Heat Capacities of Aqueous Solutions of Lithium Sulfate, Lithium

Article pubs.acs.org/jced

Heat Capacities of Aqueous Solutions of Lithium Sulfate, Lithium Perchlorate, and Lithium Trifluoromethanesulfonate at 298.15 K Bin Hu,† Lubomír Hnědkovský,‡ 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: Isobaric heat capacities of aqueous solutions of Li2SO4, LiClO4, and LiCF3SO3 have been measured at 298.15 K and 0.1 MPa up to high concentrations using a Picker flow calorimeter. Apparent molar isobaric heat capacities, Cp,ϕ, derived from these data were fitted within the limits of experimental precision with an extended Redlich−Rosenfeld−Meyer type of equation, which was also used to estimate the standard state (infinite dilution) quantities, Cop,ϕ, for each salt. The latter values were combined with appropriate literature data to produce a robust estimate of Cop,ϕ (Li+(aq)) = −3 ± 2 J·K−1·mol−1. Where comparison was possible, Cp,ϕ(LinX) values were closely parallel to those of the corresponding acids over the whole concentration range, even when the shapes of the curves were highly unusual. In contrast, Cp,ϕ(NanX) values always exhibited a crossover with the lithium salt data at a concentration of about 1 mol·kg−1, which appears to reflect differences in the hydration of the two cations.

1. INTRODUCTION Lithium salts attract considerable interest for practical applications in battery development,1 medicine,2 automotive lubricant additives,3 and so on.4 This is largely because many of the fundamental properties of lithium salts, such as their solubility, stability, and density, are often markedly different from those of their close congeners. Of the many lithium salts available commercially, the relatively “new” lithium trifluoromethanesulfonate (LiCF3SO3; lithium triflate, LiTf) has received a great deal of attention as a battery electrolyte because of its thermal and electrochemical stability, and its exceptionally high solubility and good electrical conductivity in nonaqueous solvents.1 Lithium perchlorate (LiClO4) has also been used in nonaqueous batteries and is widely employed as a noncomplexing electrolyte for the study of chemical equilibria and kinetics.5,6 Lithium sulfate (Li2SO4) is used clinically for the treatment of certain mental disorders2,7 and as a catalyst in organic chemistry.8 In addition, Li2SO4 occurs naturally at significant concentrations in certain salt lake brines9 and so plays a key role in the industrial production of lithium and its compounds.4 Heat capacities are an important property of electrolyte solutions. From a fundamental viewpoint they provide valuable insights into the nature of ion−ion and ion−solvent interactions.10 For technological purposes, heat capacities are required for heat balance and heat flow calculations whenever materials need to be heated or cooled.11 However, in contrast with many other physicochemical properties, the availability of reliable heat capacity data for lithium salts is rather limited, especially at the high concentrations that are of most technological interest. © XXXX American Chemical Society

Of the three salts used in the present study, no published data could be found for aqueous solutions of either LiTf or LiClO4. For Li2SO4(aq), only the approximate values of Apelblat,12 obtained from the temperature dependence of the enthalpy of dissolution of Li2SO4(s), are available. However, as noted by the author,12 at high concentrations the apparent molar heat capacities, Cp,ϕ, are rather scattered (Figure 1), whereas at low molalities (m < 0.2 mol·kg−1) they are seriously in error, given that an infinite dilution value of Cop,ϕ = −156 J· K−1·mol−1 can be estimated with reasonable accuracy from the tabulated ionic quantities.13 As part of our ongoing investigations of the physicochemical properties of aqueous solutions of selected lithium salts,14 this paper reports the isobaric heat capacities of Li2SO4(aq), LiClO4(aq), and LiTf(aq) up to near-saturation concentrations (except for the ultrasoluble LiTf), measured using a Picker flow calorimeter at a temperature of 298.15 K and at 1 atm (0.1 MPa) pressure.

2. EXPERIMENTAL SECTION 2.1. Reagents. Sample descriptions are summarized in Table 1. Lithium triflate was synthesized using an approach similar to that described for lithium perchlorate.14 Briefly, trifluoromethanesulfonic (“triflic”) acid (CF3SO3H, SigmaAldrich, U.S.A., ≥ 99%) was added slowly to a stirred aqueous slurry of solid lithium carbonate (Sigma-Aldrich, ≥ 99%). When all the solid had dissolved, the resulting solution was Received: February 2, 2016 Accepted: May 20, 2016

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DOI: 10.1021/acs.jced.6b00103 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

further purification but dried at 463 K overnight at ∼5 Pa. Densities of solutions prepared from this alternative source agreed with those of the Li2SO4 stock solution to within the precision of the densimeter (±2 μg·cm−3). Working solutions for all salts were prepared from the stock solutions by weight dilutions using freshly degassed high purity water (Ibis Technology, Australia); buoyancy corrections were applied throughout. 2.2. Instrumentation. Isobaric volumetric heat capacities of the solutions were measured using a Picker flow calorimeter (Sodev, Sherbrooke, Canada) as described previously.15 The temperature was controlled to a precision of ±0.001 K with a Sodev (Model CT-L) circulator-thermostat. Test solutions or freshly degassed water were introduced into the calorimeter using a four−way chromatography valve (Hamilton, U.S.A., Model HVP). An approximate flow rate of 0.5 mL·min−1 was maintained constant with a Gilson Minipulse peristaltic pump. As discussed previously,15 all heat capacities were obtained from “first leg” (solution displacing water in the calorimeter) measurements to avoid the possible effects of incomplete flushing. Solution densities, required for the calculation of the desired massic heat capacities (eq 1), were measured with an Anton Paar (Austria) DMA 5000 M vibrating-tube densimeter calibrated with air and high purity water as described elsewhere.14 2.3. Calculations. Isobaric heat capacities per unit mass, cp/ J·K −1 ·kg−1 were obtained from the measured isobaric volumetric heat capacities σp/J·K−1·m−3 and solution densities ρ/ kg·m−3 as

Figure 1. Deviation plots (δCp,ϕ = Cp,ϕ(exptl) − Cp,ϕ(fitted)) for Li2SO4(aq) (bottom), LiClO4(aq) (center), and LiCF3SO3 (top).

raised to near-boiling temperature, sparged with high purity N2 to remove dissolved CO2, and neutralized to 5 ≤ pH ≤ 6 by the addition of small amounts of LiOH(aq) or CF3SO3H, as appropriate. This solution was evaporated until crystallization commenced then cooled to room temperature. The resultant crystals were collected by vacuum filtration (0.4 μm) and purified by recrystallizing twice from water. Because of the very strong affinity of LiTf for water, no attempt was made to dry the solid following recrystallization or before preparing stock solutions. A concentrated Li2SO4(aq) solution was prepared in a similar manner by adding analytical grade H2SO4 (Merck, U.S.A., ≥ 98%) to an aqueous slurry of Li2CO3(s) then sparging and filtering (0.4 μm). Lithium perchlorate was prepared and analyzed as described previously.14 Stock solutions of LiTf(aq) and Li2SO4(aq) were analyzed in triplicate by evaporative gravimetry, initially at 333 K then at 463 K overnight under vacuum (p ≈ 5 Pa). Concentrations were reproducible to ±0.03% and ±0.01% (relative), respectively; however, taking all factors into account (including solute purity), the overall uncertainty in the solution concentrations is estimated to be ±0.05% (relative). For Li2SO4(aq), two test solutions were also prepared directly from a commercial sample (Ajax, Australia, 99%) used without

c p = σp/ρ

(1) −1

−1

Apparent molar heat capacities, Cp,ϕ/J·K ·mol , of the solutions were calculated using the usual expression Cp, ϕ = Mc p + (c p − c pw )/m

(2)

where cpw is the massic heat capacity of water (4181.3 J·K−1· kg−1),16,17 M is the molar mass of the solute (kg·mol−1), and m is the solution molality (mol·kg−1). Molar masses were calculated using the IUPAC 2015 atomic masses18 which gave: M(Li2SO4) = 0.11000(7) kg·mol−1, M(LiClO4) = 0.10642(3) kg·mol−1, and M(LiTf) = 0.15604(4) kg·mol−1, where the numbers in parentheses are maximum uncertainties. The values of Cp,ϕ so obtained were fitted with an extended form of the “Redlich−Rosenfeld−Meyer” (RRM) equation for heat capacities19 Cp, ϕ = Cp,o ϕ + ωA Cm0.5 + BCm + CCm1.5 + DCm2 + ECm2.5 + FCm3

(3)

Table 1. Sample Sources and Purities chemical name

source

lithium triflate

synthesis

lithium perchlorate lithium sulfate lithium carbonate triflic acid perchloric acid sulfuric acid

synthesis synthesis Aldrich Aldrich Ajax Merck

initial mass fraction purity

≥0.99 ≥0.99 0.72 ≥0.98

purification method

final mass fraction purity

analysis method

recrystallization from water (×2) recrystallization from water

0.9995

evaporative gravimetry

0.9970

recrystallization from water none none none none

0.9995

evaporative gravimetry; precipitation gravimetry evaporative gravimetry

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where Cop,ϕ(= C̅ op,2) is the standard state (infinite dilution) partial molar heat capacity of the electrolyte in the solvent, ω is a valence factor reflecting the number and charges of the solute ions (ω = (νz+z−/2)3/2), AC is the Debye−Hückel limiting slope for heat capacities,16,17 and YC (Y = B... F) are empirical parameters fitted from the data. A value of AC = 31.766 J·K−1· mol−1.5·kg0.5 was used throughout. In addition to Cop,ϕ, three extra adjustable parameters (BC, CC and DC) were required to satisfactorily fit the data for LiClO4(aq), and Li2SO4(aq) though the much more soluble LiTf with a more complicated concentration dependencerequired five extra parameters. The appropriate 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 the fit at the α = 0.05 significance level.

made on the same solutions using a commercial vibrating-tube densimeter.14 The standard partial molar heat capacities, Cop,ϕ, obtained for each salt via eq 3, are listed in Table 5 together with the empirical parameters YC and their standard errors (SEs). Note that the SEs given for Cop,ϕ do not represent the overall uncertainty in this quantity, which is thought20 to be of the order of 1−2 J·K−1·mol−1. The ability of eq 3 to fit the present Cp,ϕ results within the probable experimental precision is illustrated in the deviation plots given in Figure 1. For each set of solutions the deviations are essentially random with solute concentration and are almost all less than 1 J·K−1·mol−1, albeit with differing numbers of adjustable parameters (Table 5). 3.1. Li2SO4(aq). The experimental data and the calculated Cp,ϕ values for Li2SO4(aq) are listed in Table 2. The latter are also plotted in Figure 2, together with Apelblat’s more reasonable higher-concentration (m > 0.2 mol·kg−1) results12 which, given their rather large scatter (ca. ± 20 J·K−1·mol−1), are in fair agreement with the present results. Also shown in Figure 2 for comparison are Cp,ϕ data for Na2SO4(aq).15 The shape of the curves for the two salts is broadly similar but Cp,ϕ(Na2SO4(aq)) depends more strongly on concentration such that there is a “crossover” at m ≈ 1 mol·kg−1. The origin of this effect is not known but is unlikely to be due to ion pairing because the formation constants for NaSO4−(aq) and LiSO4−(aq) are approximately equal.21,22 Note that in contrast with the perchlorate and triflate salts (see below), it is inappropriate to compare the present results for Cp,ϕ(Li2SO4(aq)) with those of Cp,ϕ(H2SO4(aq)) because the latter is in essence a 1:1 electrolyte with H+(aq) and HSO4−(aq) as the dominant species over the concentration range of interest.23 3.2. LiClO4(aq). The experimental data and Cp,ϕ values for LiClO4(aq) solutions are summarized in Table 3. The latter are also plotted in Figure 3 along with the available literature data for NaClO4(aq) and HClO4(aq) from the JESS database.24,25 These data show that there is again a crossover in Cp,ϕ for NaClO4(aq) and LiClO4(aq), analogous to that seen (Figure 2) for Li2SO4(aq) and Na2SO4(aq), albeit at a slightly lower concentration. In contrast, the variation of Cp,ϕ(HClO4(aq)) with concentration (Figure 3) closely parallels that of LiClO4(aq) over a wide range. 3.3. LiTf(aq). The experimental data for LiTf(aq) are listed in Table 4. The derived Cp,ϕ values are plotted in Figure 4; they

3. RESULTS AND DISCUSSION The densities, volumetric and massic isobaric heat capacities, and the corresponding Cp,ϕ values derived from them for aqueous solutions of Li2SO4, LiClO4 and LiTf are summarized in Tables 2 to 4. Densities were taken from measurements Table 2. Experimental Densities ρ, along with Volumetric σp, Massic cp, and Apparent Molar Cp,ϕ Isobaric Heat Capacities of Li2SO4(aq) Solutions at T = 298.15 K and p = 0.1 MPaa m/mol·kg−1

ρ/kg·m−3

10−3 σp/J·K−1· m−3

cp/J·K−1·kg−1

Cp,ϕ/J·K−1·mol−1

0.05013 0.07004 0.1008 0.2024 0.4025 0.5075 0.7061 1.001 1.503 2.001 2.681

1001.81 1003.67 1006.54 1015.83 1033.62 1042.72 1059.54 1083.62 1122.47 1158.46 1204.07

4160.6 4157.6 4153.3 4139.8 4118.0 4109.0 4091.9 4075.2 4055.1 4043.2 4038.2

4153.1 4142.4 4126.3 4075.3 3984.1 3940.7 3862.0 3760.7 3612.7 3490.2 3353.8

−106.1 −100.0 −91.9 −75.5 −51.7 −40.7 −27.4 −6.5 19.1 38.5 60.3

a

Standard uncertainties u are u(T) = 0.005 K, u(p) = 1 kPa, ur(m) = 0.0005, u(ρ) = {0.01 + 0.02m} kg·m−3, 10−3 u(σp) = 4 J·K−1·m−3, u(cp) = 4 J·K−1·kg−1, and the combined expanded uncertainty Uc is Uc(Cp,ϕ) = {(0.1/m) + 0.44} J·K−1·mol−1 (level of confidence = 0.95).

Table 3. Experimental Densities ρ14 along with Volumetric σp, Massic cp, and Apparent Molar Cp,ϕ Isobaric Heat Capacities of LiClO4(aq) Solutions at T = 298.15 K and p = 0.1 MPaa m/mol·kg−1

ρ/kg·m−3

10−3 σp/J·K−1·m−3

cp/J·K−1·kg−1


0.05269 0.07030 0.1014 0.2000 0.4002 0.6996 0.9999 2.002 3.003 4.014 5.006

1000.35 1001.44 1003.36 1009.41 1021.50 1039.12 1056.96 1110.03 1158.94 1204.04 1245.09

4161.8 4159.7 4155.6 4143.2 4118.6 4084.8 4057.1 3962.9 3885.8 3818.5 3755.9

4160.4 4153.7 4141.7 4104.6 4031.9 3931.0 3838.5 3570.1 3352.9 3171.4 3016.6

45.7 49.2 50.0 53.2 55.7 60.5 65.6 74.6 80.9 85.9 88.4

Standard uncertainties u are u(T) = 0.005 K, u(p) = 1 kPa, ur(m) = 0.0005, u(ρ) = {0.01 + 0.02m} kg·m−3, 10−3 u(σp) = 4 J·K−1·m−3, u(cp) = 4 J· K−1·kg−1, and the combined expanded uncertainty Uc is Uc(Cp,ϕ) = {(0.1/m) + 0.42} J·K−1·mol−1 (level of confidence = 0.95).

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Table 4. Experimental Densities ρ along with Volumetric σp, Massic cp, and Apparent Molar Cp,ϕ Isobaric Heat Capacities, of LiCF3SO3(aq) Solutions at T = 298.15 K and p = 0.1 MPaa m/mol·kg−1

ρ/kg·m−3

10−3 σp/J·K−1·m−3

cp/J·K−1·kg−1


0.04996 0.06998 0.1002 0.2000 0.3997 0.6998 0.9883 1.500 1.999 2.999 3.991 5.879 7.493 9.635

1001.11 1002.72 1005.12 1013.02 1028.49 1050.89 1071.53 1106.05 1137.52 1194.52 1244.20 1323.14 1377.82 1437.22

4165.2 4163.6 4161.2 4153.9 4138.9 4117.2 4096.9 4061.3 4028.3 3957.1 3882.7 3737.6 3618.6 3486.1

4160.6 4152.3 4140.0 4100.5 4024.3 3917.8 3823.4 3671.9 3541.3 3312.7 3120.6 2824.8 2626.3 2425.6

234.5 233.3 233.6 235.8 235.1 234.8 234.5 233.4 232.5 227.3 221.2 210.0 202.3 196.3

Standard uncertainties u are u(T) = 0.005 K, u(p) = 1 kPa, ur(m) = 0.0005, u(ρ) = {0.01 + 0.02m} kg·m−3, 10−3 u(σp) = 4 J·K−1·m−3, u(cp) = 4 J· K−1·kg−1, and the combined expanded uncertainty Uc is Uc(Cp,ϕ) = {(0.1/m) + 0.62} J·K−1·mol−1 (level of confidence = 0.95).

a

Table 5. Standard Molar Isobaric Heat Capacities Cop,ϕ and Fitting Parameters and their Standard Errors SE Obtained via Equation 3 for Aqueous Solutions of Li2SO4, LiClO4, and LiCF3SO3 at T = 298.15 K and p = 0.1 MPaa ω Cop,ϕ BC CC DC EC FC

Li2SO4

LiClO4

LiCF3SO3

5.1962

1

1

value

SE

value

SE

value

SE

−140.18 −59.8 38.9 −11.2

0.67 6.6 9.3 3.4

40.61 −15.9 11.2 −15.9

0.65 4.0 4.2 1.2

229.12 −66.3 70.4 −39.8 10.3 −0.98

0.50 5.7 10.1 6.7 1.9 0.20

Units for YC correspond to eq 3 expressed in Cp,ϕ/J·K−1·mol−1 and m/mol·kg−1

a

Figure 3. Apparent molar heat capacities of LiClO4(aq) (●, this work), NaClO4(aq) (blue ◆),24,25 and HClO4(aq) (red ■)24,25 as a function of concentration (√m) at T = 298.15 K and p = 0.1 MPa.

show a most unusual dependence on concentration that differs markedly from those of Li2SO4 (Figure 2) and LiClO4 (Figure 2) or, indeed, from virtually any strong electrolyte.20 Although the shape of the Cp,ϕ(√m) curve is surprising, it closely parallels that of HTf(aq) over the entire (very wide) concentration range studied (Figure 4). The unusual shape of the Cp,ϕ(√m) curve for HTf(aq) has been attributed to the formation of hydrate-like structures.25 As for the sulfates and perchlorates there is again a crossover in the Cp,ϕ values of the Li and Na salts (Figure 4) at m ≈ 1 mol·kg−1. That all three sets of salts show this crossover at broadly similar concentrations suggests that it reflects a fundamental difference between the behavior of Na+(aq) and Li+(aq) with concentration. As noted above (Section 3.1), this is unlikely to be due to variations in the degree of ion pairing. More likely, it points toward a difference in the concentration dependence of the hydration of the two cations. Such an effect has recently been invoked to account for persistent concentration-dependent differences in the volumetric proper-

Figure 2. Apparent molar heat capacities of Li2SO4(aq) (●, this work; ○, Apelblat,12 high m values only) and Na2SO4(aq) (blue ◆)15 as a function of concentration (√m) at T = 298.15 K and p = 0.1 MPa.

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obtained as the average of the Cop,ϕ values reported by Tremaine et al.26 for NaTf(aq) and HTf(aq) combined with Marcus’s single ion values for Na+(aq) and H+(aq).13 The values for Cop,ϕ(Li+) given in Column 3 of Table 6 were obtained by making the usual assumption of ionic additivity at infinite dilution: Cp,o ϕ(Li+) = {Cp,o ϕ(Li nX) − Cp,o ϕ(Xn −)}/n

(4)

The agreement among the results derived from all five salts is excellent given the probable uncertainties in the measured whole-salt quantities. The average value of Cop,ϕ(Li+) = −3 ± 2 J·K−1·mol−1 differs significantly from the value of −9 J·K−1· mol−1 recommended by Marcus13 but is better-based.

4. CONCLUSIONS The present measurements have provided, for the first time, accurate heat capacity data for aqueous solutions of Li2SO4, LiClO4, and LiTf up to high concentrations at 298.15 K and 0.1 MPa. The results obtained were fitted within the limits of experimental error using an extended RRM function. Relevant comparisons indicated that Cp,ϕ(NanX) values vary more strongly with concentration than those of the corresponding lithium salts, resulting in “crossovers” in their values at m ≈ 1 mol·kg−1. This phenomenon appears to reflect differences in the hydration of the two cations rather than ion pairing. Combination of the present Cop,ϕ(LinX) values with appropriate literature data has enabled a more robust estimate of Cop,ϕ(Li+) to be made.

Figure 4. Apparent molar heat capacities of aqueous, LiCF3SO3 (●, this work), NaCF3SO3 (blue ◆),26 and HCF3SO3 (red ■)26 at 298.15 K as a function of concentration (√m) at T = 298.15 K and p = 0.1 MPa.

ties (Vϕ values) of lithium and sodium salts possessing a common anion14 and is consistent with the differences in hydration of the two cations observed by dielectric relaxation spectroscopy.21,22 3.4. Standard Partial Molar Heat Capacity of Li+(aq). The present results, being limited to m ≥ 0.05 mol·kg−1 are not optimal for evaluating the standard state (infinite dilution) partial molar heat capacities, Cop,ϕ(LinX). Nevertheless, given the well-established extrapolative capability of the RRM equation at low concentrations,19,27 the present results can be used with some confidence, in combination with appropriate literature data, to derive a better-supported value of the single ion quantity, Cop,ϕ(Li+), than is currently available. Unfortunately, as noted in the Introduction, very few reliable heat capacity data for lithium salts exist. Table 6 lists (first column) the present

■

Corresponding Author

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

H.B. thanks the Natural Science Foundation of Qinghai Province (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

Table 6. Standard Molar Heat Capacity of the Lithium Ion, Cop,ϕ(Li+) salt

Cop,ϕ(LiX)a

Cop,ϕ(X−)b −1

Li2SO4 LiClO4 LiTf LiCl LiBr Average

−140 41 229 −60e −64e

The authors declare no competing financial interest.

■

Cop,ϕ(Li+)c

−1

J·K ·mol −138 46 231d −56 −60

AUTHOR INFORMATION

REFERENCES

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−1 −5 −2 −4 −4 −3 ± 2

a

Present results (Table 5, rounded) unless otherwise indicated. bFrom Marcus13 unless otherwise indicated; based on the TPTB assumption. c Calculated via eq 4. dObtained as described in the text. eCritically evaluated quantities from the JESS database.24

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Heat Capacities of Aqueous Solutions of Lithium Sulfate, Lithium

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