Activity coefficients of NaCl in aqueous mixtures with ɛ-increasing co-solvent: N-methylformamide–water mixtures at 298.15 K

Fluid Phase Equilibria 310 (2011) 182–191

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Activity coefficients of NaCl in aqueous mixtures with ε-increasing co-solvent: N-methylformamide–water mixtures at 298.15 K Felipe Hernández-Luis ∗ , Raquel Rodríguez-Raposo, Graciliano Ruiz-Cabrera Departamento de Química Física, Universidad de La Laguna, Tenerife, Spain

a r t i c l e

i n f o

Article history: Received 21 June 2011 Received in revised form 17 August 2011 Accepted 18 August 2011 Available online 25 August 2011 Dedicated to Professor Dr. Cesar Rodríguez, Dr. Bernardo Domínguez, Dr. María Luisa Llorente, and Dr. Mercedes Lemus on the occasion of their retirement after many years at the University of La Laguna. Keywords: NaCl N-methylformamide emf Ion selective electrode (ISE) Activity coefficient

a b s t r a c t The electromotive force of the cell containing two ion-selective electrodes (ISE), Na–ISE|NaCl(m), Nmethylformamide (Y), H2 O(100-Y) Cl–ISE has been measured at 298.15 K as a function of the weight percentage Y of N-methylformamide in the mixed solvent. Y was varied between 0 and 100% in tenunit steps and the molality of the electrolyte (m) was between ca. 0.04 and saturation. The values of the apparent standard electromotive force, E0* (molal scale), were determined using routine methods of extrapolation together with extended Debye–Hückel (DH), Scatchard (S), Pitzer (P), and modified three-characteristic-parameter-correlation (TCPC) models. The results obtained produced good internal consistency, within the normal limits of experimental error encountered in these types of measurement. Once E0* was determined, the mean ionic activity coefficients for NaCl, the standard Gibbs energy of transfer from the water to the N-methylformamide–water mixture, the standard solubility product and the primary NaCl hydration number were calculated. The variation of these magnitudes with the composition of this aqueous mixture with ε-increasing co-solvent is discussed in comparison with those containing formamide (ε-increasing co-solvent) and N,N-dimethylformamide (ε-decreasing co-solvent) in terms of the ion-solvent and ion-ion interactions and their changes with the properties of the medium. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Aquo-organic electrolyte solutions are important for a wide number of applications, and therefore new data are constantly required. In previous works by our group, the behaviour of some alkali halides has been studied both in organic–water mixtures with ε-decreasing co-solvent (i.e. methanol–water, ethanol–water, PEG–water) [1–8], as in organic–water mixtures with ε-increasing co-solvent (i.e. ethylene carbonate–water, formamide–water) [9–13]. A simple methodology was developed and applied to obtain the maximum possible information about these systems. Thus, for example, the activity coefficients were correlated as a function of the properties of the solvent, as expressed by its dielectric constant. The standard Gibbs energy of transfer from the water to the organic–water mixture, the standard solubility product and the primary hydration number of the electrolyte were also calculated and their variation with the composition of the mixture comparatively discussed. In the literature there are numerous potentiometric studies of NaCl in aqueous mixtures with ε-decreasing co-solvent

∗ Corresponding author. Tel.: +34 922 318471; fax: +34 922 318514. E-mail address: [email protected] (F. Hernández-Luis). 0378-3812/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2011.08.018

[1,5,14–30] but very few in aqueous mixtures with ε-increasing co-solvent [11,12,30]. The objective of the present research is to carry out a study for NaCl in N-methylformamide–water mixtures and to compare the results with those obtained previously for NaCl in formamide–water mixtures (ε-increasing co-solvent) [11]. The values reported in the literature for the N,Ndimethylformamide–water mixtures (ε-decreasing co-solvent) [28,29] will be also included in this comparison. Aqueous mixtures containing amides (in particular, cyclic amides) constitute an important tool in the interpretation of behaviour of complex molecules with biological interest [31,32]. A lot of work has been published on amide–water system to learn the manner in which water exercises thermodynamic and kinetic control over the chemical activities of polypeptides. The abnormally high density of H-bonds in water (strongly self-associated) and the nature donor–acceptor (–CO–NH–peptide bond) gives these water-amide systems a great interest from a structural perspective. The additional presence of an electrolyte further complicates the picture (structure making or breaking effects). Table 1 summarizes some of the most important properties of the amides studied together with those of water [33–35]. Also, in Fig. 1 the dependency, on the medium composition, of the dielectric constant, density, and viscosity of these amide–water mixtures is shown.

F. Hernández-Luis et al. / Fluid Phase Equilibria 310 (2011) 182–191

183

Table 1 Some physical constants for water (W), formamide (F), N-methylformamide (NMF) and N,N-dimethylformamide (DMF) at 298.15 K.

Mw V (cm3 mol−1 ) bp (K) fp (K)  (g cm−3 )  (mPa s)  (N/m) εr nD  (D) ı (J1/2 cm−3/2 ) ˛ (10−30 m3 ) DN (kcal mol−1 ) AN (kcal mol−1 )

Water (W)

Formamide (F)

N-methylformamide (NMF)

N,N-dimethylformamide (DMF)

18.015 18.1 373.15 273.15 0.9971 0.890 0.0718 78.38 1.3325 1.82 48.1 1.46 18.0 54.8

45.041 39.9 483.65 275.70 1.1297 3.302 0.0582 109.57 1.4468 3.37 39.3 4.23 24.0 39.8

59.068 59.1 453.15 269.35 0.9988 1.650 0.0395 182.40 1.4300 3.86 20.3 6.05 27.0 32.1

73.094 77.4 426.15 212.75 0.9440 0.802 0.0364 36.71 1.4282 3.86 24.8 7.90 26.6 16.0

By increasing the amount of co-solvent, the properties of the organic–water mixtures change. Thus, in contrast to N,N-dimethylformamide–water mixtures, both Nmethylformamide–water and formamide–water mixtures exhibit an increase in dielectric constant. In the formamide–water mixture the dielectric constant shows a maximum at about 80–90% while the N-methylformamide–water shows a monotonous increase of εr which overcome the corresponding values of the formamide–water mixture from 70 wt.%. On the other hand, a small decrease in density is observed both in N-methylformamide–water and N,N-dimethylformamide–water mixtures and a great increase (nearly linear) in the mixture containing formamide. Finally, viscosity shows a continuous increase for formamide–water in contrast to what occurs in the other two mixtures; viscosity maxima occur near 60 wt.% for N,N-dimethylformamide–water and 70 wt.% for N-methylformamide–water. From the latter two properties (density and viscosity), García et al. [31], calculated excess volumes, mixing viscosities and excess Gibbs energies of activation of viscous flow of the some amide–water mixtures. The values of these functions compared with those of the amide–alcohol mixtures, reveal an important hydration effect with strong amide–water interactions and formation of aggregates, the nature of which depends on the extent of substitution of the amides. Only the behaviour of the formamide–water mixture can be successfully predicted by a simple model. Also, Papamatthaiakis et al. [32] measured both density and ultrasonic velocity for pure amides and their binary aqueous mixtures. From these data isentropic compressibility, apparent molar compressibility, intermolecular free length and relative 200 175 NMF

100

F

75

1.20

3.50

1.15 1.10 1.05

DMF

25 0

20

40

60

80 100

NMF

1.00

wt.% co-solvent

DMF

DMF

2.50 NMF

2.00 1.50 1.00

F

0.50

0.90 0.85

3.00

F

0.95

50

0

4.00

-3

εr

125

1.25

ρ/ g cm

150

association, as well as the corresponding excess quantities were calculated. The systematic study of these parameters reveals a large deviation from ideal behaviour as a result of the strong amide–water interaction. It is well known [33–35] that, like formamide, Nmethylformamide is a highly ionized polar liquid with a dipole moment higher than water and a very large dielectric constant (it has the highest dielectric constant at room temperature of any known liquid). It is a liquid colourless, nearly odourless and completely miscible with water throughout the complete composition range, which forms a hydrogen-bonded network. N-methylformamide is closely related to other amides, notably formamide and N,N-dimethylformamide. However, industrial use is somewhat minor than the latter two. It is mainly used as a reagent in various organic syntheses and in the production of some pharmaceutical compounds. Certain antitumor activities of N-methylformamide have been estimated. With regard to the used electrolyte, it is well known that NaCl is present in many natural systems, from seawater to biological fluids such as urine. It is very soluble in water (6.146 mol kg−1 at 298.15 K) and has a smaller capacity for the association and formation of ion pairs. The studies presented here were carried out using potentiometric techniques which have been greatly improved in recent decades mainly due to the development and improvement of the ion-selective electrodes (ISE). These electrodes are not only valuable for analytical use, but also may be employed in determining thermodynamic and transport properties. The electrodes used in the present study are those which have recently been developed, in which a glass membrane is used for the Na+ and a

η / mPa s

Molecular weight Molar volume Boiling point Melting point Density Viscosity Surface tension Dielectric constant Refractive index Dipole moment Solubility parameter Polarizability Donor number Acceptor number

0

20

40

60

80 100

wt.% co-solvent

0.00

0

20

40

60

80 100

wt.% co-solvent

Fig. 1. Composition dependences of relative permittivity (εr ), density () and viscosity () in formamide (F)–water (), N-methylformamide (NMF)–water () and N,Ndimethylformamide (DMF)–water () mixtures at 298.15 K.

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solid–state membrane for the Cl− ion. These electrodes have been shown to function accurately both in water and in organic–water solutions. The measurements were carried out at 298.15 K since very few data of the dielectric constant of these mixed solvents at other temperatures are available.

NaCl, Merck pro analysis (w = 0.99), was vacuum-dried at 373 K for 72 h and then stored in a desiccators over silica gel. N-methylformamide, Sigma puris (w = 0.995), was used without prior treatment. Correction for the very small water content of the original product was considered unnecessary. All solutions were prepared by direct weighing. For each set of experiments (corresponding to a wt.% of N-methylformamide) working solutions were obtained by successively adding weighed amounts of solid NaCl to the corresponding solution prepared from Nmethylformamide and double-distilled water ( < 10–6 S cm−1 ). The solutions were continuously stirred by using a magnetic stirrer. The relative uncertainty both in the electrolyte molality and wt.% of N-methylformamide is estimated to be about 0.1%. The last addition of NaCl in the different studied Nmethylformamide–water mixtures corresponded to saturated solutions, since some salt crystals remained undissolved. The procedure to estimate the saturation molality of the NaCl, in each of the mixtures, was as follows: (a) the solution (with excess of NaCl) was decanted for 10 h, maintaining a constant temperature of 298.15 K; (b) approximately 2 g of sample was taken from the supernatant solution; (c) the samples were dried by solvent evaporation until a constant weight was reached. On the basis of the last weight and that of the initial sample, the saturation molality was then calculated. In order to obtain a good estimation, the process was quadruplicated and the average value subsequently calculated. The relative uncertainty of the saturation molality is estimated to be about 0.2%, approximately. The electrodes, cells, apparatus, temperature control system, as well as the measurement procedure employed in the present study have been described previously [7–13]. The temperature relative uncertainty was estimated to be 0.02%. Depending on the mass fraction of N-methylformamide in the mixture, the electromotive force uncertainty can be estimated between 0.1 and 0.3 mV, approximately.

Table 2 shows E values for different mixtures of Nmethylformamide–water as a function of NaCl molality. As can be observed in this table, two studies were carried out in pure water (0 wt.% of N-methylformamide), one when the experiments began and another after 15 days, when all the studies were completed. Since the activity coefficients of NaCl in pure water are well known [39], the values of E that appear in Table 2 for 0 wt.% of N-methylformamide allow a calibration of the electrode system to be carried out, using Eq. (2). The value obtained for Nernst slope, k, when applying a least-squares regression analysis to the previous plots, were 58.18 ± 0.10 mV and 58.31 ± 0.06, respectively, with standard deviation of 0.31 mV and 0.30 mV, and correlation coefficients greater than 0.99999 in both cases. The average value of k (58.25 ± 0.08 mV) differs only by about 1.5% from the theoretical value (59.16 mV) and will be taken as the value of k for the successive calculus achieved in this work. This is above acceptable levels for a system containing two ion selective electrodes. In this calculation it has been assumed that kNa ∼ = kCl ∼ =k∼ = (kNa + kCl )/2. Another remarkable point is the arithmetic media of the intercepts (−220.69 ± 0.09 mV). The small standard deviation indicates that the potential of asymmetry of the electrodes has scarcely varied in the 15 days that elapsed between both calibrations. This allows us to work with the cell Na–ISE|NaCl (m), N-methylformamide (Y), H2 O(100 − Y)|Cl–ISE directly, applying the Eq. (2), and without using a reference cell to correct the daily changes of the asymmetry potential, as occurred in some previous works by our group [1,40,41]. Once the electrodes have been calibrated and found to be operating correctly, the most important and decisive goal in this type of study is to determine the apparent standard potential in the cell, E0* , as accurately as possible for each mixture studied, since this affects the precision of the activity coefficients and the other thermodynamic functions subsequently calculated. The determination of E0* was carried out following a method similar to that proposed by Hitchcock [42] and using the classical extended equation of Debye–Hückel [43,44], Scatchard [45,46] and Pitzer [47,48] to represent the dependency of log  on concentration. For the first time, we also use for this purpose the most recent modified three-characteristic-parameter-correlation (TCPC) model [49–51]. For 1:1 electrolytes, these equations may be written as:

3. Results

- Extended Debye–Hückel equation [43,44]

2. Experimental

√ A m √ + cm + dm2 − log(1 + 0.002 m M) + Ext 1 + Ba m (3)

Mean ionic activity coefficient values for NaCl in Nmethylformamide–water mixtures were determined from the emf measurements of the following cells without transference:

log  = −

Na–ISE|NaCl (m), NMF (Y ),

being a is the ion size parameter, c and d are the ion-interaction parameters, M is the average molecular mass of mixed solvent and Ext is the contribution of the extended terms. A and B are the Debye–Hückel constants given by:

H2 O(100 − Y )|Cl–ISE

(1)

In these cells, m is the molality of NaCl (moles NaCl/kg mixed-solvent) in the working solution and Y the wt.% of Nmethylformamide in the mixture. Applying the Nernst–Nikolsky equation, the following expression can be deduced: E = E 0∗ − 2k log m

(2)

where E is the emf of the cell, k = (ln 10)RT/F, is the Nernst theoretical slope and m and  are the molality and stoichiometric mean ionic activity coefficient of NaCl. E0* is the apparent standard potential (molal scale) of the cell and contains the potential of asymmetry of both selective electrodes [36–38].

A=

B=

1.8247 × 106 1/2 (εr T )3/2 50.29011/2 (εr T )1/2

kg1/2 mol−1/2

kg1/2 mol−1/2 Å

−1

(3a)

(3b)

where , εr and T stand for the density, relative permittivity (static dielectric constant) of the solvent and the temperature, respectively. An additional parameter, d, has been including in the Eq. (3) to cover the entire concentration range studied [43,44].

F. Hernández-Luis et al. / Fluid Phase Equilibria 310 (2011) 182–191

185

Table 2 Experimental electromotive force, E, and mean ionic activity coefficients, , at different NaCl molalities and wt.% of N-methylformamide in N-methylformamide–water mixtures at 298.15 K. 0a wt.%

10 wt.%

m

−E



0.1857 0.3711 0.6871 1.1390 1.7705 2.3945 3.5872 4.6544 5.6926 6.0855

120.10 151.96 180.91 205.82 228.66 245.64 271.05 289.38 305.24 311.10

0.733 0.689 0.659 0.651 0.657 0.680 0.750 0.830 0.929 0.976

m

−E



0.0457 0.1269 0.2078 0.2984 0.4484 0.7108 1.0567 1.2301 1.4596 2.1025 2.4386 2.8510 2.9312 2.9920

96.71 145.02 168.78 186.31 206.47 229.85 250.77 259.26 269.08 290.86 300.12 308.76 310.44 311.82

0.852 0.797 0.779 0.767 0.760 0.761 0.774 0.787 0.805 0.860 0.890 0.903 0.908 0.914

± ± ± ± ± ± ± ± ± ±

0.008 0.007 0.007 0.007 0.007 0.007 0.008 0.009 0.010 0.010

40 wt.%

20 wt.%

m

−E



0.0851 0.2161 0.3955 0.6328 0.8478 1.3070 1.7691 2.3475 2.8432 3.2829 3.7360 4.2773 5.3544

93.27 134.81 162.90 185.43 200.26 222.65 239.24 255.96 268.19 277.90 286.84 296.33 312.41

0.779 0.697 0.664 0.648 0.648 0.654 0.671 0.704 0.740 0.777 0.814 0.858 0.942

m

−E



0.0475 0.1355 0.2724 0.4157 0.6342 1.2439 1.7924 1.9279 2.0823 2.3507 2.3684

111.21 161.53 195.76 216.86 238.52 275.06 296.65 300.94 305.29 311.47 312.31

0.863 0.817 0.799 0.795 0.799 0.839 0.892 0.903 0.911 0.912 0.920

± ± ± ± ± ± ± ± ± ± ± ± ±

0.006 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.006 0.006 0.006 0.007 0.007

50 wt.%

± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003

80 wt.% −E



0.0424 0.1102 0.1345 0.1590 0.2075 0.2578 0.3500 0.4204 0.5755 0.7126 0.8716 1.0113

147.83 195.45 205.51 214.16 227.77 239.09 255.41 265.14 282.55 293.85 304.24 311.44

0.915 0.901 0.901 0.904 0.907 0.913 0.928 0.937 0.965 0.974 0.979 0.972

± ± ± ± ± ± ± ± ± ± ± ±

0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001

−E



0.0500 0.1514 0.4274 0.6631 1.1514 1.6784 2.0111 3.0872 4.0021 4.2669 4.4204

80.05 130.19 178.86 200.40 228.45 249.06 259.80 287.00 303.96 307.94 310.45

0.823 0.733 0.679 0.670 0.672 0.693 0.715 0.797 0.860 0.872 0.885

m

−E



0.0976 0.1703 0.2943 0.4199 0.5249 0.6583 0.8562 1.0853 1.2289 1.4739 1.7480 1.8310

161.46 188.72 215.93 234.00 245.54 257.48 271.80 285.21 292.60 302.56 311.34 314.17

0.841 0.826 0.818 0.820 0.824 0.832 0.849 0.873 0.892 0.905 0.908 0.917

± ± ± ± ± ± ± ± ± ± ±

0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.004 0.004 0.004

60 wt.%

± ± ± ± ± ± ± ± ± ± ±

0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002

90 wt.%

m

30 wt.%

m

−E



0.0450 0.0511 0.0635 0.1063 0.1266 0.1577 0.2300 0.2424 0.4060 0.6161

164.89 171.24 182.24 208.54 217.68 229.08 249.10 251.75 279.49 299.78

0.942 0.941 0.941 0.945 0.951 0.956 0.974 0.974 1.006 0.990

± ± ± ± ± ± ± ± ± ±

0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003

−E



0.0402 0.1463 0.2794 0.4303 0.6759 1.0459 1.4139 1.8420 2.2957 2.9678 3.2434 3.6739

79.34 139.15 169.77 190.72 213.02 235.70 252.19 267.56 281.28 297.52 302.94 310.85

0.847 0.759 0.728 0.715 0.707 0.716 0.733 0.763 0.803 0.856 0.872 0.900

m

−E



0.0553 0.1226 0.1650 0.2277 0.3176 0.5000 0.7285 0.9845 1.1998 1.3390

147.24 186.50 201.32 217.63 234.63 258.52 278.82 295.75 306.54 312.66

0.898 0.880 0.876 0.876 0.879 0.896 0.918 0.949 0.964 0.975

m

−E



0.0496 0.1979 0.3096 0.4571 0.5916 0.8318 1.2118 1.8703 2.6244 3.8110 5.1419 5.4427 5.8911 6.0316 6.1000

58.63 123.04 143.83 162.07 174.26 190.65 209.33 232.18 251.64 275.87 297.76 302.31 308.93 310.90 312.05

0.819 0.733 0.707 0.686 0.675 0.663 0.659 0.670 0.702 0.780 0.891 0.921 0.970 0.985 0.997

± ± ± ± ± ± ± ± ± ± ± ±

0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.003 0.003 0.003

± ± ± ± ± ± ± ± ± ±

0.006 0.006 0.006 0.006 0.006 0.006 0.007 0.007 0.007 0.007

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.005 0.005 0.006 0.006 0.006 0.006 0.006

70 wt.%

± ± ± ± ± ± ± ± ± ± ± ±

0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001

0b wt.%

100 wt.%

m

m

m

−E



0.0396 0.0520 0.0642 0.1020 0.1375 0.1655 0.1934

182.77 196.49 207.02 230.54 245.63 254.69 262.22

0.986 0.985 0.983 0.984 0.984 0.978 0.971

± ± ± ± ± ± ±

0.011 0.011 0.011 0.011 0.011 0.011 0.010

Units: m in mol kg−1 ; E in mV. a First calibration. b Second calibration. Table 3 Values of average molecular mass (M), relative permittivity (εr ), density (), Debye–Hückel (A, B), Pitzer (A ) and Scatchard (S) constants, and Bjerrum parameters (q) as a function of the weight percentage of N-methyformamide in N-methylformamide–water mixtures at 298.15 K. wt.%

M (g mol−1 )

εr

0 10 20 30 40 50 60 70 80 90 100

18.015 19.361 20.924 22.761 24.952 27.610 30.901 35.084 40.576 48.107 59.070

78.38 80.61 83.24 86.37 90.18 94.95 101.17 109.71 122.34 143.03 182.40

a b

Refs. [31,32]. Refs. [34,35].

a

b (g cm−3 )

A (kg1/2 mol−1/2 )

B (kg1/2 mol−1/2 A˚ −1 )

A (kg1/2 mol−1/2 )

S (kg1/2 mol−1/2 )

q (Å)

0.9971 1.0114 1.0255 1.0392 1.0527 1.0659 1.0788 1.0915 1.1041 1.1168 1.1298

0.5100 0.4925 0.4726 0.4501 0.4246 0.3955 0.3617 0.3222 0.2752 0.2190 0.1529

0.3285 0.3262 0.3233 0.3195 0.3147 0.3086 0.3008 0.2905 0.2767 0.2574 0.2292

0.3915 0.3781 0.3628 0.3455 0.3260 0.3036 0.2777 0.2473 0.2113 0.1681 0.1174

−1.1744 −1.1342 −1.0884 −1.0366 −0.9779 −0.9107 −0.8330 −0.7420 −0.6338 −0.5042 −0.3522

3.57 3.48 3.37 3.24 3.11 2.95 2.77 2.55 2.29 1.96 1.54

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F. Hernández-Luis et al. / Fluid Phase Equilibria 310 (2011) 182–191

- Scatchard equation [45,46] ln  =

1 2



2Sm1/2 1 + am1/2

+ 2a(1) m +



3 (2) 2 4 (3) 3 5 (4) 4 a m + a m + a m 2 3 4 (4)

where S = −3A␾ and a, a(1) , a(2) , a(3) and a(4) are the characteristic interaction parameters of the model. - Pitzer equation [47,48] ln  = f  + B m + C  m2 where f





= −A

 √ √ m 2 √ + ln(1 + b m) b 1+b m 

2ˇ1 B = 2ˇ + 2 1− ˛ m 

(5)



0

√ ˛2 m 1+˛ m− 2

(5a)



√



exp(−˛ m)

(5b)

In these equations ˛ and b are assumed to be constant with values of 2.0 and 1.2 kg1/2 mol−1/2 , respectively, both in water and in N-methylformamide–water mixtures [47,48,52–54]; ˇ0 , ˇ1 and C are solute-specific interaction parameters and A is the Debye–Hückel constant for the osmotic coefficients defined by: A =

1.4006 × 106 1/2 (εr T )3/2

kg1/2 mol−1/2

(5c)

all symbols having their usual meaning. For those Nmethylformamide–water mixtures where the solubility of the NaCl did not reach 2.0 mol kg−1 , Eq. (5) with C = 0, was also tried as suggested by Pitzer [47,48]. - Modified three-characteristic-parameter-correlation (TCPC) [49–51]

 ln  = −A

 √ √ m S m2n 2 √ + ln(1 + b m) + T 2 b 1+b m

(6)

b is treated as an adjustable parameter to represent the closest distance between the cation and anion; S is an electrolyte-specific parameter that describes the incorporate solvation effects of the cation and anion; n, is the parameter which is related to the distance between the ion and solvent molecule. The other symbols have their usual meaning. The values of density and dielectric constant for the Nmethylformamide–water mixtures were taken from the literature [31,32,34,35] and they are shown in Table 3 together with those for M, A, B, A , S and q (Bjerrum’s parameter) [43,44]. By combining Eqs. (2) and (3), (2) and (4), (2) and (5) or (2) and (6), the values of E0* according to the different models used, can be optimized, as well as the characteristic interaction parameters of each model. In Tables 4 and 5, these values are presented as well as the corresponding standard deviation of the fit. The values of the adjustable parameters of the Scatchard equation are not included, as they do not provide any additional significant information. 4. Discussion As can be observed from Table 4, the values of E0* obtained with DH, S and P models are in very good agreement. The standard deviations of the fits are comparable, although each of the models has a different number of adjustable parameters. Optimization using the Debye–Hückel extended equation with the inclusion of the parameter d allows the fit to be made in the entire range of concentration with a very good standard deviation. Whether the extended terms are considered or not does not significantly alter the results. Both the a and c parameters are within

the expected order of magnitude, with the exception perhaps of 90 and 100 wt.% of N-methylformamide, where the value of a is smaller than usual. Up to 70–80 wt.% N-methylformamide, the parameter ˚ a (related to the ionic size) remains almost constant at 3.4 ± 1.0 A, with a similar value than the sum of the crystallographic radii of Na+ and Cl− . These a values are also slightly higher than the q parameter of Bjerrum’s (last column of Table 3), suggesting that there is no considerable ion association. Optimization using the Pitzer equation, allows reasonable values for ˇ0 (which can be identified with interactions of like and unlike charged ions) and ˇ1 (which can be identified with the interactions between unlike-charged ions) to be obtained. For wt.% N-methylformamide values greater than 60, C␥ (which represents triple ionic interactions) it can be considered zero, without losing precision, because the molality of NaCl is less than 2 mol kg−1 [47,48]. The optimization was also performed using the Scatchard equation. A very good standard deviation was obtained, although as we said above its characteristic parameters have no physical meaning and therefore they are not shown. The average values for E0* which appear in the last column of Table 4 were calculated considering the three models (DH, S and P). These average values were used to calculate the mean ionic coefficients  which are listed in Table 2 for each molality of NaCl and each percentage weight of N-methylformamide. The standard deviations of our activity coefficients compared to those reported in the literature were calculated to be less than ±0.007 in pure water, showing good agreement between both sets of data, particularly if the wide range of concentrations studied is taken into account. E0* values obtained in the TCPC model optimization, which are shown in Table 5, were not taken into account in average aforementioned. These values are systematically lower than those obtained with the other three methods. Also, the standard deviation of the fit are always higher than those obtained with the DH, S or P methods. This may be due to the peculiar mathematical form of Eq. (6), which introduces a fit parameter (n) as an exponent. It is possible that many more experimental data are necessary to obtain a good result. Since the TCPC model was initially applied by its proponents [49–51] on the activity coefficients previously calculated, we have done the same. Thus, Table 5 summarizes, in parentheses, the results obtained when the TCPC method is directly applied to the calculated activity coefficients which are shown in Table 2. The fitting parameters thus obtained are slightly different from those previously calculated and deviations in  are almost acceptable. Fig. 2 shows log  vs. m1/2 for several of the percentages in weight of N-methylformamide studied as well as for pure water. The broken line corresponds to NaCl activity coefficients obtained by way of the Debye–Hückel limiting law in pure water. Likewise, for comparison purposes, in Fig. 3 is shown the log  vs. m1/2 variation for three wt.% of co-solvent, for the three water–amide mixtures compared. The following are noteworthy points from Figs. 2 and 3: (a) All the curves show a typical profile of the variation of log  with concentration which, as is well known, is governed by two types of interactions [43,44,55], including those of ion-ion (“ion-pair”) and ion-solvent (“solvation”). (b) Regarding those obtained in pure water, for each given concentration, log  clearly increases with the wt.% of co-solvent (increase in dielectric constant) in mixtures with εincreasing co-solvent (formamide and N-methylanformamide) and decrease with the wt.% of co-solvent (decrease in dielectric constant) in mixtures with ε-decreasing co-solvent (N,Ndimethylformamide). Noting, as shown by various authors [43,44,55–57], that when ion-pair association decreases, ionic solvation increases and vice versa, it is concluded that in

F. Hernández-Luis et al. / Fluid Phase Equilibria 310 (2011) 182–191

187

30 100%

0.0

80% 40%

25

20%

-0.1

20 -1

0%

ΔG0t / kJ mol

log γ

60%

-0.2

NMF

10

LL,0% 0.0

DMF

15

0.5

1.0 1/2

m

1.5 1/2

/ mol kg

2.0

F

2.5

5

-1/2

Fig. 2. Plot of log  vs. m1/2 for NaCl in some of the N-methylformamide–water mixtures studied at 298.15 K.

0 0



-0.10

DMF

NMF

Water

log γ

-0.10

log γ

log γ

-0.10

-0.20

asym

− Ew



)

(7)

F

F -0.05

NMF

asym

60% co-solvent

0.00

-0.05

-0.15

100

where E0 , E0* , and Easym stand for the standard potential difference, the apparent standard potential difference and the total asymmetry asym asym potential (εNa + εCl ), respectively. Subscript “s” refers to mixed solvent and “w” to water. All of the other symbols have their usual meaning. As mentioned previously, in our case, Easym is a constant value, small and is independent of the composition of the solvent, asym asym which allows us to affirm, that (Es − Ew ) is negligible com0∗ ), and thus Eq. (7) may be used without any pared to (Es0∗ − Ew problem, although the studied cell is not exactly thermodynamic

-0.05

Water

80

0 0∗ ) = −zF (Es0∗ − Ew ) − (Es Gt0 = −zF(Es0 − Ew

40% co-solvent

0.00

F

60

ily calculated from the values of E0* according to the expression [11,38]:

The standard Gibbs energy of transfer, (“medium effect”) [58–60], is perhaps one of the most useful parameters available for understanding the different behaviours of a solute in both pure and mixed solvent. Gt0 is defined as the difference between the standard Gibbs energy per mole of electrolyte in a pure solvent, usually water, and that in another pure or mixed solvent, is a measure of the change in the total energy of the solute when it is transferred from one solvent to another at infinite dilution and can be eas-

20% co-solvent

40

Fig. 4. Plot of the standard Gibbs energy of transfer vs. wt.% of co-solvent for NaCl at 298.15 K. () formamide–water; () N-methylformamide–water; ()N,Ndimethylformamide–water.

Gt0

0.00

20

wt.% co-solvent

the system containing formamide or N-methylformamide as co-solvent the ion-solvent interactions (solvation) are much more important than the ion-ion interactions (association), in contrast with the N,N-dimethylformamide–water mixture, in which association may be favoured with respect to solvation. (c) Given that all measurements were carried approximately to saturation molality, it is clearly observed that the solubility of NaCl decreases in all the cases with the increase of the wt.% of cosolvent, both for ε-increasing or ε-decreasing co-solvent. No direct relationship appears to exist therefore between solubility and ionic association.

NMF Water

-0.15

-0.15

-0.20

-0.20

DMF -0.25

-0.25 0

1 1/2

m

2 1/2

-1/2

/ mol kg

-0.25 0

1 1/2

m

2 1/2

/ mol kg

-1/2

DMF 0

1 1/2

m

2 1/2

/ mol kg

-1/2

Fig. 3. Plot of log  vs. m1/2 for NaCl in various amide–water mixtures with 20, 40 and 60 wt.% of amide at 298.15 K (F: formamide; NMF: N-methylformamide; DMF: N,N-dimethylformamide).

0.07 −220.35 ± 0.12

−220.73 ± 0.19

0.11 −346.16 ± 4.24

−346.83 ± 0.27

0.10 −324.61 ± 0.15

−324.80 ± 0.10

0.10 −312.28 ± 0.16

−312.29 ± 0.02

0.08 −299.32 ± 0.18

−299.18 ± 0.18

± ± ± ± ± ± ± −220.99 −230.56 −241.44 −250.36 −260.92 −272.90 −287.96 0.11 0.28 0.36 0.23 0.18 0.17 0.23

0.0864

0.0473

0.0245

0.0119

0.0014 0.0025 0.0025 0.0042 0.0089 0.0148

0.0391 0.0475 0.0341 0.0442 0.0665 0.0876 0.0658 0.0424 0.0361 0.0609 0.0337 0.0768 0.1115 0.1126 0.0500 0.13 0.0006 ± 0.0001 0.0562 ± 0.0014 3.92 ± 0.09 −220.95 ± 0.15

F



(8)

0 Ksp,s

0 0 = Ec0 = Ecs − Ecw = nhydr

 RT F

ln w

(9)

where 0 + 2k log ds Ec0 = Em

(10)

and w =

Fixed values.

0

( Gt0 )c

a

0.44 −0.6858 ± 0.1600 0.36 ± 0.14 −347.30 ± 2.34 100

0.5187 ± 0.2026

0.07 −0.4009 ± 0.0159 0.73 ± 0.11 −324.86 ± 0.06 90

0.5532 ± 0.0256

0.10 −0.1447 ± 0.0116 2.19 ± 0.67 −312.32 ± 0.19 80

0.3395 ± 0.0311

0.08 −0.0342 ± 0.0042 5.40 ± 0.56 −299.35 ± 0.18 70

0.1645 ± 0.0109

(mV)

0.53 0.52 0.59 0.37 0.38 0.45 0.48 ± ± ± ± ± ± ±

E0* (S) (mV)

−220.89 −230.88 −241.48 −250.40 −260.74 −272.75 −287.94

0.39 0.34 0.35 0.23 0.25 0.29 0.23 0.53 0.08 0.23 0.10 0.46 0.07 0.46 0.07 0.15 0.34

(mV) C␥ (kg2 mol−2 )

0.0019a −0.0113 ± −0.0175 ± −0.0225 ± −0.0315 ± −0.0504 ± −0.0925 ± – −0.0797 ± – −0.3366 ± – −0.9529 ± – −0.4303 ± – 0.0019a 0.2664a 0.0045 −0.0097 ± 0.0074 −0.0477 ± 0.0061 0.0045 ± 0.0090 0.0902 ± 0.0158 0.0932 ± 0.0256 −0.0116 ± 0.0070 0.5054 ± 0.0140 0.2090 ± 0.0054 0.4777 ± 0.0234 −0.0815 ± 0.0159 0.7175 ± 0.0354 −0.3256 ± 0.00261 1.1823 ± 0.0559 0.9847 ± 0.0143 1.5325 ± 0.2664a 0.0765a 0.1259 ± 0.1388 ± 0.1481 ± 0.1567 ± 0.1781 ± 0.2234 ± 0.0838 ± 0.1844 ± 0.0916 ± 0.3594 ± 0.0412 ± 0.5844 ± 0.1244 ± −0.2355 ± −0.5117 ± 0.0765a

ˇ1 (kg mol−1 )

= RT ln

0 Ksp,w

0 0 and Ksp,s represent the standard solubility product of where Ksp,w NaCl in water (38.051 mol2 kg−2 [39]) and in organic–water mix0 with ture, respectively. In Fig. 5a a significant decrease of ln Ksp,s co-solvent wt.% is clearly observed, being the order of the decrease N,N-dimethylformamide > N-methylformamide > formamide (further decrease as the dielectric constant decreases). This agrees well with the order of the NaCl solubility shown in the plots of Fig. 5b where, in addition to the values estimated in this work for the saturation molality of NaCl in N-methylformamide–water and N,N-methylformamide–water mixtures, are shown those previously estimated for formamide–water [11]. A plot of log(mss /mw vs. (1/εsr − 1/εw for various s ) r ), organic–water mixtures, is shown in Fig. 6. Approximately linear behaviour, similar to that obtained by Izmailov [61], is observed. Two aspects of this plot can be pointed out: On one hand, the positive value of the slope for the formamide–water and N-methylformamide–water mixtures (ε-increasing co-solvent) in contrast to what occurs with the other mixtures (ε-decreasing co-solvent). On the other hand, the similarity between the slopes of the methanol and ethanol (or formamide and N-methylformamide) containing mixtures, possibly due to the similar chemical nature of the co-solvents. Although ethylene-glycol (ethane-1,2-diol) and glycerol (propane-1,2,3-triol) are also alcohols, their slopes are quite different due to the presence of two and three OH groups, respectively. The same applies to N,N-dimethylformamide with regard to formamide and N-methylformamide. Finally, in order to complete the thermodynamic description of NaCl dissolved in N-methylformamide–water, an interesting correlation deduced by Feakins and French [62] and widely discussed by Mussini et al. [16,24,63] will be used. For a 1:1 electrolyte, the said correlation connects the primary medium effect on the molar scale ( Gt0 )c with the volume fraction of the water in the solvent mixture, w , according to:

0.94 0.48 0.40 0.26 0.29 0.38 0.47 0.69 0.15 0.27 0.17 0.51 0.13 0.47 0.15 0.17 0.41

ˇ0 (kg mol−1 )



Gt0

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 3.53 3.38 2.26 2.59 3.27 3.47 2.68 0.20 0.43 0.42 0.28 0.34 0.43 0.54 ± ± ± ± ± ± ±

a (Å)

due to the presence of the aforementioned potential asymmetry (any extra-thermodynamic assumption has been explicitly made). Fig. 4 shows a plot of the standard Gibbs energy of transfer, Gt0 , for NaCl, against wt.% co-solvent in the formamide–water, N-methylformamide–water and N,N-dimethylformamide–water mixtures. In all cases it is verified that Gt0 > 0, which indicates that the transference process is not spontaneous. The positive values of Gt0 imply also that the process of dissolution of the electrolyte is not favoured in any of the cases by the presence of co-solvent [60] as will be explained below. According to Kalidas et al. [60], the standard Gibbs energy of transfer to the whole salt, Gt0 , is related to the standard solubility 0 , of the electrolyte in the two solvents by: product, Ksp

−220.50 −230.11 −241.20 −250.19 −260.93 −272.92 −287.89 −285.60 −299.40 −298.63 −312.27 −310.51 −324.94 −322.81 −347.26 −346.62 −220.90

E0* (P) (mV)

(mV)

0.10 0.31 0.33 0.23 0.26 0.30 0.23 0.0001 0.0009 0.0013 0.0012 0.0019 0.0039 0.0073 ± ± ± ± ± ± ±

d (kg2 mol−2 )

0.0008 −0.0040 −0.0068 −0.0085 −0.0120 −0.0200 −0.0388 0.0016 0.0063 0.0100 0.0076 0.0107 0.0176 0.0294 ± ± ± ± ± ± ±

c (kg mol−1 )

0.09 0.17 0.22 0.19 0.35 0.58 0.75 −221.56 −230.67 −241.64 −250.49 −261.10 −273.02 −288.05 0 10 20 30 40 50 60

± ± ± ± ± ± ± E0* (DH) (mV) Y (wt.%)

0.0593 0.1086 0.1235 0.1281 0.1309 0.1513 0.2031

E0*  (mV)

0.31 0.23 0.13 0.09 0.10 0.08 0.05

F. Hernández-Luis et al. / Fluid Phase Equilibria 310 (2011) 182–191 Table 4 Summary of both standard emf for the cell Na–ISE|NaCl(m), N-methylformamide (Y), H2 O(100 − Y)|Cl–ISE and the NaCl ionic parameter values obtained for the Debye–Hückel (DH), Pitzer (P) and Scatchard (S) equations, in the different N-methylformamide–water mixtures at 298.15 K.

188

ww /dw ww /dw + wNMF /dNMF

(11)

0 is the standard electromotive force in molal scale (up to Em now we have denoted it E0 for simplicity), nhydr indicates the primary hydration number of the electrolyte (number of firmly bound moles of water per mol of electrolyte) and all the other symbols have their usual meaning. Eq. (11) is only fulfilled in mixtures rich in water and, in principle, is thermodynamically exact

F. Hernández-Luis et al. / Fluid Phase Equilibria 310 (2011) 182–191

a

b

5 4

5

ms / mol kg-1

ln K0sp,s

7 6

3 F

2 NMF

1 0

4 3

F

2

DMF

-1 -2

189

NMF

1

0

20

40

60

80

100

0

DMF

0

20

% co-solvent

40

60

80

100

% co-solvent

0 Fig. 5. Influence of the co-solvent content on the variation of the solubility of the NaCl at 298.15 K. (a) ln Ksp,s vs. wt.% co-solvent; (b) ms vs. wt.% co-solvent; () formamide–water; () N-methylformamide–water; () N,N-dimethylformamide–water.

Table 5 Summary of both standard emf for the cell Na–ISE|NaCl(m), N-methylformamide (Y), H2 O(100 − Y)|Cl–ISE and characteristic parameters obtained for NaCl with the modified three-characteristic-parameter-correlation model (TCPC), in the different N-methylformamide–water mixtures at 298.15 K. Y (wt.%) 0 10 20 30 40 50 60 70 80 90 100 0

E0* (TCPC) (mV) −220.64 ± −228.42 ± −239.76 ± −248.87 ± −259.33 ± −271.23 ± −284.82 ± −297.91 ± −309.01 ± – – −220.30 ±

0.29 4.73 0.38 3.59 4.98 8.56 0.38 10.03 47.93

0.11

b (mol−1/2 kg1/2 ) 2.268 (2.115) 1.020 (1.064) 1.118 (1.154) 1.257 (1.276) 1.597 (1.657) 1.871 (1.864) 2.644 (2.075) 2.418 (2.489) 4.629 (2.939) –((7.170) –((10.274) 2.502 (2.275)

S (K mol−2n kg2n )

n

62.549 (68.440) 190.305 (160.101) 174.843 (149.815) 176.181 (154.707) 173.941 (147.320) 169.606 (146.396) 153.714 (145.971) 173.192 (154.412) 147.931 (146.346) –((70.549) –((25.604) 57.385 (65.660)

(mV) 0.555 (0.539) 0.384 (0.420) 0.389 (0.424) 0.387 (0.421) 0.359 (0.404) 0.349 (0.402) 0.331 (0.396) 0.336 (0.396) 0.262 (0.390) –((0.323) –((0.126) 0.569 (0.545)

0.10 0.64 0.73 0.59 0.51 0.60 0.53 0.26 0.59 – – 0.08

() (0.002) (0.014) (0.014) (0.012) (0.011) (0.013) (0.012) (0.007) (0.015) (0.020) (0.003) (0.002)

Values in brackets are explained in the text

solvent anion acid-base interactions, respectively), and polarisability ˛ (accounting for induced dipole-induced dipole interactions). Logically, in accord with Eq. (9), these same five contributions will also appear to influence the values of the primary hydration numbers, nhydr . In a simplified way [16,63], it appears that an essential condition for reliable determinations nhydr is that in the aquo-organic mixture, the organic component must have a dipole moment close to 0, to avoid competitive solvation. Indeed, Table 1

0.0 -0.5 w

-1.0

s

log(ms / ms )

only if E0 means standard electromotive force of reversible cell [63]. However, our research group has applied the said equation to cells containing selective electrodes (cells that are not exactly reversible, due to the presence of the asymmetric potential, among others), and has obtained quite reasonable results [3,9–13]. This “stroke of luck” is possibly due to the fulfilment of the condiasym asym 0∗ ). Note that, as stated above, no tion (Es − Ew ) (Es0∗ − Ew extra-thermodynamic supposition has been imposed a priori for this research to be carried out. It is worthwhile to remember that earlier Bald [38] verified that the effect of the asymmetric potentials upon the determination of Gt0 did not prove to be significant and can be disregarded. Likewise, Clune et al. [64] stress the excellent agreement found between the values of Gt0 obtained, for the same system, with amalgam electrodes or with selective electrodes. According to Eq. (9), Fig. 7 shows the dependence of Ec0 vs. (RT/F) ln w . A very good linear relationship is observed (r = 0.999) up to 40–50 wt.%, approximately, with the value of nhydr obtained for NaCl of 3.1. Applying the same calculation to the mixtures formamide–water and N,N-dimethylformamide–water 3.1 (r = 0.999) and 4.9 (r = 0.999) values are obtained, respectively. These values are very low compared with those obtained from literature (6 ± 2) [65], especially the first two. Falciola et al. [63], who presented an interesting review of Feakins’ theory, state that five contributions to the primary medium effect should be considered, each one described by the variation with respect to water, of a specific physical property, namely: relative permittivity ε (accounting for ion–dielectric interaction), dipole moment  (accounting for ion–dipole interactions), donor or acceptor numbers DN and AN (accounting for solvent cation and

-1.5 -2.0 -2.5 -3.0 -0.005 0.000 0.005 0.010 0.015 0.020 0.025 0.030

(1/εrs-1/εrw) s Fig. 6. Test of the Izmailov et al. equation [61]: log(mss /mw s ) = A(1/εr − 1/εw r ). () formamide (A = 100.2); () N-methylformamide (A = 157.6); () N,Ndimethylformamide (A = −195.8); (䊉) ethylene glycol (A = −73.8); () methanol (A = −89.0); () ethanol (A = −88.4).

190

F. Hernández-Luis et al. / Fluid Phase Equilibria 310 (2011) 182–191

0.00

V w wt.% Y z

Δ E 0c / V

-0.03

-0.06

-0.09

-0.12

-0.15 -0.06

-0.04

-0.02

0.00

(RT/F) ln φw Fig. 7. Plot of Ec0 vs. a function of the water volume fraction for NaCl in N-methylformamide–water mixtures at 298.15 K.

shows that for the three amides considered, its dipole moment is about twice that of water, which explains that nhydr is smaller than expected. On the other hand, the discrepancy between the nhydr values obtained for mixtures containing N-methylformamide or N,N-dimethylformamide (which have the same dipole moment) may perhaps be related to other effects such as the molar volume (59.1 and 77.4 cm3 mol−1 , respectively) or the size and shape of the molecule, which would produce a steric impediment to approach the ions, displacing thus less water molecules of the solvation sphere. List of symbols Debye–Hückel equation constants A, B A␾ Debye–Hückel constant for the Pitzer equation a ion size parameters a(i) characteristic parameters of Scatchard equation b constant of Pitzer equation; constant of TCPC equation c ion interaction parameter of Debye–Hückel equation; also molarity triple-ion interaction parameter of Pitzer equation C␥ cor Correlation index d ion interaction parameter of Debye–Hückel equation E electromotive force total asymmetry potential Easym E0 standard electromotive force E0* apparent standard electromotive force contribution of the extended terms of Debye–Hückel Ext equation F Faraday constant standard Gibbs energy of transfer Gt0 ISE ion selective electrode 0 Ksp standard solubility product constant k Nernst’s theoretical slope [(ln 10)RT/F = 59.16 mV at 25 ◦ C] average molecular mass of mixed solvent M m molality ms saturation molality n constant of TCPC equation nhydr primary hydration number q Bjerrum interionic distance parameter R gas constant Debye–Hückel constant for the Scatchard equation; conS stant of TCPC equation T absolute temperature

molar volume purity weight percent weight percent charge

Greek letters polarisability ˛ ˇ0 , ˇ1 solute-specific interaction parameters of Pitzer equation  mean ionic activity coefficient viscosity  εasym electrode asymmetry potential εr relative permittivity (relative static dielectric constant) w volume fraction of water in the mixed solvent  dipole moment  density

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