Densities and Apparent Molar Volumes of Aqueous Solutions of

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Densities and Apparent Molar Volumes of Aqueous Solutions of Li2SO4 and LiCF3SO3 at Temperatures from 293 to 343 K Bin Hu,† Lubomir Hnedkovsky,‡ and Glenn Hefter*,‡ †

CAS Key Laboratory of Salt Lake Resources and Chemistry, Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, Xining 810008, China ‡ Chemistry Department, Murdoch University, Murdoch, Western Australia 6150, Australia ABSTRACT: Densities of aqueous solutions of lithium sulfate (Li2SO4) and lithium trifluoromethanesulfonate (LiCF3SO3) at solute molalities ranging from 0.05 to 2.7 or 9.6 mol·kg−1, respectively, have been measured by vibrating-tube densimetry over the temperature range 293.15 ≤ T/K ≤ 343.15 at 0.1 MPa pressure. The apparent molar volumes (Vϕ) of Li2SO4(aq) and LiCF3SO3(aq) derived from these data were fitted using an extended Redlich−Rosenfeld−Meyer equation. The Vϕ values for the two systems exhibit quite different dependences on concentration and temperature, as do the isobaric expansibilities. A combination of the present and literature data reveals that the densities for Li2SO4(aq) given in standard compilations are unreliable at low concentrations. Comparison of the present results with literature data for related salts shows that Vϕ(LinX) and Vϕ(NanX) exhibit a crossover at ≈0.5 mol·kg−1 for both systems, similar to those observed previously for other lithium and sodium salts. Consideration of an appropriate series of lithium salts suggests that anion size influences departures from the Debye−Hückel limiting law for volumes, whereas for a series of sulfate salts cation size does not appear to be a major factor.

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INTRODUCTION Lithium salts have attracted much attention for scientific and industrial applications and are now produced commercially on a large scale. Much of the interest in lithium salts is because the lithium cation is so much smaller, r(Li+) = 69 pm,1 at least in the solid state, than its alkali metal congeners. For example, Na+ has a solid-state radius of 102 pm,1 which corresponds to a more than 3-fold difference in volume. Such differences often cause the properties of lithium salts and their solutions to depart considerably from those of the other alkali metals.2,3 The size of the lithium ion is, for example, thought to be a factor in the pharmacological efficacy of lithium salts in the treatment of manic-depressive psychoses.4,5 Another consequence of the unusually small size of Li+ is that it often produces solid salts with relatively small lattice energies, due to the mismatch of cation and anion volumes. Because of this, lithium salts often have remarkably high solubilities, not just in water but in many organic solvents.1,5 Coupled with the low atomic mass (and hence density) of Li and its large electrode potential (Eo(Li+(aq)|Li) = −3.0 V vs SHE at 298.15 K),1 the high solubilities of lithium salts have made them attractive for use in primary and secondary (rechargeable) batteries.6 Among the many lithium salts of interest in battery development, lithium trifluoromethanesulfonate (LiCF3SO3; lithium triflate, LiTf) is one of the most commonly employed because of its thermal and electrochemical stability, and its often prodigious solubility (in excess of 20 mol·kg−1 in water at 298.15 K).5 On the other hand, lithium sulfate (Li2SO4) is used clinically and has been employed as a catalyst in organic chemistry.7 More importantly, Li2SO4 occurs naturally in certain salt lake brines8 © XXXX American Chemical Society

that are used for the industrial production of lithium and its compounds. Knowledge of the volumetric properties of salts such as LiTf and Li2SO4, and how they vary with temperature and concentration, is useful for both scientific and technological purposes. Such data provide valuable insights into the influence of ion size on chemical and electrochemical behavior, and are required for engineering calculations involving mass transfer and for the interconversion of concentration units. As such, they play an important role in developing more efficient methods of extraction of lithium compounds on an industrial scale. To the best of our knowledge, no volumetric data have been reported for LiTf(aq) in the open literature. In contrast, the densities of Li2SO4(aq) have received a reasonable amount of attention, sometimes up to high temperatures and pressures. The experimental studies reported to date9−16 are summarized in Table 1. In addition, Söhnel and Novotný17 and Aseyev and Zaytsev18 have presented smoothed densities (to four and five significant figures, respectively) along with polynomial fitting equations covering the approximate molality and temperature ranges: 0.19 ≤ m/mol·kg−1 ≤ 2.9 and 273 ≤ T/K ≤ 373, at 0.1 MPa pressure, based on the then-available literature sources. Their values at 298.15 K, expressed here as apparent molar volumes (Vϕ), are plotted in Figure 1 as a function of molality (√m) along with the experimental results reported in a crosssection of the studies listed in Table 1. While most of the Received: June 23, 2016 Accepted: September 2, 2016

A

DOI: 10.1021/acs.jced.6b00519 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Literature Data for the Densities of Aqueous Solutions of Lithium Sulfate conditions author(s)

year

experimental method

temp (K)

pressure (MPa)

concentration (mol·kg−1)

Kohner9 Pearce and Eckstrom10 Kaminsky11 Puchkov et al.12 Maksimova et al.13 Cartón et al.14 Abdulagatov and Azizov15 Hervello and Sánchez16

1928 1937 1956 1976 1984 1995 2003 2007

pycnometry pycnometry pycnometry hydrostatic balanceb pycnometry vibrating tube piezometer vibrating tube

298 298 288−316 298−588 293−363 278−338 297−573 283−298

0.1 0.1 0.1 ?c 0.1 0.1 3.9−40 0.1

0.4−2.7 0.1−3.1 0.001−0.2a 0.005−3.0 0.09−2.2 0.4−3.2 0.09−0.9 0.21−3.1

In mol·L−1. bPycnometric measurements are also reported at 298 ≤ T/K ≤ 363. cPressure not specified but is presumed to be 0.1 MPa at 298 ≤ T/ K ≤ 373, and the saturated vapor pressure is at 373 ≤ T/K ≤ 588.

a

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EXPERIMENTAL SECTION Reagents. Lithium triflate was synthesized, as described in detail previously,19 by the reaction of trifluoromethanesulfonic acid (CF3SO3H, Sigma-Aldrich, USA, mass fraction ≥ 99%) with solid Li2CO3 (Sigma-Aldrich, mass fraaction ≥ 99%) and recrystallized twice from water. A concentrated stock solution of Li2SO4(aq) solution was prepared by neutralizing Li2CO3(s) with H2SO4 (Merck, AR, mass fraction ≥ 98%), sparging with nitrogen to remove CO2, and filtering (0.4 μm) (Table 2).19 Parent solutions of both salts were analyzed in triplicate by evaporative gravimetry, initially at 60 °C then overnight at 190 °C under vacuum (p ≈ 5 Pa); concentrations were reproducible to ±0.02% and ±0.01% (relative) for LiTf and Li2SO4, respectively. Further checks on the accuracy of the concentrations are described elsewhere19 but taking all factors, except salt purity, into account the overall relative uncertainty in the solution concentrations is estimated to be ±0.03%. Working solutions were prepared by weight dilution using freshly degassed high purity water (Ibis Technology, Australia); buoyancy corrections were applied throughout. Density Determinations. Densities were measured using an Anton Paar (Austria) model 5000 M vibrating tube densimeter following the experimental protocol described in detail previously.20 Temperature was controlled to ±0.002 K over the range 293.15 ≤ T/K ≤ 343.15. As found previously, density reproducibility decreased with increasing solute concentration but was always within the range ±(2 to 10) μg·cm−3, corresponding to ±0.02 cm3·mol−1 or better in Vϕ. Measurements of the densities of five solutions of NaCl(aq) at m/mol· kg−1 = 2, 3, 4, 5, and 6 agreed with those calculated via Archer’s equation21 to within 0.002% (relative). The experimental pressure was measured using the internal sensor of the DMA 5000 densimeter.

Figure 1. Selected literature values for the apparent molar volume Vϕ of aqueous solutions of Li2SO4 as a function of molality (√m) at 298.15 K and 0.1 MPa pressure: ●, Söhnel and Novotný;17 blue ⧫, Aseyev and Zaytsev;18 purple +, Maksimova et al.;13 green ▲, Cartón et al.;14 red ■, Hervello and Sánchez.16 The lines are visual guides only.

independently measured Vϕ values in Figure 1 are in reasonable agreement with each other (and with the present results, see later) there are marked differences between the two compilations.17,18 These disparities are particularly concerning, especially at lower molalities, given that differences of up to 10 cm3·mol−1 have been omitted from Figure 1 for representational convenience. Comparisons of the data at other temperatures (not shown) exhibit similar characteristics. Accordingly, this paper reports a systematic study of the densities of aqueous solutions of Li2SO4 and LiTf over the temperature range 293.15 ≤ T/K ≤ 343.15 and at molalities from 0.05 mol·kg−1 to 2.8 mol·kg−1 (for Li2SO4, which is close to its solubility limit) or 9.6 mol·kg−1(for the much more soluble LiTf) using high precision vibrating-tube densimetry.

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RESULTS AND DISCUSSION Densities of Lithium Sulfate and Lithium Triflate Solutions. The present experimental densities of Li2SO4(aq) and LiTf(aq) solutions are summarized in Tables 3 and 4,

Table 2. Sample Sources and Purities chemical name

CASRN

source

lithium triflate lithium sulfate lithium carbonate triflic acid sulfuric acid

33454-82-9 10377-48-7 554-13-2 1493-13-6 7664-93-9

synthesis synthesis Aldrich Aldrich Merck

initial mass fraction purity

purification method

final mass fraction purity

analysis method

0.9995 0.9995

evaporative gravimetry evaporative gravimetry

≥0.99 ≥0.99 ≥0.98

recrystallization from water (×2) recrystallization from water none none none B



Article

Table 3. Experimental Density Differences, Δρ, and Apparent Molar Volumes, Vϕ, of Li2SO4(aq) as a Function of Molality, m, at Temperatures 293.15 ≤ T/K ≤ 343.15 and Pressure p = 0.1 MPaa m

Δρ

Vϕ

m

Δρ

Vϕ

m

Δρ

Vϕ

m

Δρ

Vϕ

mol·kg−1

kg·m−3

cm3·mol−1

mol·kg−1

kg·m−3

cm3·mol−1

mol·kg−1

kg·m−3

cm3·mol−1

mol·kg−1

kg·m−3

cm3·mol−1

T = 293.15 0.05013 0.07004 0.10081 0.20240 0.40250 0.49930 0.50752 0.70609 0.99690 1.0010 1.5033 2.0008 2.6814 T = 303.15 0.05013 0.07004 0.10081 0.20240 0.40250 0.49930 0.50752 0.70609 0.99690 1.0010 1.5033 2.0008 2.6814 T = 313.15 0.05013 0.07004 0.10081 0.20240 0.40250 0.49930 0.50752 0.70609 0.99690 1.0010 1.5033 2.0008 2.6814 T = 323.15 0.05013 0.07004

K, ρw = 998.207 kg·m−3 4.788 14.27 6.663 14.63 9.539 15.09 18.889 16.23 36.769 17.86 45.199 18.51 45.919 18.54 62.796 19.70 86.613 21.17 86.962 21.16 125.89 23.22 161.91 24.94 207.48 26.94 K, ρw = 995.649 kg·m−3 4.740 15.03 6.593 15.42 9.442 15.85 18.696 16.98 36.417 18.53 44.779 19.15 45.489 19.19 62.252 20.28 85.933 21.66 86.276 21.66 125.07 23.59 161.04 25.21 206.67 27.10 K, ρw = 992.216 kg·m−3 4.714 15.27 6.559 15.64 9.392 16.08 18.595 17.22 36.228 18.75 44.553 19.36 45.261 19.39 61.963 20.45 85.584 21.78 85.929 21.78 124.67 23.65 160.64 25.23 206.33 27.07 K, ρw = 988.035 kg·m−3 4.707 15.08 6.550 15.43

T = 298.15 0.05013 0.07004 0.10081 0.20240 0.40250 0.49930 0.50752 0.70609 0.99690 1.0010 1.5033 2.0008 2.6814 T = 308.15 0.05013 0.07004 0.10081 0.20240 0.40250 0.49930 0.50752 0.70609 0.99690 1.0010 1.5033 2.0008 2.6814 T = 318.15 0.05013 0.07004 0.10081 0.20240 0.40250 0.49930 0.50752 0.70609 0.99690 1.0010 1.5033 2.0008 2.6814 T = 328.15 0.05013 0.07004

K, ρw = 997.047 kg·m−3 4.760 14.74 6.624 15.09 9.486 15.52 18.779 16.68 36.568 18.26 44.959 18.90 45.674 18.93 62.486 20.05 86.225 21.46 86.573 21.46 125.42 23.45 161.41 25.11 207.02 27.05 K, ρw = 994.033 kg·m−3 4.724 15.22 6.574 15.57 9.412 16.02 18.635 17.16 36.306 18.69 44.644 19.30 45.353 19.34 62.080 20.41 85.723 21.76 86.068 21.76 124.83 23.65 160.79 25.25 206.44 27.11 K, ρw = 990.213 kg·m−3 4.709 15.21 6.552 15.58 9.381 16.03 18.570 17.19 36.182 18.72 44.503 19.32 45.209 19.36 61.895 20.41 85.503 21.74 85.847 21.74 124.59 23.60 160.58 25.16 206.31 26.99 K, ρw = 985.693 kg·m−3 4.711 14.80 6.553 15.20

T = 323.15 K, ρw = 988.035 kg·m−3 0.10081 9.375 15.92 0.20240 18.561 17.07 0.40250 36.164 18.61 0.49930 44.479 19.21 0.50752 45.184 19.25 0.70609 61.869 20.30 0.99690 85.477 21.63 1.0010 85.821 21.63 1.5033 124.57 23.48 2.0008 160.59 25.04 2.6814 206.38 26.88 T = 333.15 K, ρw = 983.196 kg·m−3 0.05013 4.717 14.47 0.07004 6.561 14.88 0.10081 9.389 15.39 0.20240 18.581 16.60 0.40250 36.194 18.19 0.49930 44.518 18.79 0.50752 45.225 18.83 0.70609 61.923 19.90 0.99690 85.560 21.25 1.0010 85.906 21.24 1.5033 124.73 23.12 2.0008 160.83 24.69 2.6814 206.74 26.54 T = 343.15 K, ρw = 977.765 kg·m−3 0.05013 4.736 13.62 0.07004 6.586 14.05 0.10081 9.426 14.56 0.20240 18.644 15.85 0.40250 36.302 17.51 0.49930 44.651 18.13 0.50752 45.363 18.17 0.70609 62.099 19.28 0.99690 85.799 20.66 1.0010 86.145 20.66 1.5033 125.08 22.58 2.0008 161.30 24.19 2.6814 207.37 26.08

T = 328.15 K, ρw = 985.693 kg·m−3 0.10081 9.379 15.69 0.20240 18.565 16.87 0.40250 36.170 18.43 0.49930 44.486 19.04 0.50752 45.193 19.07 0.70609 61.878 20.14 0.99690 85.496 21.47 1.0010 85.840 21.46 1.5033 124.62 23.32 2.0008 160.68 24.88 2.6814 206.52 26.73 T = 338.15 K, ρw = 980.551 kg·m−3 0.05013 4.725 14.08 0.07004 6.572 14.49 0.10081 9.406 15.00 0.20240 18.608 16.25 0.40250 36.239 17.88 0.49930 44.574 18.49 0.50752 45.284 18.53 0.70609 61.998 19.62 0.99690 85.662 20.98 1.0010 86.008 20.98 1.5033 124.88 22.87 2.0008 161.04 24.45 2.6814 207.03 26.32

a

Standard uncertainties u are u(T) = 0.002 K, u(p) = 1 kPa, u(Δρ) = {0.002 + 0.0004m} kg·m−3, ur(m) = 0.0003 (level of confidence = 0.68), and the combined expanded uncertainty Uc is Uc(Vϕ) = 0.04 cm3·mol−1 (level of confidence = 0.95).

respectively. Solution densities, ρ, at the target temperatures were based on the densities of water, ρw, at those temperatures. The latter were calculated from the International Association of the Properties of Water and Steam IAPWS-95 formulation22 and for convenience are also listed in Tables 3 and 4. It should be noted that the measured quantity, Δρ = ρ − ρw, is independent of the model used for representing ρw. The values of ρ can be trivially calculated from the data in Tables 3 and 4. Apparent and Standard Molar Volumes of Li2SO4(aq) and LiTf(aq). Apparent molar volumes (Vϕ) were calculated from the experimental densities (Tables 3 and 4) using the usual relationship:

Vϕ =

ρ − ρw Ms − ρ mρρw

(1)

where ρ and ρw are respectively the densities of the solution and of pure water at the specified temperature and pressure, m is the molality of the solution (mol-solute/kg-water) and Ms is the molar mass of the solute. The molar masses of Li2SO4 and LiCF3SO3 were calculated to be (110.00 ± 0.06) g·mol−1 and (156.04 ± 0.03) g·mol−1, respectively, using 2015 atomic masses.23 Almost all of the uncertainty in Ms arises from the atomic mass of Li, whose accuracy has been significantly downgraded in recent years. C



Article

Table 4. Experimental Density Differences, Δρ, and Apparent Molar Volumes, Vϕ, of LiTf (aq) as a Function of Molality, m, at Temperatures 293.15 ≤ T/K ≤ 343.15 and Pressure p = 0.1 MPaa m

Δρ

Vϕ

m

Δρ

Vϕ

m

Δρ

Vϕ

m

Δρ

Vϕ

mol·kg−1

kg·m−3

cm3·mol−1

mol·kg−1

kg·m−3

cm3·mol−1

mol·kg−1

kg·m−3

cm3·mol−1

mol·kg−1

kg·m−3

cm3·mol−1

T = 293.15 0.04996 0.06998 0.10020 0.20000 0.39970 0.69980 0.98830 1.4996 1.9995 2.9985 3.9912 5.8794 7.4931 9.6345 T = 303.15 0.04996 0.06998 0.10020 0.20000 0.39970 0.69980 0.98830 1.4996 1.9995 2.9985 3.9912 5.8794 7.4931 9.6345 T = 313.15 0.04996 0.06998 0.10020 0.20000 0.39970 0.69980 0.98830 1.4996 1.9995 2.9985 3.9912 5.8794 7.4931 9.6345 T = 323.15 0.04996 0.06998

K, ρw = 998.207 kg·m−3 4.072 74.22 5.691 74.28 8.127 74.32 16.076 74.45 31.641 74.51 54.196 74.55 74.988 74.57 109.79 74.64 141.56 74.68 198.98 74.81 249.09 74.98 328.65 75.40 383.91 75.76 443.30 76.27 K, ρw = 995.649 kg·m−3 4.026 75.13 5.627 75.18 8.034 75.23 15.884 75.40 31.257 75.47 53.509 75.53 74.011 75.56 108.30 75.64 139.59 75.69 196.07 75.83 245.35 75.99 323.74 76.35 378.37 76.65 437.24 77.09 K, ρw = 992.216 kg·m−3 3.983 75.98 5.567 76.03 7.950 76.06 15.719 76.22 30.920 76.31 52.913 76.39 73.165 76.43 107.00 76.53 137.87 76.58 193.54 76.73 242.10 76.89 319.49 77.21 373.53 77.47 431.96 77.84 K, ρw = 988.035 kg·m−3 3.946 76.72 5.514 76.79

T = 298.15 0.04996 0.06998 0.10020 0.20000 0.39970 0.69980 0.98830 1.4996 1.9995 2.9985 3.9912 5.8794 7.4931 9.6345 T = 308.15 0.04996 0.06998 0.10020 0.20000 0.39970 0.69980 0.98830 1.4996 1.9995 2.9985 3.9912 5.8794 7.4931 9.6345 T = 318.15 0.04996 0.06998 0.10020 0.20000 0.39970 0.69980 0.98830 1.4996 1.9995 2.9985 3.9912 5.8794 7.4931 9.6345 T = 328.15 0.04996 0.06998

K, ρw = 997.047 kg·m−3 4.048 74.69 5.657 74.76 8.079 74.79 15.975 74.95 31.444 75.00 53.838 75.06 74.479 75.09 109.01 75.16 140.54 75.20 197.47 75.33 247.15 75.50 326.10 75.89 381.04 76.22 440.17 76.69 K, ρw = 994.033 kg·m−3 4.002 75.60 5.596 75.62 7.989 75.68 15.798 75.83 31.085 75.90 53.203 75.97 73.576 76.01 107.63 76.10 138.70 76.15 194.77 76.29 243.67 76.45 321.54 76.79 375.87 77.07 434.51 77.47 K, ρw = 990.213 kg·m−3 3.965 76.34 5.540 76.42 7.912 76.44 15.643 76.60 30.767 76.69 52.643 76.78 72.778 76.83 106.41 76.95 137.08 77.00 192.39 77.16 240.63 77.31 317.56 77.61 371.35 77.85 429.56 78.19 K, ρw = 985.693 kg·m−3 3.930 77.03 5.489 77.15

T = 323.15 K, ρw = 988.035 kg·m−3 0.10020 7.873 76.83 0.20000 15.570 76.97 0.39970 30.620 77.07 0.69980 52.384 77.16 0.98830 72.413 77.22 1.4996 105.86 77.33 1.9995 136.33 77.41 2.9985 191.30 77.56 3.9912 239.25 77.71 5.8794 315.75 77.99 7.4931 369.31 78.21 9.6345 427.32 78.53 T = 333.15 K, ρw = 983.196 kg·m−3 0.04996 3.912 77.40 0.06998 5.467 77.46 0.10020 7.810 77.46 0.20000 15.438 77.64 0.39970 30.350 77.76 0.69980 51.901 77.87 0.98830 71.729 77.94 1.4996 104.82 78.07 1.9995 134.96 78.16 2.9985 189.30 78.32 3.9912 236.72 78.46 5.8794 312.48 78.71 7.4931 365.60 78.90 9.6345 423.25 79.18 T = 343.15 K, ρw = 977.765 kg·m−3 0.04996 3.884 77.96 0.06998 5.426 78.05 0.10020 7.750 78.07 0.20000 15.319 78.24 0.39970 30.098 78.41 0.69980 51.462 78.53 0.98830 71.105 78.62 1.4996 103.87 78.77 1.9995 133.71 78.86 2.9985 187.50 79.03 3.9912 234.47 79.16 5.8794 309.59 79.38 7.4931 362.32 79.54 9.6345 419.67 79.78

T = 328.15 K, ρw = 985.693 kg·m−3 0.10020 7.842 77.14 0.20000 15.502 77.31 0.39970 30.482 77.42 0.69980 52.138 77.52 0.98830 72.062 77.59 1.4996 105.32 77.72 1.9995 135.63 77.79 2.9985 190.28 77.94 3.9912 237.95 78.09 5.8794 314.07 78.36 7.4931 367.40 78.56 9.6345 425.22 78.86 T = 338.15 K, ρw = 980.551 kg·m−3 0.04996 3.897 77.70 0.06998 5.446 77.76 0.10020 7.779 77.77 0.20000 15.376 77.95 0.39970 30.219 78.10 0.69980 51.678 78.21 0.98830 71.410 78.28 1.4996 104.33 78.43 1.9995 134.32 78.51 2.9985 188.38 78.68 3.9912 235.56 78.82 5.8794 310.99 79.05 7.4931 363.91 79.22 9.6345 421.40 79.48

a Standard uncertainties u are u(T) = 0.002 K, u(p) = 1 kPa, u(Δρ) = {0.002 + 0.0004 m} kg·m−3, ur(m) = 0.0003 (level of confidence = 0.68), and the combined expanded uncertainty Uc is Uc(Vϕ) = 0.05 cm3·mol−1 (level of confidence = 0.95).

Hückel) slope for volumes, ω (= [z+z−(z+ + z−)/2]3/2 is a valence factor having the value of 5.19615 for Li2SO4 and 1.00000 for LiCF3SO3), and YV (Y = B, C, D, E) are temperature-dependent empirical parameters obtained from fitting the experimental data. Debye−Hückel slopes were calculated using the equation of state of Wagner and Pruss22 for the dielectric constant of water. For convenience the slopes so obtained are listed as a function of temperature in Table 5, together with the values of Vo for Li2SO4(aq) and LiTf (aq). At 298.15 K, the present Vo values of

The temperature and molality dependences of Vϕ (Figures 2, 3, and 4) were described using an extended Redlich−Rosenfeld− Meyer (RRM) equation:19,24 Vϕ = V o + ωAV m0.5 + B V m + C Vm1.5 + D V m2 + E V m2.5 (2)

where Vo represents the apparent molar volume of the solute at infinite dilution in water (which is equal to its standard partial molar volume, V̅ o2). The constant AV is the theoretical (Debye− D



Article

Figure 4. Lower box: apparent molar volumes of LiTf(aq) as a function of molality (√m) at T/K = 293.15, 303.15, 313.15, 323.15, and 333.15 (bottom to top); lines were calculated from eq 2 using the parameters in Tables 5 and 6. Upper box: deviations of the experimental volumes from those calculated via eq 2 (ΔVϕ = Vϕ,expt − Vϕ,calc).

Figure 2. Temperature dependence of apparent molar volumes of (a) Li2SO4 at m/mol·kg−1 = 0, 0.2, 0.7, 1.5, 2.7 (bottom to top); and (b) LiTf at m/mol·kg−1 = 0, 0.1, 2.0, 5.9, and 9.6 (bottom to top).

Table 5. Debye−Hückel Limiting Slopes (AV) and Standard Molar Volumes (Vo) for Li2SO4(aq) and LiTf(aq) at Experimental Temperatures and Pressure p = 0.1 MPaa T K 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

Vo(Li2SO4)

AV −1.5

cm ·mol 3

·kg

0.5

1.8218 1.8979 1.9800 2.0685 2.1639 2.2665 2.3768 2.4951 2.6220 2.7577 2.9028

−1

cm ·mol 3

12.20 12.61 12.87 12.98 12.96 12.83 12.58 12.23 11.79 11.26 10.65

Vo(LiTf) cm3·mol−1 73.92 74.39 74.82 75.22 75.60 75.96 76.29 76.61 76.90 77.18 77.45

a

Standard uncertainties u are u(p) = 1 kPa (level of confidence = 0.68), and the combined expanded uncertainty Uc is Uc(Vo) = 0.05 cm3·mol−1 (level of confidence = 0.95).

the upper boxes of Figures 3 and 4. Maximum deviations between the experimental Vϕ values and those calculated from eq 2 using the parameters in Tables 5 and 6 were always ≤ ±0.03 cm3·mol−1 (for Li2SO4(aq)) or ≤ ±0.05 cm3·mol−1 (for LiTf(aq)). As expected, the largest deviations mostly occur at low m where ρ → ρw. For Li2SO4(aq) the expressions for Vo and the empirical parameters YV took the following forms (where τ = T/1000):

Figure 3. Lower box: apparent molar volumes of Li2SO4(aq) as a function of molality (√m) at 293.15 K (●), 313.15 K (blue ⧫), and 343.5 K (red ■); lines were calculated from eq 2 using the parameters from Tables 5 and 6. Upper box: deviations of the experimental volumes from those calculated via eq 2 (ΔVϕ = Vϕ, expt − Vϕ, calc).

12.6 and 74.4 cm3·mol−1 for Li2SO4 and LiTf respectively are in good agreement with the corresponding ionic volumes listed by Marcus,1 which sum to 12.2 and 74.6 cm3·mol−1. The number of fitting parameters for each solute was determined by the statistical F-test rejecting the hypothesis that an additional parameter would improve the goodness of fit at the α = 0.05 significance level, assuming random errors only. The abilities of eq 2 to fit the data over the investigated ranges of molality and temperature are illustrated as deviation plots in E

V o = a1τ −3 + a 2τ −1 + a3τ 2

(3)

B V = a4 ln τ + a5τ −3 + a6τ −1

(4)

C V = a 7τ 2 + a8τ −3

(5)

D V = a 9τ −3 + a10τ 2

(6) DOI: 10.1021/acs.jced.6b00519 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


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have been observed for other triflate salts and have been attributed to the formation of hydrate-like structures.25,26 Comparisons with Literature Data. As noted in the Introduction no previous studies on the volumetric properties of LiTf(aq) solutions appear to have been published. Those for Li2SO4(aq) are summarized in Table 1. While the differences among the data reported were noted in the Introduction, it is also apparent (Figure 1) that a number of these studies10,12,16 agree reasonably well with each other. At 293.15 and 298.15 K (Figure 5) they are also in good agreement with the present results at most molalities.

Table 6. Fitting Parameters for eqs 3 to 7 for Li2SO4(aq) parameter

estimate

standard error

a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11

−1.5135 28.958 −307.60 −465.7 2.135 −193.3 131.7 −0.1554 0.0329 −53.2 8.45

0.0037 0.062 0.78 3.8 0.017 1.6 2.3 0.0044 0.0016 1.6 0.41

E V = a11τ 2

(7)

The values of the 11 adjustable parameters ai obtained from fitting the Vϕ data are given in Table 6. Using eq 2 with the appropriate parameter values listed in Tables 5 and 6, enables Vϕ to be described to within ±0.03 cm3·mol−1 over the whole concentration and temperature matrix. Values of Vϕ for LiTf(aq) were calculated from the experimental densities (Table 4) using eq 1. The expressions for Vo and the empirical parameters YV took the following forms: V o = a1 + a 2τ −3

B V = a3τ

(8)

3

(9) 2

C V = a4τ + a5τ + a6τ

−1

Figure 5. Deviations of selected literature data for Vϕ(Li2SO4) from the present results at 293.15 and 298.15 K: ●, Hervello and Sánchez16 at 293.15 K; ○, Herevello and Sánchez16 at 298.15 K; red ◊, Pearce and Eckstrom10 at 298.15 K; blue ⧫, Puchkov et al.12 at 298.15 K; ΔVϕ = Vϕ,lit − Vϕ,pw. The vertical dashed line represents the upper concentration limit of the present data.

(10)

D V = a 7 /ln τ + a8τ −2

(11)

E V = a 9 /ln τ + a10τ −2

(12)

The values of the adjustable parameters ai obtained from fitting the Vϕ values are given in Table 7.

On the other hand, the agreement at temperatures above 298.15 K is rather poor (Figure 6). Thus, the 1995 data of Cartón et al.14 show scattered deviations of up to ±0.5 cm3·mol−1, with

Table 7. Fitting Parameters for eqs 8 to 12 for LiTf(aq) parameter

estimate

standard error

a1 a2 a3 a4 a5 a6 a7 a8 a9 a10

83.281 −0.23577 −79.33 10.32 4.07 −0.68 1.312 0.073 −0.1642 −0.00998

0.015 0.00046 0.75 0.38 0.49 0.02 0.041 0.003 0.0069 0.00053

The variations of Vϕ with temperature for the two salts are quite different. Thus, Vϕ(Li2SO4) shows a flat but clearly defined maximum at ≈313 K (Figure 2a) that is almost independent of concentration. In contrast Vϕ(LiTf) increases monotonically with increasing T at all molalities (Figure 2b), differing relatively little with changing m. Differences between the two salts are also evident in plots (Figures 3 and 4) of Vϕ against molality (√m), with Vϕ(LiTf) showing a most unusual “kink” at m ≈ 1 mol·kg−1 that becomes more apparent at lower temperatures while Vϕ(Li2SO4) increases monotonically with increasing m at all temperatures. Similar unusual dependences of Vϕ on molality

Figure 6. Deviations from the present results of a broad selection of literature data for Vϕ(Li2SO4) at various temperatures: ●, Cartón et al.14 at (293.15−338.15) K; violet ○, Aseyev and Zaytsev18 at (293.15− 343.15) K; red ◊, Söhnel and Novotný17 at (293.15−343.15) K; blue ⧫, Maksimova et al.13 at (293.15−333.15) K; green ▲, Puchkov et al.12 at (308.15 and 323.15) K. Note that larger deviations (Aseyev and Zaytsev18 up to +10 cm3·mol−1, Söhnel and Novotný17 down to −4 cm3· mol−1, Puchkov et al.12 up to +5 cm3·mol−1) have been omitted for representational convenience. F



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an average deviation of ±0.2 cm3·mol−1. The data of Puchkov et al.12 and Maksimova et al.13 and the smoothed values of Söhnel and Novotný,17 and Aseyev and Zaytsev18 show deviations of magnitudes up to +5, −4, and +10 cm3·mol−1, respectively. The broad consistency of the present data with many of the previous experimental investigations10,12,16 (Figure 5) indicates that reasonable confidence can be placed in the present findings and that the smoothed values proposed by Sö hnel and Novotný17 and by Aseyev and Zaytsev18 are in error at m < ca. 1 mol·kg−1 at all temperatures. Comparisons with Related Electrolytes. Figure 7 plots the present apparent molar volumes of Li2SO4(aq) along with its

Figure 8. Apparent molar volumes of LiTf (green ●, this work); NaTf (blue ▲);26,30 HTf (red ⧫)25 as a function of molality at 298.15 K and atmospheric pressure.

Effects of Ion Size on Electrolyte Behavior. It is well established that the geometric size of an ion, commonly expressed in terms of its crystallographic radius, is the major contributor to its volume in solution, at least at near-ambient temperatures.34,35 The effects of cation and anion size on the behavior of Vϕ as a function of molality at 298.15 K are shown in Figures 9 and 10 for a series of univalent sulfate and lithium salts,

Figure 7. Apparent molar volumes of aqueous solutions of the alkali metal sulfates at 298.15 K and atmospheric pressure as a function of molality: Na2SO4 (blue ⧫);27,28 Li2SO4 (green ●, present work); K2SO4 (red ■);28 Cs2SO4 (▲).29 Addends have been used for K2SO4 (−15 cm3·mol−1) and Cs2SO4 (−30 cm3·mol−1) for representational convenience.

alkali metal congeners, for which reasonable quality volumetric data are available from the literature. All salts exhibit similar, almost parallel, concentration dependences but Vϕ(Li2SO4) and Vϕ(Na2SO4) show a clear “crossover” at m ≈ 0.4 mol·kg−1, which will be discussed below. Unfortunately, of the other alkali metal triflates, only Vϕ(NaTf) values are available25,26,30 and then only to m ≈ 1.7 mol·kg−1. These results are plotted along with the present Vϕ(LiTf) values in Figure 8. As for the corresponding sulfate salts (Figure 7), Vϕ(LiTf) and Vϕ(NaTf) exhibit a clear crossover, albeit at m ≈ 0.6 mol·kg−1. Also shown in Figure 8 are the Vϕ(HTf) values of Tremaine et al.,25,26 whose dependence on molality is broadly similar to that of Vϕ(LiTf). This behavior parallels that observed for the apparent molar heat capacities of the aqueous solutions of these two salts.19 The crossovers of Vϕ(LinX) and Vϕ(NanX) in Figures 7 and 8 are at first glance apparently inconsequential. However, such differences, of similar magnitude and occurring at roughly similar molalities, have been noted previously for the Vϕ values of the Na+ and Li+ salts of Cl−, Br−, and ClO4− (see Figure 7 of ref 20). This phenomenon is also evident in the apparent molar heat capacities, Cpϕ, for the Na+ and Li+ salts of SO42−, ClO4−, and Tf−19 and therefore seems to be rather general. Because ion pairing is probably not significant in these essentially strong electrolyte systems,31 the most likely explanation is that it arises from differences in the hydration of Li+(aq)32 and Na+(aq).33 As discussed previously,19,20 such an interpretation is consistent with dielectric spectroscopic data.

Figure 9. Departures of Vϕ from the Debye−Hückel limiting law (dashed line) for selected alkali metal sulfates at 298.15 K and 0.1 MPa pressure: Li2SO4 (present work, green ●); Cs2SO4 (▲);29 K2SO4 (red ■);28 Na2SO4 (blue ⧫).27,28

respectively. To facilitate comparison, the data are plotted as departures from the Debye−Hückel limiting law (Vϕ − Vo − ωAV√m). Cation size does not appear to have a systematic effect on the concentration dependence of Vϕ(M2SO4(aq)). Thus, the curves in Figure 9 follow an irregular sequence with Vϕ magnitudes in the order: Li+(69) < Na+(102) ≈ K+(138) > Cs+(170), where the numbers in parentheses are the crystallographic ionic radii in pm.1 It is possibly noteworthy that Li2SO4(aq) is the only sulfate salt with negative deviations from the limiting Debye−Hückel line. In contrast to the cations, the effect of anion size on the concentration dependence of (Vϕ − Vo − ωAV√m) is systematic, following the order: OH−(133) > Cl−(181) > Br−(196) > ClO4−(240) > I−(220) > Tf−, with only I− out of sequence. G



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Figure 10. Departures of Vϕ from the Debye−Hückel limiting law (dashed line) for selected univalent lithium salts at 298.15 K: LiTf (present work, green ●); LiI (blue ⧫);36 LiClO4 (▲);20 LiBr (purple line);37 LiCl (red ■);38 LiOH (◊).39

Figure 11. Calculated isobaric expansibilities, α = −(∂ ln ρ/∂T)p, of aqueous solutions of Li2SO4 (blue lines) and LiTf (red lines) as a function of ionic strength, I, at temperatures from 293.15 to 343.15 K (bottom to top for each salt) at 5 K intervals.

(Marcus1 does not list a radius for Tf− but on the basis of geometric considerations and its molar volume in solution1 it can be safely assumed to be considerably larger than ClO4−.) Note that almost identical sequences for cations and anions are obtained if Vo values are substituted for ionic radii, which suggests that anion size is indeed the critical factor in determining the sequence in Figure 10. It is possible that the systematic variation of the data in Figure 10 with anion size might reflect differences in ion association. This is because Vϕ(MX) normally increases with increasing association due to the release of water molecules from the hydration shells of the ions as a result of charge neutralization.31,40 Certainly, LiOH(aq) is known to be significantly associated41 while LiCl appears to be slightly associated at high concentrations;32 however, the other salts in Figure 10 are not known to be appreciably associated. The absence of a similar effect for cations (at least for the sulfate salts, Figure 9) may reflect the subtle interplay between ion hydration and very weak ion association, bearing in mind that MSO4−(aq) species, insofar as they form, are almost certainly solvent-separated ion pairs.31,33 In this context it would be of interest to have the appropriate data for other alkali metal triflate salts that, unlike their perchlorate counterparts, are all reasonably soluble in water.5 Temperature Effects. The variation of Vϕ with temperature is summarized in Figure 2 for both Li2SO4 and LiTf. An alternative way of representing the volumetric effects of temperature is via the isobaric expansibility, α = −(∂ ln ρ/ ∂T)p. The values of this quantity, calculated using the relevant parameters from Tables 5 and 6, are summarized in Figure 11. The shapes of the curves for the two salts are distinctively different. The effect of added LiTf on α is that of a structurebreaker. Thus, at lower temperatures, increasing the molality of LiTf, causes the solution to become considerably more expandable than pure water. At higher temperatures added LiTf contributes little to the already-disrupted water structure. The effect of added Li2SO4 appears to be exactly opposite (Figure 11). While there is little difference between the expandability of pure water and the concentrated solutions at lower T, at higher T the added Li2SO4 more than counteracts the loosening of the solvent structure, making the solutions significantly less expandable. This indicates that Li2SO4(aq) acts as structure maker and therefore that the hydration of SO42−

and Tf− is very different. Of course such effects may to some extent reflect differences in ion association, particularly at higher temperatures where LiSO4−(aq) is likely to form to a greater extent.41

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CONCLUSIONS Densities of aqueous solutions of lithium sulfate and lithium triflate, and the apparent molar volumes derived from them, show smooth dependencies on solute molality and temperature over wide ranges. However, the nature of these dependences is quite different for the two salts. The molar volumes for both salts can be fitted with high precision using an extended Redlich− Rosenfeld−Meyer equation. The present data for Li2SO4(aq) reveal that the densities listed in standard compilations are unreliable, especially at low-to-intermediate molalities (m ≤ ca. 1.0 mol·kg−1) and at higher temperatures (T ≥ 343 K). Comparisons of the present volumetric data with those of related salts reveal several interesting features: a crossover in Vϕ(LinX) and Vϕ(NanX) at m ≈ 0.5 mol·kg−1, and that anion, but not cation, size seems to influence departures of Vϕ from Debye− Hückel limiting law behavior.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +61 8 93602226. Funding

H.B. thanks the Natural Science Foundation of Qinghai Province (Project 2012-Z-917Q) and the Youth Innovation Promotion Association of the Chinese Academy of Sciences for financial support. This work was otherwise funded by Murdoch University. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Profs Vladimir Valyashko (Moscow), Richard Buchner (Regensburg) and Peter May (Murdoch) for providing key literature references and data. H



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