Densities and Molar Volumes of Aqueous Solutions of Li2SO4 at

Article pubs.acs.org/jced

Densities and Molar Volumes of Aqueous Solutions of Li2SO4 at Temperatures from 343 to 573 K Lubomir Hnedkovsky,*,† Bin Hu,†,‡ and Glenn Hefter† †

Chemistry Department, Murdoch University, Murdoch, WA 6150, Australia CAS Key Laboratory of Salt Lake Resources and Chemistry, Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, Xining 810008, China

‡

S Supporting Information *

ABSTRACT: Densities of aqueous solutions of lithium sulfate (Li2SO4) at solute molalities ranging from 0.05 to 2.7 mol·kg−1 have been measured by vibratingtube densimetry over the temperature range 373.15 ≤ T/K ≤ 573.15 at pressures close to the saturated vapor pressure of pure water. The apparent molar volumes (Vϕ) of Li2SO4(aq) calculated from these data together with previously published data at 323.15 and 343.15 K were fitted using a modified Redlich−Rosenfeld− Meyer equation, which in turn was used to extrapolate the experimental data to infinite dilution to obtain the standard partial molar volumes. A comparison of the present and literature data revealed the latter are inaccurate at low concentrations and are increasingly unreliable at higher temperatures. The combination of the present results with selected literature data produced a reliable equation of state for Li2SO4(aq) covering the temperature and pressure ranges 323.15 ≤ T/K ≤ 573.15 and 0.1 ≤ p/MPa ≤ 40. The volumetric behavior of Li2SO4(aq) was found to differ dramatically from that of Na2SO4(aq) and K2SO4(aq), especially at higher temperatures, higher concentrations, and lower pressures, reflecting the exceptional character of lithium ion hydration. Isobaric expansibilities indicated that Li2SO4(aq) remains a water structure maker over the investigated conditions.

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for the densities of Li2SO4(aq) at elevated temperatures9−13 are listed in Table 1. Of the various experimental investigations at T > 343 K, the approximate pycnometric data of Maksimova et al.10 at T ≤ 363 K are of historic interest only. A representative plot (at T = 373 K) of the remaining studies, with the data expressed as apparent molar volumes, is given in Figure 1; similar plots are obtained at other temperatures. As can be seen, the scatter among the various independent studies is quite large, especially at lower concentrations. Of particular note are the differences between the values listed in the well-known compilations of Söhnel and Novotný11 and of Aseyev and Zaytsev,12 which at this temperature are up to 6 cm3·mol−1. Such differences are well outside the expected experimental uncertainties.7 Given that for Li2SO4(aq) the databases for these two compilations11,12 would be expected to be very similar, if not identical, such large discrepancies most probably result from insufficiently constrained extrapolations beyond the limits of the experimental data rather than simple typographical errors. The remaining high temperature experimental studies (Table 1), of Puchkov et al.9 and of Abdulagatov and Azizov,13 are also in rather poor agreement (Figure 1). The quantification of the volumetric properties of Li2SO4(aq) at high temperatures is manifestly unsatisfactory. Accordingly, this paper presents a study of the densities and

INTRODUCTION Aqueous solutions of lithium sulfate, Li2SO4(aq), are of ongoing interest because they have wide application in the extraction, synthesis, and recycling of the strategically critical lithium element and its compounds.1−4 For example, such solutions frequently represent a key intermediate stage in the extraction of lithium values from spodumene (the main mineral source of lithium) and other Li-containing minerals.1,2 They are also encountered in the processing of naturally occurring Lirich brines (which currently provide about 2/3 of global production),1,2 in aqueous Li batteries,5 and in the recycling of most types of spent Li batteries.3,4 Many of these processes involve the formation of Li2SO4(aq) at high temperatures (up to 650 K in some situations).1 Of the various properties utilized for process control and optimization, solution densities are of particular relevance. Such data are a prerequisite for reliable mass transfer calculations and are needed for the interconversion of concentration units.6 It follows that precise knowledge of the densities of Li2SO4(aq) over wide ranges of concentration, temperature and pressure is of considerable technological interest. Scientifically, the volumetric characteristics of electrolyte solutions such as Li2SO4(aq) are also of interest because of the insights they provide into the nature of these solutions.7 The volumetric properties of Li2SO4(aq) at temperatures up to 343 K and concentrations up to near-saturation have been reviewed and quantified in an earlier paper from this laboratory.8 For convenience the available literature sources © 2017 American Chemical Society

Received: June 21, 2017 Accepted: August 16, 2017 Published: August 29, 2017 3593

DOI: 10.1021/acs.jced.7b00570 J. Chem. Eng. Data 2017, 62, 3593−3602

Journal of Chemical & Engineering Data

Article

Table 1. Literature Sources for the Densities of Aqueous Solutions of Lithium Sulfate at Temperatures T ≥ 343 K conditions authors

year

method

temperature (K)

pressure (MPa)

concentration (mol·kg−1)

Puchkov et al.9 Maksimova et al.10 Söhnel and Novotný11 Aseyev and Zaytsev12 Abdulagatov and Azizov13

1976 1984 1985 1996 2003

hydrostatic balancea pycnometry compilation compilation piezometer

298−573 293−363 283−373 283−373 297−573

b 0.1 0.1 0.1 3.9−40

0.005−2.77 0.09−2.87 0.19−2.56 0.19−2.87 0.09−0.9

Pycnometric measurements are also reported at 298 ≤ T/K ≤ 363. bPressure not specified, but on the basis of the densities reported for pure water, it is probably 0.1 MPa at 298 ≤ T/K ≤ 373 and the saturated vapor pressure of water at 373 ≤ T/K ≤ 573.

a

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EXPERIMENTAL SECTION Reagents. Details of the sources and purities of the chemicals used in this study are summarized in Table 2. Briefly, a concentrated (near-saturated) stock solution of Li2SO4(aq) solution was prepared by neutralizing solid Li2CO3 with H2SO4, heating to near boiling, sparging with nitrogen gas to remove CO2, and filtering (0.45 μm). Further details are given elsewhere.15 The main impurities in Li2CO3(s) as stated by the manufacturer were sulfate anions (≤0.3 mass %) and sodium cations (≤0.1 mass %). The presence of moderate amounts of Na+ has a negligible effect on the apparent molar volume of lithium salts. The stock solution of Li2SO4(aq) was analyzed in triplicate by evaporative gravimetry, initially at 60 °C, then overnight at 190 °C under reduced pressure (p ≈ 5 Pa); the concentration of the solute was reproducible to ±0.01% (relative). Further checks on the accuracy of the concentrations of the solutions employed are described elsewhere,15 but taking all factors into account the overall relative uncertainty is estimated to be ±0.05%. 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 the custom-built vibrating-tube densimeter described in detail previously.16 The temperature of the vibrating tube was controlled to ±0.002 K and measured using a secondarystandard platinum resistance thermometer (Burns Engineering, USA) with an accuracy of 0.02 K. Pressure within the densimeter was maintained via a thermostated back-pressure regulator (Dresser Grove Mity-Mite, USA, model 91XW) and measured by a pressure transducer (GE Druck, USA, model 282 DPI) calibrated by the manufacturer, with a stated uncertainty of 0.1%. The calibration constant of the densimeter was determined at each temperature and pressure, using the known densities of two fluids. The calibrating fluids were pure water17 and four solutions of NaCl(aq),18 of accurately known molalities: m/ mol·kg−1 ≈ 3, 4, 5, and 6, for all temperatures except 573.15 K. At this temperature the densities of highly concentrated NaCl(aq) solutions calculated via Archer’s equation18 are not sufficiently reliable,19 and thus, gaseous nitrogen20 (Linde, 99.99%) was used as the second calibrating fluid. The calibration constant at 573.15 K so obtained was then checked

Figure 1. Present and selected literature values for the apparent molar volume, Vϕ, of Li2SO4(aq) as a function of solute molality (√m) at 373.15 K and 0.1 MPa pressure: ●, this work; blue ◆, Aseyev and Zaytsev;12 ×, Abdulagatov and Azizov;13 green ▲, Söhnel and Novotný;11 red ■, Puchkov et al.9 The line is a fit of the present data using eq 3.

molar volumes of well-characterized aqueous solutions of Li2SO4 at concentrations approaching the solubility limit14 and over the temperature range 373 ≤ T/K ≤ 573 at close-tosaturation pressures using a purpose-built vibrating-tube densimeter. These data represent a significant extension of our previous study8 of the aqueous solutions of this key salt, which was restricted to T ≤ 343 K and p = 0.1 MPa. Table 2. Sample Sources and Purities chemical name [CAS RN]

source

lithium sulfate [10377-48-7] lithium carbonate [554-13-2] sulfuric acid [7664-93-9]

synthesis Aldrich Merck

initial mass fraction purity

purification method

final mass fraction purity

analysis method

0.9995

evaporative gravimetry

≥0.99 ≥0.98

neutralization reaction, filtration none none 3594



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Table 3. Experimental Density Differences, Δρ = ρ − ρw, and Apparent Molar Volumes, Vϕ, of Li2SO4(aq) at Molalities, m, Temperatures 373.15 ≤ T/K ≤ 573.15 K, Pressures, p; Along With Values Extrapolated to the Saturated Vapour Pressure of Water, psata experimental pressure m (mol·kg−1)

Δρ (kg·m−3)

Vϕ (cm3·mol−1)

saturated vapor pressure Uc(Vϕ) (cm3·mol−1)

Δρ (kg·m−3)

Vϕ (cm3·mol−1)

Uc(Vϕ) (cm3·mol−1)

T = 373.15 K

0.10081 0.20240 0.40250 0.50752 0.70609 0.99690 1.5033 2.0008 2.6814

0.10081 0.20240 0.40250 0.50752 0.70609 0.99690 1.5033 2.0008 2.6814

0.05013 0.07004 0.10081 0.20240 0.40250 0.49930 0.50752 0.70609 0.99690 1.5033 2.0008 2.6814

0.05013 0.07004 0.10081 0.20240 0.40250 0.49930 0.70609 0.99690 1.5003 2.0008 2.6814

9.670 19.08 37.02 46.31 63.23 87.31 127.12 163.83 210.65

p = 0.30 MPa ρw = 958.442 kg·m−3 10.24 11.92 14.10 14.73 16.22 17.81 20.06 21.89 23.98

10.29 20.20 39.02 48.73 66.39 91.43 132.61 170.33 218.37

p = 0.90 MPa ρw = 917.249 kg·m−3 −1.32 1.27 4.51 5.51 7.62 9.93 13.17 15.80 18.68

5.787 7.993 11.34 22.02 42.15 51.53 52.40 71.05 97.33 140.34 179.72 229.50

p = 2.00 MPa ρw = 864.998 kg·m−3 −26.94 −25.12 −22.81 −17.78 −12.20 −10.16 −10.21 −6.77 −2.98 2.07 5.89 10.10

6.660 9.129 12.86 24.62 46.49 56.65 77.44 105.48 150.78 191.93 243.92

p = 5.00 MPa ρw = 800.085 kg·m−3 −69.48 −65.38 −60.82 −50.97 −40.59 −37.13 −30.87 −24.57 −16.42 −9.98 −3.54

0.10 0.10 0.10 0.09 0.09 0.09 0.08 0.08 0.07 T = 423.15 K

0.12 0.12 0.11 0.11 0.10 0.10 0.09 0.09 0.08 T = 473.15 K

0.15 0.15 0.15 0.14 0.13 0.13 0.13 0.12 0.12 0.11 0.10 0.09 T = 523.15 K

0.21 0.20 0.20 0.18 0.17 0.17 0.16 0.15 0.13 0.12 0.11

3595

9.665 19.07 36.99 46.27 63.17 87.21 126.95 163.58 210.27

psat = 0.10 MPa ρw = 958.349 kg·m−3 10.29 11.96 14.17 14.80 16.30 17.90 20.16 22.01 24.11

0.11 0.12 0.10 0.10 0.10 0.10 0.09 0.09 0.08

10.29 20.20 39.03 48.74 66.41 91.46 132.67 170.43 218.53

psat = 0.48 MPa ρw = 917.008 kg·m−3 −1.36 1.23 4.46 5.46 7.56 9.87 13.11 15.73 18.60

0.12 0.12 0.12 0.11 0.11 0.11 0.10 0.09 0.09

5.780 7.985 11.32 22.01 42.14 51.53 52.40 71.08 97.41 140.57 180.14 230.23

psat = 1.55 MPa ρw = 864.658 kg·m−3 −26.83 −25.03 −22.74 −17.76 −12.23 −10.22 −10.27 −6.87 −3.13 1.85 5.62 9.77

0.16 0.16 0.16 0.14 0.14 0.14 0.14 0.13 0.13 0.13 0.13 0.12

6.629 9.090 12.81 24.55 46.44 56.64 77.54 105.81 151.68 193.60 246.87

psat = 3.98 MPa ρw = 798.895 kg·m−3 −68.94 −64.91 −60.44 −50.81 −40.74 −37.39 −31.33 −25.27 −17.41 −11.20 −5.02

0.26 0.25 0.23 0.20 0.19 0.19 0.20 0.22 0.23 0.24 0.26



Article

Table 3. continued experimental pressure −1

m (mol·kg )

−3

Δρ (kg·m )

saturated vapor pressure −1

Vϕ (cm ·mol ) 3

−1

Uc(Vϕ) (cm ·mol ) 3

−3

Δρ (kg·m )

Vϕ (cm3·mol−1)

Uc(Vϕ) (cm3·mol−1)

T = 573.15 K

0.05013 0.07004 0.10081 0.20240 0.40250 0.49930 0.70609

8.165 11.08 15.44 28.99 53.63 64.79 87.57

p = 10.00 MPa ρw = 715.288 kg·m−3 −162.71 −153.04 −142.44 −121.22 −99.19 −91.55 −78.96

0.31 0.30 0.29 0.27 0.24 0.23 0.22

8.087 10.99 15.33 28.87 53.52 64.75 87.70

psat = 8.59 MPa ρw = 712.138 kg·m−3 −161.79 −152.55 −142.38 −121.86 −100.21 −92.80 −80.54

0.35 0.33 0.30 0.31 0.34 0.36 0.38

a Standard uncertainties, u, are u(T) = 0.02 K, u(p) = 0.01 MPa, ur(m) = 0.0005, ur(Δρ) = 0.001 (level of confidence = 0.68), and for the combined expanded uncertainty Uc(Vϕ) level of confidence = 0.95.

by measuring the densities of 2 and 3 mol·kg−1 NaCl(aq), which agreed well with the interpolated experimental values reported previously.19 The densities of the calibrating solutions of NaCl(aq) were checked regularly at 298.15 K using an Anton Paar (Austria) densimeter DMA5000 and agreed with those calculated via Archer’s equation18 to within 0.002% (relative). As discussed in more detail elsewhere,16 the overall uncertainty in the densimeter calibration constant is thought to be 0.1% or better for all experimental conditions. Measurements at 573.15 K were made only up to 0.7 mol·kg−1 to minimize a risk of solid Li2SO4 formation in the vibrating tube due to the diminished solubility of Li2SO4 at high temperatures.14

Table 3 together with the estimated combined uncertainties, Uc(Vϕ). The variation of Vϕ with temperature at psat at selected solution concentrations is presented in Figure 2. The observed

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RESULTS AND DISCUSSION Densities and Apparent Molar Volumes of Aqueous Solutions of Lithium Sulfate. The present experimental density differences, Δρ = (ρ − ρw), between Li2SO4(aq) and water are summarized in Table 3. The densities of pure water, ρw, were calculated from the IAPWS-95 formulation17 and for convenience are also listed in Table 3. Solution densities, ρ, can be trivially calculated using the observed values of Δρ and ρw at the specified experimental conditions (T, p). Apparent molar volumes (Vϕ) of Li2SO4(aq) were calculated from the experimental densities (Table 3) using the usual relationship:

(1)

Figure 2. Temperature (T) dependence of apparent molar volumes, Vϕ, of Li2SO4(aq) at molalities m/mol·kg−1 = 0, 0.1, 0.7, 1.5, and 2.7 (bottom to top): blue symbols, present work; red symbols, previous work at 323 K ≤ T ≤ 343 K.8 Solid lines are fits of eq 3; the dotted lines at higher molalities represent extrapolations of Vϕ beyond the experimental matrix; the dashed line represents the values of Vϕ at infinite dilution.

where ρ and ρw are respectively the densities of the solution and of pure water at a specified temperature and pressure, m is the molality of the solution, and Ms = 110.00 g·mol−1 is the molar mass of the solute calculated using the current IUPAC atomic masses.21 To prevent an accidental pressure drop, and thus possible solid phase formation in the vibrating tube, the experimental pressure was maintained slightly above psat, the saturated vapor pressure of pure water. Densities at psat were obtained from the experimental values by an appropriate correction using the pressure derivative of the density data of Abdulagatov and Azizov13 (see later). The corrections applied to Vϕ were of the same magnitude (averaging ±0.1 cm3·mol−1) as the experimental uncertainty at T ≤ 473 K but became significant (ranging from −0.9 to +1.6 cm3·mol−1) at higher temperatures. The values of Δρ and Vϕ corrected to psat are also recorded in

behavior is similar to that of other aqueous strong electrolyte solutions22 with Vϕ becoming strongly negative at high temperatures. This pattern is generally attributed to the increasing compressibility of the solvent and its decreasing dielectric constant with increasing temperature. Both of these effects result in increasing electrostriction of the solvent molecules by the electric fields of the ions. Previous measurements of Vϕ at 323.15 and 343.15 K and atmospheric pressure8 in our laboratory are also included in Figure 2. The consistency between the two data sets is excellent. The concentration dependence of Vϕ becomes very steep at high temperatures. This is better seen in Figure 3, which plots Vϕ(Li2SO4(aq)) against √m at various temperatures. The amelioration of the effects of temperature with increasing solute molality is thought to arise from ion pairing effects (which reduce electrostriction) and the hard-sphere character of the

Vϕ =

ρ − ρw Ms − ρ mρρw

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where ai are adjustable parameters and φi are the basis functions. The number of fitting parameters was determined via the Bayesian information criterion (BIC),24 combined with a stepwise exclusion of all parameters/functions that were statistically insignificant at the 95% confidence level (i.e., with a |t-statistic| 373 K the saturated vapor pressure may be a more suitable independent variable than temperature Comparisons with Literature Data. For the purposes of comparison, the available literature data for Vϕ(Li2SO4(aq)) were divided into two subsets: those measured at T ≤ 373.15 K at 0.1 MPa, and those measured at higher temperatures along the saturation-pressure line. The deviations from the present values of Vϕ of the first (0.1 MPa) subset are shown in Figure 5. The differences are quite large, especially at lower m which, as is well-understood, is mostly due to a lack of resolution in the density measurements.7

(2)

∑ aiφi(ρw , AV , m)

−429.74 −1.2178 410.22 40.03 −20.055 10.13 −245.99 250.09 −10.405 22.126 −27.349 8.793 −1.842 −0.9362 0.3160 −0.2288

σ(ai)a

a Standard error at the 95% confidence level. bUnits are Vϕ/cm3·mol−1, ρw/g·cm−3, m/mol·kg−1, and Av/cm3·mol−1.5·kg0.5.

Vϕ = V o + ωAV m0.5 + B V m + C Vm1.5 + D V m2 + E V m2.5

Vϕ = ωAV m0.5 +

ai

(3) 3597



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Figure 5. Deviations, δVϕ = Vϕ,lit − Vϕ,pw, of literature data for Li2SO4(aq) from the present results (pw) at T ≤ 373.15 K and 0.1 MPa: blue +, Söhnel and Novotný11 from 343 to 373 K; ○, Aseyev and Zaytsev12 from 343 to 373 K; red ◆, Maksimova et al.10 at 353 and 363 K; green ▲, Puchkov et al.9 from 348 to 373 K.

markedly with the average density deviation of the present work of 0.045 kg·m−3. Apart from their lack of precision, the data of A−A and Puchkov et al. exhibit noticeable systematic trends (cf. the present data) toward lower densities. Because of these large disparities, the densities, rather than the much more sensitive Vϕ values, are compared with the present work in Figure 6. While the deviations shown are broadly consistent with the claimed average uncertainties in the densities (0.06% for A−A13 and 3 kg·m−3 for Puchkov et al.9), they reveal their systematic character. The A−A data were analyzed further to try to uncover the source of disagreement from the present results. First, the

Figure 4. Deviations, δVϕ = Vϕ,exp − Vϕ,fit, of experimental apparent molar volumes from those calculated via fitting eq 3, as a function of the experimental temperature, T, (upper box) and of the experimental molality, m, (lower box): blue ◆, present work; red ◇, ref 8.

At higher temperatures (T > 373.15 K) the agreement between the literature and present values is also poor, with a high degree of scattering. When fitted as separate data sets, the average deviation in density was 0.25 kg·m−3 for the data of Abdulagatov and Azizov (hereafter: “A−A”)13 and 0.70 kg·m−3 for those reported by Puchkov et al.9 These values contrast

Table 5. Standard Molar Volumes (Vo), Debye−Hückel Limiting Slopes (AV), Fitting Parameters YV (eq 2a) for Li2SO4(aq), and the Saturated Vapour Pressure of Pure Water (psat) at Rounded Temperatures (T)

a

T (K)

psat (MPa)

343.15 353.15 363.15 373.15 383.15 393.15 403.15 413.15 423.15 433.15 443.15 453.15 463.15 473.15 483.15 493.15 503.15 513.15 523.15 533.15 543.15 553.15 563.15 573.15

0.101 0.101 0.101 0.101 0.143 0.199 0.270 0.362 0.476 0.618 0.792 1.003 1.255 1.555 1.908 2.320 2.797 3.347 3.976 4.692 5.503 6.417 7.442 8.588

Vo (cm3·mol−1) 10.59 9.10 7.31 5.20 2.77 −0.01 −3.17 −6.75 −10.77 −15.31 −20.43 −26.21 −32.74 −40.16 −48.62 −58.32 −69.53 −82.59 −97.97 −116.29 −138.47 −165.81 −200.36 −245.38

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.15 0.18 0.20 0.22 0.24 0.25 0.25 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.27 0.27 0.28 0.30 0.31 0.34 0.37 0.40 0.44 0.49

AV

BV

CV

DV

EV

2.9035 3.2248 3.5918 4.0113 4.4911 5.0414 5.6741 6.4044 7.2510 8.2371 9.3922 10.754 12.370 14.303 16.635 19.476 22.975 27.337 32.854 39.946 49.239 61.696 78.859 103.32

−11.095 −12.891 −14.910 −17.196 −19.799 −22.788 −26.245 −30.282 −35.037 −40.693 −47.487 −55.736 −65.859 −78.423 −94.205 −114.28 −140.18 −174.10 −219.26 −280.54 −365.54 −486.49 −663.92 −934.04

8.7449 9.9800 11.409 13.067 15.000 17.267 19.944 23.129 26.950 31.578 37.236 44.228 52.966 64.017 78.176 96.575 120.85 153.44 198.01 260.30 349.50 480.97 681.46 1000.1

−3.0423 −3.4840 −4.0123 −4.6456 −5.4070 −6.3260 −7.4406 −8.8002 −10.469 −12.533 −15.104 −18.337 −22.440 −27.706 −34.544 −43.543 −55.564 −71.897 −94.521 −126.57 −173.14 −242.96 −351.53 −528.14

0.33955 0.40476 0.48530 0.58475 0.70769 0.85998 1.0492 1.2852 1.5809 1.9535 2.4257 3.0286 3.8046 4.8124 6.1349 7.8908 10.253 13.481 17.967 24.332 33.579 47.402 68.785 103.29

Units for eq 2 are Vϕ/cm3·mol−1 and m/mol·kg−1. 3598



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accurate densities of the present work at psat enables the present data to be extended to much higher pressures. This approach provides more reliable density values for Li2SO4(aq) in the compressed-liquid region than those obtained directly from A−A’s results. The procedure can be thought of as shifting each isotherm and isopleth in A−A’s density set to intersect with the present data near psat (Figure 8). All such

Figure 6. Deviations in densities, δρ = ρlit − ρpw, of literature data for Li2SO4(aq) from the present results at psat and the reported temperatures and molalities: blue ◆, Puchkov et al.;9 red ▲, Abdulagatov and Azizov.13

densities for each A−A isotherm and isopleth were smoothed (to ±0.02 kg·m−3) to uniform pressures using a quadratic function. Densities so obtained were then extrapolated to psat and used to calculate Vϕ, which were then plotted against √m. The slope of many of these Vϕ(√m) plots (not shown) changed abruptly from positive to negative at the lowest concentration. This typically happens when the density of water is (slightly) incorrect at low m as such an error disproportionately affects Vϕ (eq 1). This suggests that the piezometer used by A−A may not have been accurately calibrated at all T, p. To test this hypothesis, A−A’s densities at smoothed p were extrapolated to m = 0 to extract ρw. The deviations between the ρw values so obtained and the literature densities (IAPWS-95) were of the same pattern as the deviations between A−A’s Li2SO4(aq) densities and the present results (Figure 7). To put it another way: the densities and Vϕ values reported by A−A are not consistent with IAPWS-95 water densities.

Figure 8. Standard molar volumes, Vo, of Li2SO4(aq) as a function of pressure at temperatures, T/K = 323, 373, 423, 448, 473, 498, 523, 548, and 573 K (top to bottom curves). The points represent the Vo values reported by Abdulagatov and Azizov;13 the dotted vertical lines connect those points with their corresponding isotherms; the dashed line represents Vo at psat.

shifts (corrections to densities) were within ±0.2%. On the basis of the corrected densities, a new set of Vϕ values, covering temperatures 323.15 ≤ T/K ≤ 573.15, pressures psat ≤ p/MPa ≤ 40, and concentrations 0 ≤ m/mol·kg−1 ≤ 0.9 was generated and fitted with the extended version of eq 3. The standard molar volumes obtained in this way are shown in Figure 8. The data embodied in this diagram serve to remind researchers about how tiny errors in experimental densities (no more than 0.2% in this case) can impact significantly upon the Vϕ values calculated from them, especially in the dilute region. Details of the fitting of the high-pressure data and Vϕ values at rounded T, p, and m are given as Supporting Information. Comparisons with Related Electrolytes. It is interesting to compare the present Vo values for Li2SO4(aq) with those of the other alkali metal sulfates. Unfortunately, appropriate data have been published only for Na 2 SO 4 (aq) 25,26 and K2SO4(aq).25,26 Figure 9 shows how the Vo values for Li2SO4(aq) and K2SO4(aq) differ from those of Na2SO4(aq) at pressures of 10 and 30 MPa over the temperature range 323 ≤ T/K ≤ 573. As electrolyte (and hence ionic) volumes are strictly additive at infinite dilution7,27 the difference Vo(M2SO4) − Vo(Na2SO4) must be equivalent to 2[Vo(M+, aq) − Vo(Na+, aq)]. For M+ = K+ this difference is 20.4 cm3·mol−1 at 298 K and 0.1 MPa, decreasing steadily to 14.8 cm3·mol−1 at 473 K and 2 MPa, at least according to Marcus.28,29 However, no such decrease is apparent in Figure 9, which reveals an almost constant difference up to ∼525 K. This discrepancy probably arises because Marcus based his Vo(ion) values entirely on the

Figure 7. Discrepancies, δρw = ρw,calc − ρw,exp between densities of pure water calculated from the IAPWS-95 formulation, ρw,calc, and those reported by Abdulagatov and Azizov,13 ρw,exp: red □, obtained from comparison of Vϕ with the present data (see text); blue ◇, obtained from Abdulagatov and Azizov’s data alone by extrapolation to m = 0.

Apparent Volumes at High Pressures. While minor calibration errors of A−A’s piezometer would introduce significant systematic errors into their density measurements, their effect on the pressure derivatives of their densities would be expected to be rather less. If this is a reasonable assumption, the combination of A−A’s pressure derivatives with the 3599



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Figure 9. Differences between the standard molar volumes, Vo, of aqueous solutions of Na2SO425,26 and those of Li2SO4 (present work; blue ◆, ◇) and K2SO4 (red ●, ○),25,26 as a function of temperature, T, at pressures p = 10 MPa (filled symbols) and 30 MPa (unfilled symbols).

Figure 10. Differences in apparent molar volumes, Vϕ(M2SO4) − Vϕ(Na2SO4), as a function of solute concentration (√m) at selected temperatures and 10 MPa pressure: M+ = K+ at 298 to 523 K, ◆; all other symbols M+ = Li+, at T/K = 298 (at 0.1 MPa),8 ×; 323, blue ○; 348, red △; 373, violet □; 423, +; 473, green ◇; 523, orange ▽. Curves for K+ at all T and for Li+ at 573 K were omitted for visual clarity.

pioneering work of Ellis,30 which is almost certainly less accurate than that obtainable using modern vibrating tube densimetry (see e.g., present and literature25,26 data; note that he pressure difference is unlikely to be important at these relatively low temperatures). It is noteworthy that the difference in the Vo values for K+ and Na+ is much larger than the 7.9 cm3·mol−1 calculated from their hard-sphere volumes. This serves to emphasize the composite character of ionic volumes in aqueous solution.7,27 Nevertheless, it is surprising that the magnitude of Vo(K+, aq) − Vo(Na+, aq) is almost constant over such wide ranges of temperature and pressure. Clearly, whatever changes occur in the hydration of Na+(aq) as a function of temperature and pressure are closely matched by those of K+(aq). The same is evidently not true for Li+(aq). The difference between Vo(Li2SO4) and Vo(Na2SO4) is +0.6 cm3·mol−1 at 298 K and 0.1 MPa28 [i.e., Vo(Li+, aq) > Vo(Na+, aq)] but rapidly becomes negative with increasing T [i.e., Vo(Li+, aq) < Vo(Na+, aq)]. At ca. 550 K the Vo values of Li+(aq) and Na+(aq) again reverse (Figure 9). Furthermore, a major divergence between the volume differences at 10 and 30 MPa occurs at T > 500 K. Analogous patterns in volume differences are observed at finite concentrations (Figure 10). Thus, the differences between the Vϕ values for K+ and Na+ salts vary reasonably smoothly with both concentration and temperature while those between Li2SO4 and Na2SO4 exhibit changes in slope (and curvature) against √m and even a significant reversal at high T (Figure 10). These variations must reflect a fundamental difference in the hydration behavior of Li+(aq) cf. that of Na+(aq) and K+(aq). Similar effects have been noted for the volumes8 and heat capacities15 of a number of other lithium salts in aqueous solution under near-ambient conditions. Isobaric Expansibilities and Isothermal Compressibilities. The present results together with relevant literature data25,26 were used to evaluate the isobaric expansibilities, α = −(∂ ln ρ/∂T)p, of the aqueous solutions of lithium, sodium, and potassium sulfates. The values obtained, expressed relative to the expansibility of pure water for representational convenience, are compared in Figure 11. These plots reveal that the

Figure 11. Isobaric expansibilities, α = −(∂ ln ρ/∂T)p of M2SO4(aq) solutions relative to that of pure water (αw) at T/K = 373.15, 423.15, 473.15, 523.15, and 573.15 (top to bottom for each set). Solid black lines, Li2SO4 this work; red dashed lines, Na2SO4;26 blue dotted lines, K2SO4.26

effect of solute concentration on expansibility is much greater than that of temperature and also that aqueous solutions of the alkali metal sulfates are much less expandable than pure water. Similar trends to those shown in Figure 11 are observed for the isothermal compressibility, β = (∂ ln ρ/∂p)T, of M2SO4(aq). Indeed, the similarity was such that the related coefficient of tension, α/β = (∂ρ/∂T)p is only weakly dependent on the concentration of Li2SO4(aq), especially at lower temperatures. This in turn suggests that the pressure dependence of the density of dilute Li2SO4(aq) can be estimated from the temperature dependence of the solution density and the pressure−temperature derivative for pure water: 3600


Journal of Chemical & Engineering Data ⎛ ∂ρsoln ⎞ ⎛ ∂ρ ⎞ ⎛ ∂T ⎞ ⎜ ⎟ ≈ ⎜ soln ⎟ ⎜ ⎟ ⎝ ∂p ⎠T ⎝ ∂T ⎠ p⎝ ∂p ⎠ ρ ,water

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REFERENCES

(1) Tran, T.; Luong, V. T. Lithium production processes. In Lithium Process Chemistry; Elsevier: Amsterdam, 2015; Chapter 3, pp 81−124. (2) Choubey, P. K.; Kim, M.-S.; Srivastava, R. R.; Lee, J.-C.; Lee, J.-Y. Advance review on the exploitation of the prominent energy-storage element: Lithium. Part I: From mineral and brine resources. Miner. Eng. 2016, 89, 119−137. (3) Xu, J.; Thomas, H. R.; Francis, R. W.; Lum, K. R.; Wang, J.; Liang, B. A review of processes and technologies for the recycling of lithium-ion secondary batteries. J. Power Sources 2008, 177, 512−527. (4) Zhang, X.; Xie, Y.; Lin, X.; Li, H.; Cao, H. An overview on the processes and technologies for recycling cathodic active materials from spent lithium-ion batteries. J. Mater. Cycles Waste Manage. 2013, 15, 420−430. (5) Kim, H.; Hong, J.; Park, K.-Y.; Kim, H.; Kim, S.-W.; Kang, K. Aqueous rechargeable Li and Na ion batteries. Chem. Rev. 2014, 114, 11788−11827. (6) Koryta, J.; Dvořaḱ , J.; Kavan, L. Principles of Electrochemistry; John Wiley: Chichester, UK, 1993; p 473. (7) Hefter, G. T. Molar volumes of electrolyte solutions. In Volume Properties: Liquids, Solutions and Vapours; Wilhelm, E., Letcher, T. M., Eds.; RSC Publishing: Cambridge, UK, 2015; pp 493−511. (8) Hu, B.; Hnedkovsky, L.; Hefter, G. Densities and apparent molar volumes of aqueous solutions of Li2SO4 and LiCF3SO3 at temperatures from 293 to 343 K. J. Chem. Eng. Data 2016, 61, 3618−3626. (9) Puchkov, L. V.; Kurochkina, V. V.; Matveeva, R. P. Density of Aqueous Lithium, Sodium, and Potassium Sulfate up to 315 °C. VINITI, Dep. Doc.; Moscow, 1976; pp 3474−76. (10) Maksimova, I. N.; Pack, J. S.; Pravdin, N. N. Physical and Chemical Properties of Electrolyte Solutions in a Wide Range of Temperatures and Concentrations. VINITI, Dep. Doc.; Leningrad, 1984; pp 4113−84. (11) Söhnel, O.; Novotný, P. Densities of Aqueous Solutions of Inorganic Substances; Elsevier: New York, 1985. (12) Aseyev, G. G.; Zaytsev, I. Z. Volumetric Properties of Electrolyte Solutions: Estimation Methods and Experimental Data; Begell House: Danbury, 1996. (13) Abdulagatov, I. M.; Azizov, N. D. PVTx Measurements and Partial Molar Volumes for Aqueous Li2SO4 Solutions at Temperatures from 297 to 573 K and at Pressures up to 40 MPa. Int. J. Thermophys. 2003, 24, 1581−1610. (14) Linke, W. F.; Seidell, A. Solubilities of Inorganic and MetalOrganic Compounds; American Chemical Society: Washington, DC, 1965; Vol. II, p 434. (15) Hu, B.; Hnědkovský, L.; Hefter, G. T. Heat Capacities of Aqueous Solutions of Lithium Sulfate, Lithium Perchlorate, and Lithium Trifluoromethanesulfonate at 298.15 K. J. Chem. Eng. Data 2016, 61, 2149−2154. (16) Hnedkovsky, L.; Königsberger, E.; Königsberger, L.-C.; Cibulka, I.; Schrödle, S.; May, P. M.; Hefter, G. T. Densities of Concentrated Alkaline Aluminate Solutions at Temperatures from (323 to 573) K and 10 MPa Pressure. J. Chem. Eng. Data 2010, 55, 1173−1178. (17) Wagner, W.; Pruss, A. The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. J. Phys. Chem. Ref. Data 2002, 31, 387−535. (18) Archer, D. G. Thermodynamic Properties of NaCl + H2O System. II Thermodynamic Properties of NaCl(aq), NaCl·2H2O(cr), and Phase Equilibria. J. Phys. Chem. Ref. Data 1992, 21, 793−829. (19) Hynek, V.; Hnedkovsky, L.; Cibulka, I. A New Design of a Vibrating-tube Densimeter and Partial Molar Volumes of Phenol(aq) at Temperatures from 298 to 573 K. J. Chem. Thermodyn. 1997, 29, 1237−1252. (20) Span, R.; Lemmon, E. W.; Jacobsen, R. T.; Wagner, W.; Yokozeki, A. A Reference Equation of State for the Thermodynamic

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CONCLUSIONS The densities of Li2SO4(aq) and the apparent molar volumes calculated from them varied smoothly with solute concentration up to 2.7 mol·kg−1 and temperatures from 343 to 573 K at saturation pressures. The volumes were well fitted with an extended Redlich−Rosenfeld−Meyer equation. The combination of these data with earlier measurements8 and pressure derivatives from the literature13 enabled the development of an equation that accurately described the volumetric properties of Li2SO4(aq) at concentrations up to saturation over the temperature range 323 ≤ T/ K ≤ 573 at pressures 0.1 ≤ p/ MPa ≤ 40. This represents a significant expansion of the volumetric database for these technologically important salt solutions. The comparison of Vϕ values for Li2SO4(aq) with the corresponding data for Na2SO4(aq) and K2SO4(aq) showed that the lithium salt behaved differently as a function of concentration and temperature. This was attributed to differences in the hydration of Li+. From its effect on solution expansibility, it was concluded that Li2SO4(aq) remains a solvent structure maker over the investigated conditions. ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00570. Apparent molar volumes (Table S1) of Li2SO4(aq) at rounded temperatures, molalities, and pressures calculated from fitted experimental data of the present work and pressure derivatives of density13 from the literature. All pure water properties were calculated via the IAPWS formulation17 (PDF)

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ACKNOWLEDGMENTS

The authors thank Dr. Aleks Nikoloski (Murdoch University) for providing useful references.

It can be noted that, consistent with its diminution of the expansibility of the solutions cf. pure water (Figure 11), dissolved Li2SO4 continues to act, as at near-ambient temperatures,8 as a solvent structure maker under all of the investigated conditions. The same appears to be true for Na2SO4 and K2SO4, suggesting that, at least for these salts, the effect of the anion on solvent structure far outweighs those of the cations.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +61 8 9360 6091. ORCID

Lubomir Hnedkovsky: 0000-0002-1928-6999 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. 3601



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Properties of Nitrogen for Temperatures from 63.151 to 1000 K and Pressures to 2200 MPa. J. Phys. Chem. Ref. Data 2000, 29, 1361−1433. (21) Commission on Isotopic Abundances and Atomic Weights, 2015. http://www.ciaaw.org/atomic-weights.htm (accessed May 18, 2017). (22) Fernández-Prini, R. J.; Corti, H. R.; Japas, M. L. Electrolyte Solutions. In High-Temperature Aqueous Solutions: Thermodynamic Properties; CRC Press: Boca Raton, 1992; Chapter 3, pp 73−79. (23) Redlich, O.; Meyer, D. M. The Molal Volumes of Electrolytes. Chem. Rev. 1964, 64, 221−227. (24) Schwarz, G. E. Estimating the Dimension of a Model, Annals of Statistics 1978, 6, 461−464. (25) Obšil, M.; Majer, V.; Hefter, G.; Hynek, V. Densities and Apparent Molar Volumes of Na 2SO4(aq) and K2SO4(aq) at Temperatures from 298 to 573 K and at Pressure up to 30 MPa. J. Chem. Eng. Data 1997, 42, 137−142. (26) Obšil, M.; Majer, V.; Grolier, J-P. E.; Hefter, G. Volumetric Properties of, and Ion-pairing in, Aqueous Solutions of Alkali-metal Sulfates under Superambient Conditions. J. Chem. Soc., Faraday Trans. 1996, 92, 4445−4451. (27) Marcus, Y.; Hefter, G. T. Standard partial molar volumes of electrolytes and ions in nonaqueous solvents. Chem. Rev. 2004, 104, 3405−3452. (28) Marcus, Y. The Standard Partial Molar Volumes of Ions in Solution. Part 4. Ionic Volumes in Water at 0−100 °C. J. Phys. Chem. B 2009, 113, 10285−10291. (29) Marcus, Y. The Standard Partial Molar Volumes of Ions in Solution. Part 5. Ionic Volumes in Water at 125−200 °C. J. Phys. Chem. B 2012, 116, 7232−7239. (30) Ellis, A. J. Partial Molal Volumes in High-temperature Water. Part III. Halide and Oxyanion Salts. J. Chem. Soc. A 1968, 1138−1143.

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Densities and Molar Volumes of Aqueous Solutions of Li2SO4 at

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