Electrical Conductivity in Dimethyl Sulfoxide + Potassium Iodide

Article pubs.acs.org/jced

Electrical Conductivity in Dimethyl Sulfoxide + Potassium Iodide Solutions at Different Concentrations and Temperatures ́ Iwona Płowaś,* Jolanta Swiergiel, and Jan Jadzẏ n Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland ABSTRACT: The direct current conductivity of DMSO + KI solutions was determined with the use of the impedance spectroscopy. The measurements were performed in the whole solubility range of KI and in the temperature range from (293.15 to 323.15) K. The limiting molar conductivities Λo(T) and λoI−(T), as well as the constant KA of ionic association, K+ + I−, were determined at different temperatures with the use of the Fuoss-Onsager method. The obtained data on KA, together with the literature data referred to the K+ + I− association in different solvents, allowed us to formulate an empirical dependence of KA on the molecular dipolar polarizability of the solvent used, KA ∝ exp(−μi2), where μi is the dipole moment of the molecules of ith solvent.

1. INTRODUCTION Dimethyl sulfoxide (DMSO) is a widely used highly polar organic solvent,1−3 the physical properties of which are really unusual. Its high polarity results from two reasons: first, the molecules of DMSO are strongly polar (the dipole moment of a single molecule is about 4 D), and second, an exceptional geometrical structure of DMSO molecules leads to an essential reduction of their ability to the antiparallel dipolar aggregation. That circumstance reflects itself in a relatively high value of the dielectric constant of the solvent (ε ≈ 47.09, at 293.15 K),4 what makes dimethyl sulfoxide very useful in electrochemistry.5 Due to a high polarity, DMSO, in its neat state as well as in the mixtures with other liquids, stands for promising nonaqueous medium for uses in the high-energy batteries6,7 and double-layer capacitors.8,9 Hence, knowledge on the DMSO ability to dissociate ionic compounds of different nature, an extent of the ions solvation by the molecules of the solvent, and finally, the ionic association processes which essentially influence the conductivity of the electrolyte is necessary for understanding ionic conductivity in DMSO and, consequently, for designing new electrochemical devices of high performance. In this paper we present the results of studies on the electrical conductivity of KI dissolved in DMSO as a function of concentration of the electrolyte (in the whole solubility range of KI) and the temperature of the solutions. There are two aims of the paper: (i) to determine the limiting total molar conductivity of KI dissolved in DMSO and hence (lacking in the literature) the limiting molar conductivity of iodide ions, I−, in that solvent and (ii) to determine the association constant of K+ and I− ions and the extent of the solvation of the ions by DMSO molecules.

in a desiccator over silica gel, and DMSO, additionally, with the molecular sieves (4 Å). The purity of the compounds is presented in Table 1. The measurements were performed for Table 1. Sample Information

a

source

mass fraction purity

dimethyl sulfoxide potassium iodide

Sigma-Aldrich Sigma-Aldrich

0.999a 0.994a

Given in the Certificate of Analysis.

DMSO + KI mixtures in the whole solubility range of the electrolyte (the highest KI mole fraction is xmax ≈ 0.07). The density of such diluted solutions, necessary for calculation of the molar concentration of KI, were taken as the density of neat DMSO10 due to the lack of corresponding experimental data. The density measurements performed for analogous solutions [(DMSO + LiBr, DMSO + NaBr and DMSO + KBr)11 or (methanol + KI)12] show that the difference between the density of neat solvent and the density of solution with electrolyte concentration close to xmax used in the presented studies, is less than 0.5 %, so, it can be found as insignificant for the problems discussed in this paper. The solutions were prepared by weighing (the balance A&D, model HR - 120) with an accuracy of ± 1·10−4 g. The standard uncertainty for the mole fraction determination u(x) was 2· 10−4. 2.2. Conductivity Measurements. The complex impedance spectra of the DMSO + KI electrolyte solutions, Z*(ω), were recorded with the use of an HP 4194A impedance/gain phase analyzer in the frequency range within 100 Hz to 5 MHz.

2. EXPERIMENTAL SECTION 2.1. Materials. Dimethyl sulfoxide, (CH3)2SO, and potassium iodide (KI), both from Sigma-Aldrich, were stored © XXXX American Chemical Society

chemical name

Received: August 23, 2013 Accepted: July 4, 2014

A

dx.doi.org/10.1021/je4010678 | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 2. Direct Current Electrical Conductivity (σDC) of (1 − x)DMSO + xKI Solutions of Different Mole Fractions (x) of KI, Under Pressure of 1013 hPaa σDC/mS·cm−1 T/K 293.15 295.15 297.15 299.15 301.15 303.15 305.15 307.15 309.15 311.15 313.15 315.15 317.15 319.15 321.15 323.15 T/K

−4

x = 1.281·10

0.0573 0.0602 0.0630 0.0656 0.0683 0.0711 0.0737 0.0763 0.0790 0.0818 0.0848 0.0879 0.0918 0.0954 0.1000 0.1042 x = 5.707·10−3

293.15 295.15 297.15 299.15 301.15 303.15 305.15 307.15 309.15 311.15 313.15 315.15 317.15 319.15 321.15 323.15 a

1.829 1.903 1.977 2.052 2.127 2.202 2.278 2.353 2.430 2.506 2.582 2.659 2.736 2.813 2.889 2.964

−4

x = 1.586·10

0.0687 0.0718 0.0749 0.0782 0.0814 0.0847 0.0880 0.0920 0.0954 0.0991 0.1027 0.1066 0.1102 0.1142 0.1180 0.1223 x = 0.0100

x = 3.312·10−4 0.1470 0.1528 0.1586 0.1646 0.1709 0.1773 0.1842 0.1908 0.1981 0.2051 0.2122 0.2198 0.2274 0.2360 0.2451 0.2544 x = 0.0197

3.481 3.625 3.770 3.916 4.064 4.212 4.361 4.507 4.652 4.800 4.942 5.082 5.223 5.356 5.491 5.628

x = 6.135·10−4

x = 1.098·10−3

x = 2.002·10−3

0.2675 0.2792 0.2910 0.3030 0.3152 0.3276 0.3397 0.3520 0.3643 0.3764 0.3887 0.4006 0.4125 0.4241 0.4356 0.4467 x = 0.0400

0.4573 0.4749 0.4929 0.5108 0.5291 0.5472 0.5657 0.5841 0.6027 0.6212 0.6399 0.6581 0.6763 0.6941 0.7115 0.7287 x = 0.0499

0.7783 0.8093 0.8406 0.8722 0.9040 0.9360 0.9685 1.000 1.033 1.065 1.097 1.128 1.159 1.189 1.219 1.246 x = 0.0707

8.279 8.651 9.006 9.366 9.737 10.11 10.47 10.83 11.24 11.61 11.95 12.33 12.71 13.09 13.44 13.86

9.283 9.694 10.13 10.51 10.90 11.32 11.69 12.08 12.46 12.82 13.19 13.66 13.90 14.34 14.66 15.23

9.369 9.785 10.23 10.67 11.12 11.52 11.99 12.44 12.86 13.42 13.74 14.08 14.69 15.27 15.67 16.07

6.047 6.316 6.592 6.861 7.134 7.409 7.676 7.943 8.225 8.486 8.736 8.996 9.220 9.452 9.682 9.875

Standard uncertainties u are u(σDC) = 0.3 %, u(x) = 0.0002 and u(T) = 0.01.

gathered in Table 2 and the σDC(x) and σDC(T) dependences are jointly depicted in Figure 1. In the figure, the lines of isotherms represent the best fit of the equation:

The measurements were performed for increasing temperature from the range of (293.15 to 323.15) K. The temperature of the measuring cell was controlled with a “Scientific Instruments” device, model 9700, within ± 2·10−3 K. The details on the used experimental setup can be found in recent paper.13 The impedance spectra were transformed into conductivity spectra, σ*(ω), according to the relation: σ *(ω) =

εo CoZ*(ω)

i=3

σDC(x) =

∑ Ai x i i=0

(2)

to the experimental data. Table 3 contains the values of Ai parameters for all temperatures of measurements. The temperature dependences of the conductivity are presented in Figure 1 in the form of an Arrhenius dependence: σDC(T) = σo exp(−EA/RT), and as can be seen in the figure, the ln σDC vs T−1 plots are linear in the whole KI concentration range. The obtained activation energies of the ionic conductivity are equal to EA = (14 ± 1) kJ·mol−1, irrespective of the KI mole fraction in DMSO. It is worth noticing that the electrical conductivity− temperature behavior of the studied DMSO + KI mixtures is somewhat different from that recorded for DMSO + NH4NO3 solutions14 where σDC(T) dependences do not fulfill the Arrhenius equation and rather the Vogel−Fulcher−Tammann formalism is more suitable for reproduction of the experimental data. However, despite that difference in the thermal behavior,

(1)

where ω is the angular frequency of the probing electric field, C0 is the electric capacity of the empty measuring cell and εo = 8.85 pF/m is the permittivity of free space. From the real part of the conductivity spectra the direct current conductivity of the studied solution, σDC, can be obtained and next, the molar conductivity can be calculated as Λ = σDC/c, where c is the molar concentration of KI in a given solution.

3. RESULTS AND DISCUSSION The values of σDC obtained from the analysis of the conductivity spectra of studied KI solutions in DMSO are B



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Figure 2. Comparison of the dc electrical conductivity dependences on the mole fraction (x) of ionic compounds of different nature: KI (circles) and NH4NO3 (triangles),14 dissolved in DMSO. Full and open points refer to (293.15 and 323.15) K, respectively.

Figure 1. Direct current conductivity of DMSO + KI electrolyte mixtures of different KI mole fractions (x) and at different temperatures. The solid isotherms represent the best fit of eq 2 to the experimental data and the straight lines traced at constant mole fraction of KI, represent an Arrhenius-type temperature dependence of the conductivity.

the concentration behavior of the conductivities of the electrolytes are nearly exactly the same, as shown in Figure 2. That experimental finding seems to be interesting and important as it concerns two quite different in nature ionic compounds, KI and NH4NO3, dissolved in DMSO. Figure 3 presents the molar conductivity of DMSO + KI mixtures, Λ(c) = σDC/c, as a function of the molar concentration c1/2 of KI. The dependences are traced for four chosen temperatures. In a very low concentration region one observes, typical for strong electrolytes, a moderate decreasing in the conductivity. The conductivity data of that region, depicted in Figure 4, are very important because they can be used for determination of the limiting molar conductivity, Λ(c → 0) = Λo and the ionic association constant, KA. For this purpose we used the Fuoss−Onsager equation:15 Λ(c) = Λo − S

Figure 3. Molar conductivity (Λ) dependence on KI concentration in DMSO, at different temperatures.

where Λo is the molar conductivity at infinite dilution, α is the fraction of total solute molecules which have dissociated, and the coefficients S and E are the functions of the static permittivity and viscosity of neat solvent.16,17 The S and E values were calculated basing on the experimental data for neat DMSO, presented in the literature.4,18,19 The coefficient J1 is the function of the parameter R, representing the center-tocenter distance of solvent-separated ion-pair:20

αc αc ⎛ αc ⎞ αc αc + E o ln⎜ o ⎟ + J1 o − KA Λo o ; ⎝c ⎠ co c c c

(c o = 1 mol ·dm ‐3)

(3)

(4)

R=r+d

Table 3. Coefficients of eq 2 and Standard Deviation u(σ) for Direct Current Electrical Conductivities σDC(x) for (1 − x)DMSO + xKI Solutions at all Studied Temperatures T K 293.15 295.15 297.15 299.15 301.15 303.15 305.15 307.15 309.15 311.15 313.15 315.15 317.15 319.15 321.15 323.15

A0 mS·cm

A1 −1 −3

−5.720·10 −7.430·10−3 −8.510·10−3 −1.172·10−3 −1.440·10−3 −1.576·10−3 −1.885·10−3 −2.081·10−3 −2.474·10−3 −2.873·10−3 −2.824·10−3 −2.470·10−3 −3.163·10−3 −3.924·10−3 −3.062·10−3 −1.851·10−3

mS·cm

A2 −1

A3 −1

mS·cm

mS·cm

−5.720·10 −5.948·103 −6.176·103 −6.504·103 −6.803·103 −7.037·103 −7.382·103 −7.691·103 −7.989·103 −8.394·103 −8.616·103 −8.633·103 −9.221·103 −9.798·103 −9.698·103 −9.405·103

2

3

3.986·10 4.157·102 4.327·102 4.514·102 4.699·102 4.873·102 5.063·102 5.245·102 5.437·102 5.634·102 5.796·102 5.931·102 6.148·102 6.366·102 6.464·102 6.526·102 C

u(σ) −1 4

2.775·10 2.873·104 2.981·104 3.198·104 3.380·104 3.474·104 3.715·104 3.917·104 4.073·104 4.409·104 4.489·104 4.341·104 4.909·104 5.451·104 5.228·104 4.801·104

mS·cm−1 0.171 0.179 0.194 0.199 0.205 0.214 0.217 0.226 0.225 0.225 0.232 0.243 0.226 0.218 0.225 0.223



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⎛ ⎞ βκ y′± = exp⎜ − ⎟· ⎝ 2(1 + κR ) ⎠

(7)

In eq 7, κ is the Debye parameter which can be calculated using the following equation:20

κ2 =

2NAe 2αc εoεkBT

(8)

and β is twice the Bjerrum distance:

e2 4πεoεkBT

β=

(9)

In eqs 8 and 9, e is the elementary charge, ε is the relative permittivity of the solvent, εo is the permittivity of free space, kB and N A are the Boltzmann and Avogadro constants, respectively. The best fit of eq 3 to the experimental molar conductivity data, performed with a nonlinear least-squares procedure, taking into account the calculated values of S, E, and J1, and eqs 6 to 9, provides us with the values of the coefficients Λo and KA. Due to the lack in the literature of the values of the association constant for studied mixture, the KA were first estimated from the Arrhenius−Ostwald relation23 (Table 4) and then the constants were determined using eq 3. The solid lines in Figure 4 represent the best fit of eq 3 to the experimental data. In the figure the stars denote the literature data24 obtained for the studied system at 298.15 K. The estimated values of the molar conductivities at infinite dilution, Λo, the association constants, KA determined at different temperatures, are gathered in Table 4. The table contains also the calculated values of the parameter R and the molar conductivity standard deviation, u(Λ), calculated with the formula:

Figure 4. Concentration dependence of molar conductivity in diluted DMSO + KI solutions, at chosen temperatures. Solid lines represent the results of the best fit of eq 3 to experimental data (points). The stars present the conductivity data of Sears et al., measured at 298.15 K.24

where r is the sum of the ionic van der Waals radii (aK+ = 0.133 nm aI− = 0.216 nm, calculated from Pauling crystallographic radius,)21 and d is an average distance between the ions given by20 d = 1.183(M /ρ0 )1/3

20

(5)

where M and ρ0 are the molecular weight and density of neat solvent, respectively. The coefficients J1 were calculated using the formula from the Barthel’s low-concentration chemical model.16 The association constant, KA, occurring in eq 3 can be expressed as20,22 1−α KA = 2 2 α cy′± (6)

⎛ ∑ (Λexp − Λcalc)2 ⎞1/2 ⎟⎟ u(Λ) = ⎜⎜ nd − n p ⎝ ⎠

where (1 − α) is the fraction of oppositely charged ions acting as ion pairs, y′± is the mean activity coefficient of the free ions which can be described as follows:20,22

(10)

Table 4. Total Limiting Molar Conductivities of DMSO + KI Solutions, Λo, and Limiting Ionic Conductivities, λoK+, λoI−, Association Constant, KA, the Distance Parameter R and the Stokes radii, rs,K+, rs,I− T K 293.15 295.15 297.15 299.15 301.15 303.15 305.15 307.15 309.15 311.15 313.15 315.15 317.15 319.15 321.15 323.15

Λo S·cm ·mol 2

34.27 36.29 37.96 39.63 41.24 42.97 44.56 46.21 47.97 49.77 51.63 53.80 56.07 58.34 61.04 63.65

λoK+a −1

λoI− −1

S·cm ·mol 2

13.23 13.89 14.56 15.26 15.98 16.72 17.49 18.28 19.10 19.94 20.81 21.71 22.63 23.58 24.56 25.56

KAb −1

S·cm ·mol 2

21.04 22.40 23.40 24.37 25.26 26.25 27.07 27.93 28.87 29.82 30.82 32.09 33.44 34.76 36.48 38.09

KA −1

dm ·mol

dm ·mol

8.38 9.56 9.98 10.22 10.58 11.00 10.75 11.04 11.46 11.93 12.51 13.77 15.04 16.34 18.39 20.45

8.73 9.80 10.17 10.39 10.73 11.12 10.75 11.04 11.46 11.92 12.49 13.82 15.03 16.30 18.29 20.18

3

3

R −1

nm 0.839 0.839 0.839 0.840 0.840 0.840 0.841 0.841 0.841 0.841 0.842 0.842 0.842 0.843 0.843 0.843

u(Λ)

rs,K+ −1

S·cm ·mol 2

0.58 0.58 0.51 0.52 0.54 0.56 0.36 0.36 0.41 0.44 0.46 0.64 0.70 0.77 0.78 0.72

rs,I−

nm

nm

0.280 0.278 0.276 0.274 0.272 0.270 0.268 0.266 0.264 0.261 0.251 0.257 0.254 0.252 0.250 0.247

0.176 0.173 0.172 0.172 0.172 0.172 0.173 0.174 0.174 0.175 0.179 0.174 0.172 0.171 0.168 0.166

a

The values obtained by interpolation of the literature data28 to the temperatures of our measurements. bThe association constants obtained using the Arrhenius-Ostwald relation.24 D



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where nd and np denote the number of the experimental points and the number of the parameters, respectively. On the basis of the theory of ionic conductance kinetics25,26 and the obtained total limiting molar conductivities of DMSO + KI solutions, Λo(T), the Eyring’s activation enthalpy for the charge transport, ΔH≠Λ, was determined by the use of the following equation:25,26 ln Λo +

ΔHΛ≠ 2 ln ρ0 = − +B 3 RT

(11)

where ρ0 is the density of neat DMSO. From temperature dependence of the limiting conductivities, presented in Figure 5, the determined ΔH≠Λ equals to about 15.2 kJ·mol−1.

Figure 6. An Arrhenius temperature dependence of: ● the experimental limiting molar conductivity (Λo) of DMSO + KI mixtures obtained with the use of eq 3, □ the literature data of the limiting conductivity of potassium cation (λoK+)27 and the values interpolated to the temperatures of our measurements, ▼ the limiting conductivity of iodide anion (λoI−), calculated from eq 12. Open stars and ▲ present the experimental data of Izutsu23 and Sears et al.,24 respectively.

rs =

(13)

where z is the charge of the ion and η (in Pa·s) is the viscosity of the neat solvent and F is the Faraday constant. The rs values obtained from eq 13 for studied ions are gathered in Table 4. The data show that the Stokes radii of K+ and I− are differently related to their van der Waals radii,21 namely rs of cation is approximately two-times higher and that of anion is somewhat lower than its van der Waals radius. The similar effect was observed for I− in other solvents like dimethylformamide29 and water.30 For the ion concentration higher than the limiting one, the ion−solvent and the ion−ion interactions coexist and different entities composed of the ions and solvent molecules are formed. The composition and the structure of these entities are resultant of the competition between these two interactions. That problem is strictly related to our second conclusion. The ionic association constant KA describes the ion−ion interactions in a given medium. From other side, it seems to be obvious that the main physical quantity which determines the strength of the ion−solvent interaction is the polarizability of the solvent molecules. So, one can expect that the higher dipolar polarizability (which is proportional to the molecular dipole moment squared, μ2) should lead to an increase of the ion−solvent interaction strength and consequently to decrease of the ion−ion association constant. The experimental data presented in Figure 7 seem to confirm that expectation. The association constant for K+ and I− ions, determined in solvents of different dipolar polarizabilities [DMSO (data of this paper), acetonitrile,31 tetramethylene sulfone (sulfolane)32 and propylene carbonate33] significantly decreases with an increase of μ2 of the solvent used. The data presented in the figure can be well reproduced (solid line) with a function of KA ∝ exp(−μi2) type. We believe that that conclusion of our work has a much more general significance than only for KI electrolytes. As formation of the electrically inert ion-pairs can decisively reduce of the electrical conductivity of electrolytes, the results obtained in this paper show a potential way of (even partial) elimination of that parasite effect: the molecules of the solvent used should have as high as possible permanent dipole moment.

3 −1 Figure 5. Plot of ln(Λo·ρ2/3 for KI in DMSO. 0 ) as a function of 10 T Solid line represents the best fit of eq 11 to experimental data (points).

The following conclusions result from the studies presented in this paper. The first concerns the limiting conductivities. As the limiting molar conductivity of the 1:1 electrolyte presents a sum of those of cation (λo+) and anion (λo−), for studied KI electrolyte the following relation can be written: Λo = λ Ko+ + λIo−

F 2|z| 6πNAλ±oη

(12)

In the literature one can find the conductivity values of λoK+ in DMSO, determined at different temperatures,27 while for the iodide anion, the λoI−conductivity in DMSO can be found at 298.15 K,23 only. So, having our experimental data on Λo(T) and the literature data on λoK+(T), the values of λoI− can be calculated with the use of eq 12. High accuracy data on λoK+ (±0.2 %), presented in ref 27, have been obtained with the use of the conductometer at the frequency of probing electric field equal to 1 kHz. Table 4 contains the values of both λoK+(T) (the literature data27 have been interpolated to the temperatures o used in our experiment) and calculated λI− (T) for all temperatures used. Figure 6 presents the Arrhenius temperature dependences of the total limiting molar conductivity of DMSO + KI solutions, Λo(T), and those of ions present in the studied electrolyte: λoK+(T) and λoI−(T). The thermal activation energies of limiting conductivity of K+ and I− ions are very close to each other (15 kJ·mol−1 and 17 kJ·mol−1, respectively). An importance of the limiting ionic conductivities, λo± , results from the fact that they are determined for infinite dilution of the ions in a given medium, i.e. in conditions where the ion−ion interactions can be neglected. So, the conductivities contain valuable information on the ion−solvent interactions and can be used for evaluation of the Stokes radius of the ions moving in a given solvent. The evaluation can be done with the use of the well-known equation:28 E



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conductivity of concentrated nonaqueous electrolyte solutions and the dielectric constant and viscosity of the solvents. J. Power Sources 2002, 107, 80−89. (8) Conway, B. E. Electrochemical Supercapacitors; Kluwer Academic/ Plenum Publishers: New York, 1999. (9) Kötz, R.; Carlen, M. Principles and applications of electrochemical capacitors. Electrochim. Acta 2000, 45, 2483−2498. (10) Ciocirlan, O.; Iulian, O. Vapor Pressure, Density, Viscosity and Refractive Index of Dimethyl Sulfoxide + 1,4-Dimethylbenzene System. Hung. J. Ind. Chem. 2003, 31, 23−29. (11) Zamir, T. Thermodynamical Behavior of 1−1 Strong Electrolytes in Water, Dimethyl Sulfoxide and Water-Dimethyl Sulfoxide Mixtures, PhD thesis; University of Balochistan: Pakistan, 2004. (12) MacInnes, D. A.; Dayhoff, M. O. The Apparent and Partial Molal Volumes of Potassium Iodide and of Iodine in Methanol at 25°C from Density Measurements. J. Am. Chem. Soc. 1953, 75, 5219− 5220. (13) Świergiel, J.; Jadżyn, J. Static Dielectric Permittivity of Homologous Series of Liquid Cyclic Ethers 3n-crown-n, n = 4 to 6. J. Chem. Eng. Data 2012, 57, 2271−2274. (14) Świergiel, J.; Płowaś, I.; Jadżyn, J. Temperature and Concentration Dependences of the Electric Conductivity of Dimethyl Sulfoxide + Ammonium Nitrate Electrolytes. J. Chem. Eng. Data 2013, 58, 2302−2306. (15) Fuoss, R.; Hsia, K.-L. Association of 1−1 Salts in Water. Proc. Natl. Acad. Sci. U.S.A. 1967, 57, 1550−1557. (16) Barthel, J. M. G.; Krienke, H.; Kunz, W. Physical Chemistry of Electrolyte Solutions-Modern Aspects; Springer: New York, 1998. (17) Chen, M.−S.; Onsager, L. The Generalized Conductance Equation. J. Phys. Chem. 1977, 81, 2017−2021. (18) Grande, M. C.; Garcia, M.; Marschoff, C. M. Density and Viscosity of Anhydrous Mixtures of Dimethylsulfoxide with Acetonitrile in the Range (298.15 to 318.15) K. J. Chem. Eng. Data 2009, 54, 652−658. (19) Bhanupriya; Rajwade, R. P.; Pande, R. Partial Molar Volumes and Viscosity B-Coefficient of N-Phenylbenzohydroxamic Acid in Dimethylsulfoxide at Different Temperatures. J. Chem. Eng. Data 2008, 53, 1458−1461. (20) Fuoss, R. M. Conductance-Concentration Function for the Paired Ion Model. J. Phys. Chem. 1978, 82, 2427−2440. (21) Huheey, J. E.; Keiter, E. A.; Keiter, R. L. Inorganic Chemistry: Principles of Structure and Reactivity, 4th ed.; HarperCollins: New York, 1993. (22) Fuoss, R. M. Paired ions: Dipolar pairs as subset of diffusion pairs. Proc. Natl. Acad. Sci. U.S.A. 1978, 75, 16−20. (23) Izutsu, K. Electrochemistry in Nonaqueous Solutions; WileyVCH Verlag GmbH: Weinheim, Germany, 2002; Vol. 204, pp 214− 215. (24) Sears, P. G.; Lester, G. R.; Dawson, L. R. A study of the conductance behavior of some uni-univalent electrolytes in dimethyl sulfoxide at 25 °C. J. Phys. Chem. 1956, 60, 1433−1436. (25) Brummer, S. B.; Hills, G. J. Kinetics of ionic conductance. Part 1.Energies of activation and the constant volume principle. Trans. Faraday Soc. 1961, 57, 1816−1822. (26) Brummer, S. B.; Hills, G. J. Kinetics of ionic conductance. Part 2.Temperature and pressure coefficients of conductance. Trans. Faraday Soc. 1961, 57, 1823−1837. (27) Chauhan, M. S.; Sharma, M.; Gupta, S.; Ashwini, K.; Chauhan, S. Transport Behaviour of Ions in N,N-Dimethylformamide and Dimethyl Sulfoxide at Different Temperatures. Conductance Studies. Collect. Czech. Chem. Commun. 1995, 60, 43−54. (28) Marcus, Y. Are Ionic Stokes Radii of Any Use? J. Solution Chem. 2012, 41, 2082−2090. (29) Paul, R. C.; Singla, J. P.; Gill, D. S.; Narula, S. P. Physicochemical studies in non-aqueous solventsIII: Transference numbers of silver perchlorate and solvation studies in N,N-dimethylformamide at 25°C. J. Inorg. Nucl. Chem. 1971, 33, 2953−2957. (30) Nightingale, E. R. Phenomenological Theory of Ion Solvation. Effective Radii of Hydrated Ions. J. Phys. Chem. 1959, 63, 1381−1387.

Figure 7. Behavior of the association constant of K+ and I− ions in solvents of different molecular dipolar polarizabilities: ACN (acetonitrile),34 DMSO (dimethyl sulfoxide),35 TMS (sulfolane)36 and PC (propylene carbonate),35 at 298.15 K. μ denotes the dipole moment of the molecules of a given solvent.

4. CONCLUSIONS Based on the analysis of the electrical conductivity spectra, the direct current conductivity of DMSO + KI solutions, was determined. It was found that at constant concentration the conductivity temperature dependence fulfills an Arrhenius equation with the activation energy of 14 ± 1 kJ·mol−1 for all studied KI concentrations in DMSO. The conductivity data recorded in diluted solutions were the basis for determination of the limiting total molar conductivity and the association constant for K+ and I− ions in DMSO. With the use of the literature data on temperature dependence of the limiting molar conductivity of cation K+ in DMSO, the limiting molar conductivity for I− ions in DMSO at different temperatures are determined. The main conclusion resulting from presented investigations (and the literature data) concerns the dependence of the ionic association constant on the dipolar polarizability of the solvent molecules. Quite strong (exponential) decrease of the constant with an increase of the dipole moment squared of solvent molecules gives a useful indication in preparation of the electrolytes where the ionpairing process should be limited as much as possible.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +48 61 86 95 162. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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Electrical Conductivity in Dimethyl Sulfoxide + Potassium Iodide

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