ⎜ ⎟10((E(B)− E ′)/ s) ⎝ a2 ⎠

(6)

γ± is the molality-scale mean ionic activity coefficient of the electrolyte Mν+Xν−; z is the charge number of ion; υ = υ+ + υ− is the number of ions dissociated in one unit electrolyte formula; m is the molality of electrolyte (mol/kg); I is the ionic strength

(11) +

The potentiometric selectivity coefficient of the M ISE toward the N+ interfering ions could be determined using pure standard 2429

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Table 1. Cell Potentiometric Data and the Resulting Experimental Mean Activity Coefficients for NH4Cl versus Electrolyte Molality, in the Investigated Mixed NH4Cl + KCl Electrolyte Systems, for Various Molal Salt Ratios (r = m1/m2 = 5083.8, 2464.3, 998.6, and 100.4) at 298.15 K m1(NH4Cl)

m2(KCl)

ln γ1(±)

r = m1/m2 = 2464.3 4.06·10−06 −0.1046 2.03·10−05 −0.2055 4.06·10−05 −0.2662 1.01·10−04 −0.3600 2.03·10−04 −0.4364 3.04·10−04 −0.4802 4.06·10−04 −0.5094 5.07·10−04 −0.5302 6.08·10−04 −0.5454 8.11·10−04 −0.5652 1.01·10−03 −0.5760 1.22·10−03 −0.5813 1.42·10−03 −0.5832 1.62·10−03 −0.5829 1.83·10−03 −0.5814 2.03·10−03 −0.5792 2.07·10−03 −0.5787 r = m1/m2 = 998.6 1.00·10−05 −0.1046 5.00·10−05 −0.2055 1.00·10−04 −0.2662 2.50·10−04 −0.3600 5.00·10−04 −0.4364 7.50·10−04 −0.4803 1.00·10−03 −0.5095 1.25·10−03 −0.5303 1.50·10−03 −0.5455 2.00·10−03 −0.5653 2.50·10−03 −0.5761 3.00·10−03 −0.5815 3.50·10−03 −0.5833 4.00·10−03 −0.5830 4.50·10−03 −0.5814 5.00·10−03 −0.5792 5.10·10−03 −0.5787

0.0100 0.0500 0.1000 0.2499 0.4998 0.7497 0.9996 1.2495 1.4994 1.9992 2.4990 2.9988 3.4986 3.9984 4.4982 4.9980 5.0979 0.0100 0.0500 0.0999 0.2497 0.4995 0.7493 0.9990 1.2487 1.4985 1.9980 2.4975 2.9970 3.4965 3.9960 4.4955 4.9950 5.0949

E/mV

m1(NH4Cl)

−46.7 −10.7 4.4 24.1 38.8 47.5 53.7 58.5 62.5 68.9 74.0 78.2 81.8 85.0 87.9 90.4 90.9

0.0099 0.0496 0.0993 0.2483 0.4967 0.7452 0.9939 1.2427 1.4916 1.9898 2.4886 2.9879 3.4878 3.9882 4.4891 4.9905 5.0909

−107.5 −52.9 −30.1 −0.3 22.0 35.1 44.4 51.8 57.8 67.5 75.2 81.6 87.1 92.0 96.3 100.2 100.9

0.0099 0.0493 0.0987 0.2467 0.4934 0.7402 0.9871 1.2340 1.4810 1.9752 2.4697 2.9645 3.4595 3.9548 4.4504 4.9463 5.0455

(12)

In the used concentration range for all series of electrolyte solutions, the interfering effect of N+ on the response of the M+ ISE would be negligible when the second term in the parentheses of the above eq (K12pot (a2/a1)) could practically be ignored. Therefore, eq 12 can be reduced to the Nernst relation E(C) = E′ + s log a1

1 m1(m1 + m2)

r = m1/m2 = 5083.8 1.95·10−06 −0.1043 9.77·10−06 −0.2050 1.95·10−05 −0.2655 4.88·10−05 −0.3592 9.77·10−05 −0.4356 1.47·10−04 −0.4795 1.95·10−04 −0.5088 2.44·10−04 −0.5296 2.93·10−04 −0.5449 3.91·10−04 −0.5649 4.90·10−04 −0.5758 5.88·10−04 −0.5812 6.86·10−04 −0.5832 7.84·10−04 −0.5829 8.83·10−04 −0.5814 9.82·10−04 −0.5793 1.00·10−03 −0.5788 r = m1/m2 = 100.4 9.82·10−05 −0.1044 4.91·10−04 −0.2053 9.83·10−04 −0.2660 2.46·10−03 −0.3600 4.92·10−03 −0.4367 7.37·10−03 −0.4809 9.83·10−03 −0.5104 1.23·10−02 −0.5314 1.48·10−02 −0.5469 1.97·10−02 −0.5670 2.46·10−02 −0.5780 2.95·10−02 −0.5833 3.45·10−02 −0.5850 3.94·10−02 −0.5843 4.43·10−02 −0.5821 4.93·10−02 −0.5790 5.03·10−02 −0.5784

E/mV −120.1 −58.0 −32.0 1.8 27.2 42.1 52.7 61.1 68.0 79.0 87.7 95.0 101.3 106.8 111.8 116.2 117.1 −114.0 −47.7 −19.9 16.3 43.4 59.3 70.7 79.6 86.9 98.7 108.0 115.8 122.5 128.4 133.7 138.5 139.4

⎛ 1 ⎞ 1 ⎟Δ ln γ±MCl = θMN + (mM + mCl )ψMNCl ⎜ 2 ⎝ mN ⎠

(14)

Δ ln γ±MCl = (ln γ±MCl)exp − (ln γ±MCl)calc

(15)

where (ln γ±MCl)calc is calculated with ψMNCl = 0, θMN = 0. The slope and intercept of the linear portion of regression plot of the (1/mn) Δ ln γ±MCl versus 1/2(mM + mCl) determined the mixed ion-interaction parameters θMN and ψMNCl values.

(13)

4. RESULTS AND DISCUSSIONS The thermodynamic investigation of a mixed salt, based on potentiometric measurements, makes use of the Nernst relation (eq 13). However, as mentioned in section 3.2, in an electrolyte system containing a mixed salt, the use of the Nernst relation is only permitted if the effect of the interfering ion on the response

Finally, the mean activity coefficient values for MCl(m1) for all studied series could be calculated by γ± =

ln γ1(±)

3.3. Determination of Mixed Ion-Interaction Parameters (θMN,ψMNCl). The Pitzer graphical method3,10 was utilized for the determination of the mixed interaction parameters (θMN,ψMNCl). According to this method

MCl solutions and the above-mentioned regressed slope (s) and intercept values (E′). The cell potential (C) for the aqueous mixed MCl + NCl salt solutions can be shown by ⎡ ⎛ a ⎞⎤ E(C) = E′ + s log⎢a1⎜1 + K12pot 2 ⎟⎥ ⎢⎣ ⎝ a1 ⎠⎥⎦

m2(KCl)

10((E(C)− E ′)/2s) (14) 2430

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Table 2. Cell Potentiometric Data and the Resulting Experimental Mean Activity Coefficients for KCl versus Electrolyte Molality, in the Investigated Mixed KCl + NH4Cl Electrolyte Systems, for Various Molal Salt Ratios (r = m1/m2 = 9489.5, 3941.6, 489.7, 252.6) at 298.15 K m1(KCl) 0.0100 0.0500 0.1000 0.2499 0.4996 0.7493 0.9988 1.2483 1.4976 1.9960 2.4940 2.9916 3.4887 3.7372 0.0100 0.0502 0.1004 0.2510 0.5019 0.7526 1.0032 1.2537 1.5040 2.0043 2.5042 3.0034 3.5022 3.7514

m2(NH4Cl)

ln γ1(±)

r = m1/m2 = 252.6 3.96·10−05 −0.1044 1.98·10−04 −0.2045 3.96·10−04 −0.2645 9.89·10−04 −0.3570 1.98·10−03 −0.4326 2.97·10−03 −0.4762 3.95·10−03 −0.5053 4.94·10−03 −0.5257 5.93·10−03 −0.5404 7.90·10−03 −0.5579 9.87·10−03 −0.5649 1.18·10−02 −0.5647 1.38·10−02 −0.5592 1.48·10−02 −0.5549 r = m1/m2 = 3941.6 2.55·10−06 −0.1044 1.27·10−05 −0.2046 2.55·10−05 −0.2645 6.37·10−05 −0.3569 1.27·10−04 −0.4324 1.91·10−04 −0.4759 2.55·10−04 −0.5049 3.18·10−04 −0.5253 3.82·10−04 −0.5399 5.09·10−04 −0.5574 6.35·10−04 −0.5645 7.62·10−04 −0.5644 8.89·10−04 −0.5591 9.52·10−04 −0.5549

E/mV

m1(KCl)

−31.8 2.0 16.3 34.8 48.5 56.7 62.5 67.1 70.9 77.0 81.7 85.8 89.4 91.0

0.0100 0.0501 0.1001 0.2503 0.5006 0.7507 1.0007 1.2507 1.5005 1.9998 2.4987 2.9973 3.4954 3.7443

−52.3 −14.7 1.1 21.6 37.0 46.0 52.4 57.5 61.6 68.4 73.7 78.3 82.2 84.0

0.0100 0.0502 0.1004 0.2510 0.5019 0.7527 1.0033 1.2539 1.5042 2.0046 2.5045 3.0039 3.5028 3.7520

of the ISE could be negligilble (i.e., low value of Kpot 12 ). In such a case, eq 8 is simplified to the Nernst relation (eq 13). The effect of the interfering ion on the response of the ISE could act as a limiting factor on the ability of the ISE to be used for studying the mixed salt electrolyte system. So, in order to be sure that the Nernst relation could be used for the exploration of the corresponding mixed electrolyte system, it is first necessary to evaluate the value of Kpot 12 for the ISE being used. Tables 1 and 2 show the cell potentiometric data and the resulting experimental mean activity coefficients for the investigated ternary systems (NH4Cl + KCl and KCl + NH4Cl) versus electrolyte molality with different r values, at 298.15 K respectively. Following the above presented procedures, first the Pitzer parameter values for aqueous pure MCl was determined (β(0)NH4Cl = 0.05192, β(1)NH4Cl = 0.19340, CϕNH4Cl = −0.00298, β(0)KCl = 0.04692, β(1)KCl = 0.21905 and CϕKCl = −0.00050). Using Pitzer parameters (β(0), β(1), and Cϕ) for aqueous pure MCl and NCl solutions, the potentiometric selectivity coefficient of the M+ ISE (with M = NH4, K) toward the N+ (with N = K, NH4) interfering ions is determined. The results for potentiometric selectivity coefficient of the M+ ISE toward the N+ interfering ions and vice versa were determined and reported in Tables 3 and 4. In Table 3, the interfering effect of K+ on the response of the NH4+ ISE was deliberated outside of r ≥ 1000. Consequently,

m2(NH4Cl)

ln γ1(±)

E/mV

r = m1/m2 = 489.7 2.05·10−05 −0.1044 1.02·10−04 −0.2045 2.04·10−04 −0.2644 5.11·10−04 −0.3569 1.02·10−03 −0.4325 1.53·10−03 −0.4761 2.04·10−03 −0.5051 2.55·10−03 −0.5256 3.06·10−03 −0.5402 4.08·10−03 −0.5578 5.10·10−03 −0.5649 6.12·10−03 −0.5648 7.14·10−03 −0.5595 7.65·10−03 −0.5553 r = m1/m2 = 9489.5 1.06·10−06 −0.1044 5.29·10−06 −0.2046 1.06·10−05 −0.2645 2.65·10−05 −0.3569 5.29·10−05 −0.4324 7.93·10−05 −0.4759 1.06·10−04 −0.5049 1.32·10−04 −0.5253 1.59·10−04 −0.5399 2.11·10−04 −0.5574 2.64·10−04 −0.5644 3.17·10−04 −0.5643 3.69·10−04 −0.5591 3.95·10−04 −0.5549

−39.7 −3.7 11.5 31.1 45.9 54.5 60.7 65.5 69.5 75.9 81.1 85.4 89.2 91.0 −55.7 −17.2 −1.0 20.0 35.8 45.0 51.6 56.8 61.0 67.9 73.4 78.1 82.1 84.0

Table 3. Range of Variability of (Kpot 12 (a2/a1)) Term for All Series of Solutions (with r = m1/m2 = 5083.8, 2464.3, 998.6, and 100.4) at 298.15 K. r 100.4 998.6 2464.3 5083.8

kNH4,K (aK/aNH4) 2.8·10−4 2.8·10−5 1.1·10−5 5.5·10−6

to 5.6·10−4 to 5.7·10−5 to 2.3·10−5 to 1.1·10−5

Table 4. Range of Variability of (Kpot 12 (a2/a1)) Term for All Series of Solutions (with r = m1/m2 = 9489.5, 3941.6, 489.7 and 252.6) at 298.15 K r 252.6 489.7 3941.6 9489.5

kK,NH4 (aNH4/aK) 9.0·10−4 6.9·10−4 8.6·10−5 3.6·10−5

to 1.3·10−3 to 4.6·10−4 to 5.8·10−5 to 2.4·10−5

the second term (Kpot 12 (a2/a1)) in the parentheses of eq 12 was deleted and the NH4Cl mean activity coefficients for all series of electrolyte solutions (with r = m1/m2 = 998.6, 2464.3, 5083.8) was computed by the Nernst equation (eq 13). In the case of NH4+ the interfering effect on the response of + K ISE, as can be seen in Table 4, with the molal fraction, r ≥ 4000, Kpot 12 (a2/a1) was ignorable, and the Nernst equation (eq 2431

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present in mixed electrolyte systems caused this effect, and the effect could be proportional to the magnitude of Kpot 12 (a2/a1), while, it could not be neglected in the (1 + Kpot 12 (a2/a1)) term in eq 12. The potentiometric selectivity coefficient of the ISE membrane (Kpot 12 ) effect on the potentiometric measurement was analyzed. It may be concluded that the interfering role of ions on the ISE measurements could be counterbalanced by using the choice of a high molal fraction of mixed electrolyte systems. Effectively, as shown in the reported data, reliable mean activity coefficient values up to four decimal significant numbers correspond to the mixed electrolyte systems with molal ratio r ≥ 1000 for NH4Cl + KCl system and r ≥ 4000 for KCl + NH4Cl system.

13) was used for the determination of the KCl mean activity coefficients for all series of electrolyte solutions (with r = m1/m2 = 3941.6, 9489.5). The value of the two and three-particle mixed ionic interaction parameters (θMN,ψMNCl) was also determined from the Pitzer graphical method. The resulting interaction parameters of each series of mixed electrolyte solutions (r = m1/m2) and their resulting mean values (±SD) are presented in Tables 5 and 6. Table 5. Values of Pitzer Mixed Ion-Interaction Parameters (θNH4,K, ΨNH4,KCl) in the Investigated Ternary Electrolyte Systems, Determined According to the Pitzer Graphical Method, for Various Molal Salt Ratios (r = m1/m2 = 5083.8, 2464.3, 998.6, 100.4) at 298.15 K NH4Cl + KCl

intercept

slope

r

θNH4,K

ΨNH4,KCl

5083.8 2464.3 998.6 100.4

−0.0011 −0.0020 −0.0022 −0.0008

0.0004 0.0014 0.0009 0.0002

■

Corresponding Author

*E-mail: [email protected]. Funding

The authors acknowledge and are grateful to the Research VicePresidency of Shahid Beheshti University for financial support. Notes

The authors declare no competing financial interest. # Deceased.

■

Table 6. Values of Pitzer Mixed Ion-Interaction Parameters (θK, NH4, ΨK,NH4Cl) in the Investigated Ternary Electrolyte Systems, Determined According to the Pitzer Graphical Method, for Various Molal Salt Ratios (r = m1/m2 = 9489.5, 3941.6, 489.7, 252.6) at 298.15 K KCl + NH4Cl

intercept

slope

r

θK,NH4

ΨK,NH4Cl

9489.5 3941.6 489.7 252.6 mean (∗)

−0.0032 −0.0030 −0.0042 −0.0058 -0.0031

0.0012 0.0014 0.0011 0.0017 0.0013

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REFERENCES

(1) Harned, H. S.; Owen, B. B. The Physical Chemistry of Electrolytic Solutions, 3rd ed.; Reinhold: New York, 1958. (2) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions, 5th ed.; Butterworths: London, 1970. (3) Pitzer, K. S., Ed. Activity Coefficients in Electrolyte Solutions, 2nd ed.; CRC Press: Boca Raton, FL, 1991. (4) Deyhimi, F.; Ebrahimi, A.; Roohi, H.; Koochaki, K. Determination of Activity Coefficients, Osmotic Coefficients, and Excess Gibbs Free Energies of HCl in N,N-Dimethylformamide−Water Mixed Solvent Systems by Potentiometric Measurements. J. Chem. Eng. Data 2004, 49, 1185−1188. (5) Deyhimi, F.; Salamat-Ahangari, R.; Ghalami-Choobar, B. Determination of Activity Coefficients of NH4Cl in Methanol−Water Mixed Solvents at 25 °C by Electromotive Force Measurements. Phys. Chem. Liq. 2003, 41, 605−611. (6) Deyhimi, F.; Salamat-Ahangari, R. Potentiometric Investigation of the Thermodynamic Properties of the Ternary Mixed (NH4Cl + CaCl2 + H2O) Electrolyte System. Fluid Phase Equilib. 2008, 264, 113−121. (7) Bates, R. G. Determination of pH: Theory and Practice; John Wiley & Sons: New York, 1964. (8) Zhang, L.; Lu, X.; Wang, Y.; Shi, J. Determination of Activity Coefficients Using a Flow EMF Method. 1. HCl in Methanol−Water Mixtures at 25, 35, and 45 °C. J. Solution Chem. 1993, 22, 137−150. (9) Pitzer, K. S. Thermodynamics of Electrolytes. I. Theoretical Basis and General Equations. J. Phys. Chem. 1973, 77, 268−277. (10) Pitzer, K. S.; Kim, J. J. Thermodynamics of Electrolytes. IV. Activity and Osmotic Coefficients for Mixed Electrolytes. J. Am. Chem. Soc. 1974, 96, 5701−5707. (11) Pitzer, K. S.; Mayorga, G. Thermodynamics of electrolytes. I I. Activity and Osmotic Coefficients for Strong Electrolytes with One or Both Ions Univalent. J. Phys. Chem. 1973, 77, 2300−2308. (12) Kim, H.-T.; Frederick, W., Jr. Evaluation of Pitzer Ion Interaction Parameters of Aqueous Electrolytes at 25 °C. 1. Single Salt Parameters. J. Chem. Eng. Data 1988, 33, 177−184. (13) Deyhimi, F.; Karimzadeh, Z.; Hamidi, A. On the Potentiometric Investigation of the Thermodynamic Properties of Mixed Electrolyte Systems: a New Mixed Solution Method for the Determination of Potentiometric Selectivity Coefficients of Ion-Selective Electrodes. Phys. Chem. Liq. 2008, 46, 90−97.

It can be seen from the reported data for NH4Cl + KCl system (Table 5), for the series of solutions with r = m1/m2 = 2464.3, that the corresponding values of the interaction parameters (θMN and ψMNCl) are reasonable. Therefore, the value of θNH4K and ψNH4KCl parameters for the series of solutions with r = m1/ m2 = 2464.3 was accepted. In the case of KCl + NH4Cl system as can be seen from the reported data (Table 6), for the series of solutions with r = m1/m2 = 489.7 and 252.6, the corresponding value of interaction parameters (θKNH4, ψKNH4Cl) is considerably indiscriminate from the resulting mean values calculated of the series of solutions with r = m1/m2 = 9489.5 and 3941.6. Therefore, the value of θKNH4, ψKNH4Cl parameters for the series of solutions with r = m1/m2 = 489.7 and 252.6 were ignored in the evaluation of the final mean values.

5. CONCLUSION In the last decades, the continuous development of different carrier-based solvent polymeric membrane electrodes, led to an attractive and rapid alternative method for the electrolytic systems being studied.3−6 However, a limiting factor on the potentiometric measurements13 is observed when the ISE membrane must be used for the investigation of mixed electrolyte systems. The interfering effect of the secondary ion 2432

dx.doi.org/10.1021/je500134p | J. Chem. Eng. Data 2014, 59, 2428−2432