Molar Volumes and Heat Capacities of Aqueous Solutions of

Article pubs.acs.org/jced

Molar Volumes and Heat Capacities of Aqueous Solutions of Potassium Hydroxide and for Water Ionization up to 573 K at 10 MPa Lubomir Hnedkovsky,*,† Sebastian Bochmann,†,# Peter M. May,† and Glenn Hefter§ †

School of Engineering & Information Technology, and §Chemistry Department, Murdoch University, Murdoch, Western Australia 6150, Australia S Supporting Information *

ABSTRACT: Densities (ρ) and isobaric volumetric heat capacities (σp) of carefully purified aqueous solutions of potassium hydroxide have been measured at concentrations up to 6 mol·kg−1 at a pressure of 10 MPa over the temperature range 323 ≤ T/K ≤ 573 using a vibrating-tube densimeter and a Tian−Calvet differential calorimeter, respectively. Apparent molar volumes (Vϕ) and isobaric heat capacities (Cpϕ) calculated from these data were fitted with modified Redlich−Meyer type equations to derive the corresponding standard molar volumes and heat capacities at infinite dilution. Exact comparisons with literature data were not possible because of pressure differences but the present values, which greatly extend the database for KOH(aq) in terms of precision, temperature and concentration, are broadly compatible with most of the earlier results. Comparison of the present values of Vϕ and Cpϕ for KOH(aq) with corresponding data for solutions of the other alkali metal hydroxides indicated that all of these systems show similar behavior except for LiOH(aq), probably because of greater ion pairing in the latter. The present results for KOH(aq) were combined with reliable literature data for HCl(aq) and KCl(aq) to estimate the standard molar volume and heat capacity changes for the ionization of water up to 573 K.

■

INTRODUCTION Aqueous solutions of potassium hydroxide at high temperatures and pressures play an important role in many chemical and geochemical situations. The latter include, for example, the dissolution of quartz1 and aluminum−containing minerals like corundum,2−6 kaolinite,7 and smectite7−9 at elevated temperatures and pressures. Such processes are important because of their implications for the structural stability of soils and clays.10−12 Various computational thermodynamic packages require data for KOH(aq) in order to model hydrothermal solutions and to calculate chemical equilibria and mass transfers in geochemical processes.13,14 Beside their geochemical significance, reliable thermodynamic data for KOH(aq) are also of considerable industrial importance. Applications include the use of KOH as an electrolyte in alkaline batteries15,16 and fuel cells,17−20 as a homogeneous catalyst in the production of biodiesel,21−24 and as a precursor for the production of fertilizers25,26 and soft soaps.27,28 Potassium hydroxide solutions are also used for etching semiconductor substrates,29−31 as an additive to petroleum drilling fluids,32,33 and for the conversion of oil sludge into high−surface area adsorbents.34−36 From a purely scientific point of view, the physicochemical properties of KOH(aq) are of interest for understanding specific ion interactions in solution, especially by comparison with NaOH(aq) and the solutions of the other alkali metal hydroxides. © 2017 American Chemical Society

In view of the widespread applications of KOH(aq) it is unsurprising that numerous studies of their densities and heat capacities have been reported in the literature. The available sources are summarized in Table 1. As is commonly the situation for electrolyte solutions, there have been many more investigations of densities, over much wider ranges of temperature and concentration, than of heat capacities. Accordingly, this paper presents a detailed study of the densities and isobaric heat capacities of the aqueous solutions of KOH at concentrations up to 6 mol·kg−1 over the temperature range 323 ≤ T/K ≤ 573 at a pressure of 10 MPa. These results represent a significant expansion of the thermodynamic database for these important solutions (cf. Table 1).

■

EXPERIMENTAL SECTION Materials and Sample Preparation. Stock solutions of potassium hydroxide (∼8.8 mol/kg H2O) were prepared as required using KOH pellets (AR grade, Merck, Australia) and ultrapure water (Ibis Technology, Mt Hawthorn, Australia). To reduce the carbonate content, present even in analytical grade KOH, these stock solutions were treated according to the procedure of Sipos et al.49 and then filtered (0.45 μm, Supor Special Issue: Memorial Issue in Honor of Ken Marsh Received: February 20, 2017 Accepted: May 8, 2017 Published: May 16, 2017 2959

DOI: 10.1021/acs.jced.7b00192 J. Chem. Eng. Data 2017, 62, 2959−2972

Journal of Chemical & Engineering Data

Article

Table 1. Literature Sources for Densities, ρ, and Heat Capacities, cp, of KOH(aq)

a

quantity

molality range (mol·kg−1)

temperature range (K)

pressure range (MPa)

methoda

ref

ρ ρ ρ ρ ρ ρ ρ ρ ρ, cp ρ, cp cp cp

0.3−17.8 2−17.1 0−160 0−60 0.5−3 0.1−2.6 1−19.2 0.6−3.7 0−15.5 0−0.5 0−2.6 0−0.5

273−343 218−273 273−673 333−433 298−348 328−523 298 293−353 277−328 278−393 298 298

0.1 0.1 psat psat 0.1 0.1−4.8 0.1 1.8 0.1 0.35 0.1 0.1

pycnometer pycnometer magnetic float balance hydrostatic balance dilatometer VT-densimeter VT-densimeter VT-densimeter VT-densimeter, FC VT-densimeter, DSC DC FC

37 38 39 40 41 42 43 44 45 46 47 48

Abbreviations: VT, vibrating tube; D(S)C, differential (scanning) calorimeter; FC, flow calorimeter.

Table 2. Sample Source and Purity chemical name [CASRN] potassium hydroxide [1310-58-3]

source

initial mass fraction purity

Merck, Australia

0.99

purification method

final mass fraction purity

analysis method

0.9990

acid−base titration

precipitation of carbonate, filtration

densimeter. Once a steady value of the sample period (τ) was achieved (typically within 12 min) the water flow was rerouted to the densimeter to record a “final” baseline (τ″w). Meanwhile the sample loop was emptied, rinsed, and then filled with a fresh solution. Most sample measurements were performed in duplicate, mostly using independent fillings of the sample loop. Solution densities, ρ, were calculated from

450, Pall, Port Washington, NY, USA) under high-purity nitrogen (Table 2). Concentrations of KOH and carbonate were determined to ±0.05% by titration with standard hydrochloric acid (NIST traceable) using phenolphthalein and methyl orange as indicators. Carbonate levels were also confirmed by Raman spectroscopy.50 As small amounts of carbonate (0.4% of the total alkalinity) were still detectable in the stock solutions so prepared, such solutions were further treated with stoichiometric amounts of Ba(OH)2(aq), stirred overnight, allowed to settle for 48 h then refiltered. After this treatment, carbonate in the stock solution was ρw ≫ ρN and the sample density typically lies well outside the calibrating range). Accordingly, K values at T ≤ 523.15 K were determined using water and four independently prepared NaCl(aq) solutions of concentrations 3 ≤ m/mol·kg−1 ≤ 6. The densities of the latter were calculated using the Pitzer model of Archer.54 The calibration constants so obtained were compared with those determined using (water and) either N2(g) or a D2O sample of known isotopic composition. As the reliability of Archer’s model at T > 523.15 K is uncertain, particularly at higher m(NaCl),53 the calibration at T = 573.15 K was carried out instead with water, D2O,55 and N2. The uncertainty of the calibration constant, K, was always within ±0.2% (0.12% on average) throughout the entire temperature range. The agreement and overlap between the calibrations with NaCl(aq) and N2/D2O at T ≤ 523.15 K provides a solid basis for considering that the calibration with N2/D2O at T = 573.15 K is reliable. 2960



Article

Table 3. Experimental Density Differences, Δρ, and Calculated Apparent Molar Volumes, Vϕ, of KOH(aq) at the Specified Temperatures, T, Pressures, p, and Molalities, ma T

p

m

Δρ

Vϕ

T

p

m

Δρ

Vϕ

K

MPa

mol·kg−1

kg·m−3

cm3·mol−1

K

MPa

mol·kg−1

kg·m−3

cm3·mol−1

323.15 323.15 323.15 323.15 323.15 323.15 323.16 323.16 323.16 323.16 323.15 323.15 323.15 323.15 373.12 373.12 373.12 373.13 373.13 373.13 373.15 373.15 373.15 373.16 423.10 423.11 423.11 423.11 423.13 423.12 423.12 423.13 423.14 423.15 423.15 473.15 473.15 473.15 473.15 473.15

9.98 9.98 9.98 9.98 9.98 9.97 9.98 9.98 9.98 9.98 9.98 9.98 9.98 9.97 9.99 9.99 9.99 9.98 9.98 9.98 9.98 9.97 9.97 9.97 10.01 10.01 10.01 10.01 10.01 10.01 10.01 10.01 10.01 10.02 10.02 10.06 10.06 10.06 10.07 10.06

0.050199 0.050199 0.10156 0.10156 0.20097 0.30073 0.50085 0.70120 0.99903 1.0000 2.0124 2.9999 4.5053 6.0016 0.10156 0.20097 0.30073 0.50085 0.70120 0.99903 2.0124 2.9999 4.5053 6.0016 0.10156 0.10156 0.20097 0.30073 0.50085 0.70120 0.99903 2.0124 2.9999 4.5053 6.0016 0.10156 0.10156 0.20097 0.20097 0.30073

2.426 2.427 4.888 4.891 9.601 14.299 23.581 32.724 46.066 46.119 89.293 128.56 183.51 232.97 4.915 9.649 14.321 23.599 32.714 46.001 89.076 128.30 183.26 232.70 5.195 5.197 10.153 15.035 24.658 34.139 47.881 92.320 132.54 188.72 239.03 5.747 5.744 11.162 11.158 16.479

7.44 7.42 7.63 7.59 7.95 8.14 8.52 8.85 9.28 9.27 10.53 11.53 12.81 13.86 6.04 6.42 6.81 7.27 7.69 8.21 9.64 10.71 12.09 13.25 0.70 0.68 1.43 2.03 2.88 3.47 4.27 6.27 7.78 9.62 11.13 −10.11 −10.08 −8.69 −8.66 −7.67

473.14 473.14 473.11 473.12 473.12 473.12 473.13 473.28 523.15 523.15 523.15 523.15 523.15 523.15 523.15 523.16 523.17 523.17 523.18 523.18 523.18 523.18 523.18 523.19 573.14 573.14 573.14 573.14 573.15 573.16 573.17 573.19 573.14 573.18 573.18

10.10 10.09 10.09 10.08 10.08 10.07 10.04 10.01 10.03 10.03 10.01 10.02 10.01 10.01 10.01 10.01 10.01 10.01 10.02 10.02 10.02 10.02 10.03 10.03 10.01 10.01 10.00 10.00 9.99 9.99 9.98 9.98 9.98 9.98 9.98

0.50085 0.70120 0.99903 2.0124 2.9999 4.5053 6.0016 6.0016 0.10156 0.10156 0.20097 0.20097 0.30073 0.30073 0.50085 0.70120 0.99903 2.0124 2.9999 2.9999 4.5053 4.5053 6.0016 6.0016 0.050199 0.10156 0.20097 0.30073 0.50085 0.70120 0.99903 2.0124 2.9999 4.5053 6.0016

26.888 37.018 51.658 98.640 140.89 199.45 251.56 251.35 6.807 6.808 13.079 13.091 19.171 19.170 30.975 42.382 58.678 110.27 155.95 155.95 218.29 218.25 273.19 273.19 4.808 9.373 17.676 25.546 40.419 54.450 74.221 134.72 186.49 255.53 314.57

−6.16 −4.96 −3.53 −0.18 2.16 4.93 7.11 7.14 −33.33 −33.34 −30.12 −0.21 −27.90 −27.90 −24.68 −22.30 −19.43 −13.00 −8.75 −8.75 −3.94 −3.93 −0.36 −0.36 −108.01 −100.60 −91.20 −84.57 −75.05 −68.16 −60.51 −44.13 −34.16 −23.90 −16.68

a Standard uncertainties u are u(T) = 0.02 K, u(p) = 0.002 MPa, u(Δρ) = {0.005 + 0.001Δρ } kg·m−3, and ur(m) = 0.0005. The combined expanded uncertainty is Uc(Vϕ) = 0.2 cm3·mol−1 (level of confidence = 0.95).

Heat Capacity Measurements. Isobaric volumetric heat capacities (σp/J·K−1·cm−3) were measured using a commercial Tian−Calvet type differential microcalorimeter (Setaram, Lyon, France, model C-80, sensitivity = 5 μW, resolution = 0.1 μW) between 323 and 573 K at p = 10 MPa. The modifications of this apparatus and the experimental protocol for the determination of σp have been described in detail by Schrödle et al.56 Temperature fluctuations in the laboratory, which was thermostated to ±3 K, resulted in pressure changes of only ±0.3% during a typical experimental run, due to thermal lag. Such variations have an insignificant effect on the measured heat capacities. Matched nickel (low carbon, Ni-201) cells were used throughout. Target solutions were injected by syringe into one of the calorimetric cells. The overfilled cell was then pressurized, to 10 MPa with N2 (BOC, >99%) via a partially filled capillary tube of about 100 cm length connected to a buffer volume of about

1.0 L. After each experiment the sample was removed and the cell was rinsed several times with high purity water and dried with flowing nitrogen. The comparison cell always contained only air at atmospheric pressure. The calorimetric measurements were performed using a step procedure.56 Following initial stabilization for 5 h at 323 K, successive temperature increments (ΔT) were applied, with an isothermal equilibration period of (1.5 to 2.0) h between each step. Alternating increments of 5 K and 20 K with scan rates of (0.25 and 1.0) K·min−1 were used throughout except for the two highest temperature steps which were of 10 K at 0.50 K· min−1. A complete temperature scan therefore required about 2 days. High purity water and nitrogen were used as calibrating fluids57−59 as described later. This method has a reproducibility of ±0.1% and an accuracy of ±0.3% in σp over the entire temperature range.56 2961



■

Article

RESULTS AND DISCUSSION Densities. The results of the density measurements for KOH(aq) are summarized in Table 3. All entries are the average of two consecutive measurements using one sample loop filling. Multiple entries correspond to measurements with separate sample injections, to establish the overall reproducibility. Water densities were calculated using the IAPWS 95 formulation.57,59 The densities of the KOH solutions, ρ, can be obtained by simply adding the experimental Δρ values to the pure water density57,59 for the given experimental conditions. Apparent Molar Volumes. Apparent molar volumes, Vϕ, of KOH(aq) were calculated from the experimental densities using the usual relationship: ρ − ρw M − Vϕ = ρ m ·ρ ·ρw (2) where M is the molar mass of KOH (56.1056 g·mol−1) and m is the molality of the solution. The obtained values of Vϕ are also included in Table 3 and are plotted in Figures 1 and 2 as a function of the square root of molality and of temperature, respectively.

Figure 2. (Lower box) present values of the apparent molar volume, Vϕ, of KOH(aq) as a function of temperature, T, at selected concentrations, m/mol·kg−1 = 6, 4.5, 3, 2, 1, 0.5, 0.2, 0.1 (top to bottom); full lines correspond to the fitting equation, eq 3; the dashed line represents the standard molar volume at infinite dilution, Vo. fit (Upper box) deviations, ΔVϕ = Vexp ϕ − Vϕ , of the present results from eq 3.

are adjustable parameters. The number of parameters for the fitting equations was determined using a statistical F test to ensure that all parameters were statistically significant; the empirical functions and the values of the fitting parameters are listed in Table 4. The upper boxes of Figures 1 and 2 plot the observed deviations of the present experimental data from the fitting equation; they show a maximum deviation of ca. ±0.06 cm3· mol−1 with an average deviation of ±0.02 cm3·mol−1. As would Table 4. Empirical Functions, φ, and Fitting Parameters, a, for the Calculation of Vϕ via eq 3a

Figure 1. (Lower box) present values of the apparent molar volume, Vϕ, of KOH(aq) as a function of the square root of molality, √m, at various temperatures, T/K = 323, 373, 423, 473, 523, 573 (top to bottom); lines correspond to the fitting equation, eq 3. (Upper box) fit deviations, ΔVϕ = Vexp ϕ − Vϕ , of present results from eq 3.

For convenience, the present Vϕ values were fitted with a modified Redlich−Meyer equation60 of the form: Vϕ =

⎛ ∂ρ ⎞ M + AV m + ⎜ w ⎟ ρw ⎝ ∂p ⎠T −1.5

13

∑ aiφi(T , ρw , m) i=1

(3)

where AV/(cm ·mol ·kg ) is the theoretical Debye−Hückel slope for volumes,57,61 φi(T,ρw,m) represents empirical functions of temperature, water density, and molality, and ai 3

0.5

i

ai

σ(ai)b

φi

1 2 3 4 5 6 7 8 9 10 11 12 13

−47.174 −110.78 0.156 −0.207 −1566 1788 −736.5 −475 −101.8 220.8 −3.85 9.64 0.01613

0.085 0.12 0.010 0.035 14 16 5.5 11 5.5 6.4 0.10 0.31 0.00068

τ/ρw ρ2w ρ2w/τ4 ρ4w/τ3 ρ4wτ2m ρ3wτ2m ρwτ3m ρ4wτ4m1.5 τ4m1.5 ρwτ3m1.5 ρwm2 ρ3wτm2 ρw/τ3m2

Units: Vϕ/cm3·mol−1, τ = (T/K)/1000, ρw/g·cm−3, m/mol·kg−1, (∂ρw/∂p)T/kg·m−3·MPa−1. bStandard error. a

2962



Article

Table 5. Volumetric, σp, Massic, cp, and Apparent Molar, Cpϕ, Heat Capacities of KOH(aq) at Temperatures, T, Molalities, m, and Pressure p = 10.0 MPaa T

m

σp

cp

Cpϕ

K

mol·kg−1

J·K−1·cm−3

J·K−1·g−1

J·K−1·mol−1

325.0 337.4 349.7 362.1 374.5 386.8 399.2 411.6 423.9 436.3 448.6 461.0 473.4 485.7 498.1 510.5 522.8 535.2 547.6 555.0 564.9 325.0 337.4 349.7 362.1 374.5 386.8 399.2 411.6 423.9 436.3 448.7 461.0 473.4 485.7 498.1 510.5 522.8 535.2 547.6 555.0 564.9 325.0 337.4 349.8 362.1 374.5 386.8 399.2 411.6 423.9 436.3 448.7 461.0 473.4 485.8 498.1 510.5

0.20097 0.20097 0.20097 0.20097 0.20097 0.20097 0.20097 0.20097 0.20097 0.20097 0.20097 0.20097 0.20097 0.20097 0.20097 0.20097 0.20097 0.20097 0.20097 0.20097 0.20097 0.50085 0.50085 0.50085 0.50085 0.50085 0.50085 0.50085 0.50085 0.50085 0.50085 0.50085 0.50085 0.50085 0.50085 0.50085 0.50085 0.50085 0.50085 0.50085 0.50085 0.50085 0.99903 0.99903 0.99903 0.99903 0.99903 0.99903 0.99903 0.99903 0.99903 0.99903 0.99903 0.99903 0.99903 0.99903 0.99903 0.99903

4.1055 4.0872 4.0658 4.0436 4.0203 3.9967 3.9732 3.9508 3.9289 3.9085 3.8890 3.8705 3.8550 3.8423 3.8320 3.8272 3.8285 3.8390 3.8612 3.8827 3.9250 4.0811 4.0640 4.0431 4.0226 3.9998 3.9777 3.9546 3.9343 3.9120 3.8897 3.8700 3.8500 3.8330 3.8193 3.8063 3.8001 3.7969 3.8003 3.8150 3.8308 3.8600 4.0411 4.0302 4.0110 3.9943 3.9738 3.9543 3.9340 3.9115 3.8863 3.8651 3.8460 3.8273 3.8110 3.7936 3.7800 3.7680

4.1012 4.1085 4.1160 4.1258 4.1375 4.1519 4.1694 4.1911 4.2165 4.2471 4.2824 4.3230 4.3716 4.4289 4.4953 4.5759 4.6732 4.7938 4.9449 5.0557 5.2362 4.0208 4.0290 4.0364 4.0471 4.0582 4.0727 4.0890 4.1110 4.1340 4.1600 4.1922 4.2278 4.2708 4.3223 4.3799 4.4521 4.5358 4.6374 4.7656 4.8592 5.0058 3.8952 3.9090 3.9172 3.9303 3.9421 3.9574 3.9743 3.9915 4.0085 4.0324 4.0614 4.0940 4.1326 4.1739 4.2237 4.2806

−62.0 −54.3 −53.9 −52.0 −53.4 −56.6 −62.0 −66.4 −75.0 −84.2 −99.3 −122.5 −145.6 −173.9 −215.7 −261.2 −319.6 −392.0 −497.4 −584.4 −749.2 −52.2 −46.9 −46.7 −44.0 −45.4 −45.8 −49.8 −50.2 −58.0 −69.9 −81.1 −99.3 −118.5 −140.0 −172.4 −205.3 −253.5 −317.7 −401.4 −468.0 −598.0 −46.4 −37.7 −36.6 −32.2 −31.9 −30.9 −31.8 −36.5 −46.0 −53.5 −61.7 −73.0 −86.1 −106.2 −129.1 −159.8

2963



Article

Table 5. continued T K 522.8 535.2 547.6 555.0 564.9 325.0 337.4 349.8 362.1 374.5 386.8 399.2 411.6 423.9 436.3 448.7 461.0 473.4 485.8 498.1 510.5 522.9 535.2 547.6 555.0 564.9 325.0 337.4 349.8 362.1 374.5 386.8 399.2 411.6 423.9 436.3 448.7 461.0 473.4 485.7 498.1 510.5 522.8 535.2 547.6 555.0 564.9 325.0 337.4 349.8 362.1 374.5 386.8 399.2 411.6 423.9 436.3 448.7 461.0

σp

m

J·K ·cm

0.99903 0.99903 0.99903 0.99903 0.99903 2.0124 2.0124 2.0124 2.0124 2.0124 2.0124 2.0124 2.0124 2.0124 2.0124 2.0124 2.0124 2.0124 2.0124 2.0124 2.0124 2.0124 2.0124 2.0124 2.0124 2.0124 2.9999 2.9999 2.9999 2.9999 2.9999 2.9999 2.9999 2.9999 2.9999 2.9999 2.9999 2.9999 2.9999 2.9999 2.9999 2.9999 2.9999 2.9999 2.9999 2.9999 2.9999 4.5053 4.5053 4.5053 4.5053 4.5053 4.5053 4.5053 4.5053 4.5053 4.5053 4.5053 4.5053

3.7587 3.7593 3.7644 3.7718 3.7885 3.9812 3.9767 3.9599 3.9490 3.9354 3.9150 3.8978 3.8748 3.8565 3.8357 3.8183 3.7953 3.7800 3.7582 3.7409 3.7255 3.7130 3.7050 3.7063 3.7039 3.7020 3.9345 3.9332 3.9214 3.9120 3.9002 3.8844 3.8710 3.8513 3.8341 3.8128 3.7931 3.7750 3.7621 3.7413 3.7260 3.7052 3.6945 3.6809 3.6734 3.6714 3.6640 3.8929 3.8894 3.8833 3.8782 3.8679 3.8551 3.8450 3.8282 3.8138 3.7950 3.7830 3.7658

mol·kg

−1

cp

−1

−3

2964

−1

Cpϕ −1

J·K ·g

4.3466 4.4320 4.5324 4.6037 4.7150 3.6839 3.7025 3.7115 3.7279 3.7438 3.7551 3.7714 3.7841 3.8035 3.8226 3.8473 3.8689 3.9008 3.9287 3.9642 4.0050 4.0527 4.1101 4.1839 4.2282 4.2933 3.5133 3.5332 3.5454 3.5615 3.5769 3.5902 3.6071 3.6199 3.6367 3.6515 3.6697 3.6913 3.7202 3.7434 3.7741 3.8015 3.8413 3.8810 3.9307 3.9657 4.0111 3.3139 3.3294 3.3449 3.3628 3.3773 3.3906 3.4072 3.4190 3.4341 3.4467 3.4671 3.4845

−1

J·K ·mol−1 −200.2 −246.7 −314.6 −368.9 −467.0 −29.8 −22.5 −21.2 −16.9 −14.1 −15.4 −15.7 −20.1 −23.0 −28.7 −34.3 −45.1 −54.2 −70.4 −88.3 −110.8 −139.2 −175.3 −220.9 −260.9 −332.0 −18.4 −12.6 −10.4 −7.3 −5.3 −5.2 −4.9 −7.5 −10.1 −15.3 −21.1 −27.9 −34.6 −46.8 −60.0 −79.6 −100.8 −130.9 −169.4 −199.0 −253.2 −1.9 1.2 3.8 6.7 8.0 8.3 8.8 7.0 5.1 1.3 −1.6 −6.9



Article

Table 5. continued T

σp

m −1

K

mol·kg

473.4 485.7 498.1 510.5 522.8 535.2 547.6 555.0 564.9 325.0 337.4 349.7 362.1 374.5 386.8 399.2 411.5 423.9 436.3 448.6 461.0 473.4 485.7 498.1 510.5 522.8 535.2 547.6 555.0 564.9

4.5053 4.5053 4.5053 4.5053 4.5053 4.5053 4.5053 4.5053 4.5053 6.0016 6.0016 6.0016 6.0016 6.0016 6.0016 6.0016 6.0016 6.0016 6.0016 6.0016 6.0016 6.0016 6.0016 6.0016 6.0016 6.0016 6.0016 6.0016 6.0016 6.0016

−1

cp −3

−1

J·K ·cm

Cpϕ −1

−1

J·K ·mol−1

J·K ·g

3.7490 3.7311 3.7151 3.6931 3.6793 3.6641 3.6563 3.6516 3.6460 3.8547 3.8592 3.8554 3.8533 3.8467 3.8380 3.8280 3.8133 3.7995 3.7858 3.7732 3.7544 3.7406 3.7251 3.7104 3.6944 3.6817 3.6641 3.6598 3.6530 3.6357

−13.5 −22.0 −32.3 −47.3 −64.3 −87.3 −116.3 −138.8 −176.9 8.0 11.4 13.8 16.5 18.2 19.1 19.2 17.8 16.0 13.6 10.7 5.8 0.9 −5.6 −13.7 −24.5 −38.1 −57.3 −80.0 −98.5 −130.7

3.5039 3.5240 3.5472 3.5657 3.5926 3.6187 3.6534 3.6759 3.7109 3.1480 3.1677 3.1839 3.2034 3.2200 3.2352 3.2497 3.2607 3.2732 3.2868 3.3028 3.3150 3.3333 3.3515 3.3717 3.3909 3.4126 3.4285 3.4563 3.4702 3.4868

a

Standard uncertainties u are u(T) = 0.05 K, u(p) = 0.03 MPa, ur(σp) = ur(cp) = 0.003, and ur(m) = 0.0005. The combined expanded uncertainty is Uc(Cpϕ) = {2 + 10/m} J·K−1·mol−1 (level of confidence = 0.95).

appropriate conditions were taken from standard literature sources.57−59 Isobaric massic heat capacities, cp (J·K−1·g−1), for KOH(aq) were calculated as cp = σp/ρ using the fitted densities measured in this work and are summarized in Table 5. Apparent Molar Heat Capacities. Apparent molar heat capacities, Cpϕ, were derived from the massic heat capacities with the usual relationship:

be expected from eq 2 there is a slight decrease in the size of the deviations with increasing molality (Figure 1); on the other hand temperature does not appear to significantly affect the scatter (Figure 2). Standard molar volumes, Vo, for KOH(aq), obtained by extrapolation of eq 3 to infinite dilution, are included at rounded temperatures in the Supporting Information. Volumetric and Massic Heat Capacities. Isobaric volumetric heat capacities were obtained isoplethically from temperature T(t) and heat flow Q̇ (t) data recorded as a function of time, t. As described previously,56 the isobaric volumetric heat capacity of a sample, σsj , at the average 1 temperature of the increment, Tj̅ = 2 (T′j + Tj), where Tj = T(tj), and T′j = T(t′j) are respectively the temperature of the sample immediately before and after each temperature increment, was calculated assuming a linear response for the calorimeter: σjs = (qjs − qjw ) ·

σjw − σjN qjw − qjN

Cpϕ = M ·cp +

cp − cp,w (5)

m

where cp,w is the massic heat capacity of pure water, as given in the IAPWS 95 formulation.57,59 The apparent molar heat capacities were fitted with a modified Redlich−Meyer type equation: 16

Cpϕ = A C[ m +

∑ biφi(T , ρw , m)] i=1

−1

−1.5

(6)

where AC/(J·K ·mol ·kg ) is the theoretical Debye− Hückel slope for heat capacity, the parameters φi(T,ρw,m) are empirical functions of temperature, water density, and molality, and bi are adjustable parameters. The empirical functions and the values of the fitting parameters are listed in Table 6. As for volumes, the number of parameters for the fitting equation was determined using a statistical F test to make sure that all parameters were statistically significant and to avoid overfitting.

+ σjw (4)

where qj are instrument-specific volumetric heat capacities. The superscripts w and N indicate values for liquid water and gaseous nitrogen, respectively, which were obtained from calibration experiments performed under identical conditions. Volumetric heat capacities for water and nitrogen at the 2965

0.5



Article

Table 6. Empirical Functions, φ, and Fitting Parameters, a, for Calculation of Cpϕ via eq 6a

a b

i

bi

σ(bi)b

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

−1.27 −0.1472 21.2 30.2 62 52 −31.1 −0.0655 0.236 68.2 −7.51 −1.45 0.326 0.628 −0.0534 0.99

0.34 0.0051 4.7 9.3 29 14 2.0 0.0070 0.021 4.4 0.70 0.15 0.027 0.055 0.0057 0.12

φi ρ2w/(0.647 − ρ3w/τ3 ρ4w ρ3w/lnτ ρ4w·τ2 τ2 ρ2w·τ2·m ρ2w/(0.647 − ρw/τ·m ρ3w·τ3·m τ2·m1.5 ρ3w·τ·m1.5 ρ3w·lnτ·m1.5 ρ3w/(0.647 − ρ2w/(0.647 − τ2·m2

τ)

τ)·m

τ)·m1.5 τ)·m2

Units: Cpϕ/J·K−1·mol−1, τ = (T/K)/1000, ρw/g·cm−3, m/mol·kg−1. Standard error.

Figures 3 and 4 show the apparent molar heat capacities as a function of the square root of molality and temperature, Figure 4. (Lower box:) present values of the apparent molar heat capacities, Cpϕ, of KOH(aq) as a function of temperature T at various molalities, m/mol·kg−1 = 6, 4.5, 3, 1, 0.5, 0.2 (top to bottom); full lines correspond to the fitting equation, eq 6; the dashed line represents the standard molar heat capacity at infinite dilution, Cpο. (Upper box) fit deviations, ΔCpϕ = Cexp pϕ − Cpϕ, of the present results from eq 6.

measurements under ambient conditions. Again, there is a significant decrease in the deviations with increasing molality (Figure 3), while the effects of temperature appear to be completely random (Figure 4). Standard molar heat capacities, Cpo, for KOH(aq), obtained by extrapolation of eq 6 to infinite dilution, are listed at rounded temperatures in the Supporting Information. Equations 3 and 6 were used to generate tables of smoothed densities and massic heat capacities at rounded temperatures and molalities at p = 10 MPa. These values are provided as Supporting Information. Comparison with Previous Studies. As indicated in Table 1 and consistent with their industrial and geochemical importance, many studies of the densities of KOH(aq) solutions have been reported in the literature. Unfortunately, even though some of these studies have covered wide ranges of concentration and temperature they mostly cannot be compared directly with the present data due to differences in measurement pressure. For this reason, the available literature data were fitted together with the present data, and comparisons made via deviations from the overall fit in which equal statistical weights have been given to each fitted data source. This overall fit which has the same form as eq 3 used for present data fitting but has different fitting parameters, has been used for comparison of the present data with the literature data only. For all other calculations the original fit (eq 3 and Table 4) was used. Since the experimental temperatures, pressures, and concentrations of the literature data and the present results overlap to some extent, this provides a reasonable estimate of the level of agreement. The deviations from the fit are shown in Figure 5, and the average characteristics of the deviations of the

Figure 3. (Lower box) present values of the apparent molar heat capacities, Cpϕ, of KOH(aq) as a function of the square root of molality, √m, at various temperatures, T/K = 374, 399, 424, 449, 473, 498, 523, 548, 565 (top to bottom); the lines correspond to the fitting fit equation, eq 6. (Upper box) deviations, ΔCpϕ = Cexp pϕ − Cpϕ, of the present results from eq 6.

respectively. For clarity, only selected isotherms were included in Figure 3. The upper boxes in Figures 3 and 4 indicate a maximum deviation of the experimental results from eq 6 of ±3 J·K−1·mol−1, with an average value of ±1 J·K−1·mol−1. This scatter is almost as good as that obtained in routine calorimetric 2966



Article

individual data sets from the overall fitting equation are summarized in Table 7.

pressure (Table 1). Despite the significant pressure difference the present Cpϕ values (at p = 10 MPa) of KOH(aq) at low temperatures (≤373 K) fit seamlessly with the data of Roux et al.,45 measured using a Picker flow calorimeter at p = 0.1 MPa and 278.15 ≤ T/K ≤ 328.15. The most recent literature data are those of Patterson et al.46 who measured heat capacities at p = 0.35 MPa up to T = 393.15 K and m(KOH) ≤ 0.5 mol·kg−1, which are also in excellent agreement with the present data in the overlapping regions of temperature and concentration. On the other hand, while Ginzburg et al.62 studied KOH(aq) up to 528.18 K, presumably at saturation pressure, their heat capacities differ significantly from ours and others. Given that Ginzburg et al. provided little information about their experimental procedure, and the scatter in their results is almost an order of magnitude greater than all other studies (Table 8), their data were judged to be of doubtful reliability Table 8. Summary of Deviations of Literature and Present Apparent Molar Isobaric Heat Capacities from the Overall Fitting Equation ref Gucker and Schminke Ginzburg et al.62 Singh et al.48 Roux et al.45 Patterson et al.46 this work

47

biasa

scatterb

2.6 −8.2 1.0 0.0 −0.1 0.0

2.7 13.6 2.0 2.3 1.5 1.4

b fit −1 −1 Bias/(J·K−1·mol−1) = mean(Cexp pϕ − Cpϕ). Scatter/(J·K ·mol ) = exp fit mean(|Cpϕ − Cpϕ|).

a

fit Figure 5. Deviations (ΔVϕ = Vexp ϕ − Vϕ ) of present and literature apparent molar volumes, Vϕ, of KOH(aq) from the overall fit of all data using eq 3: ●, this work; violet +, Akerlof and Bender;37 ▽, Mashovets et al.;39 blue ▼, Tham et al.;40 red ×, Herrington et al.;41 □, Corti et al.;42 green ▲, Sipos et al.;43 ⧫, Salavera et al.;44 ○, Roux et al.;45 ◇, Patterson et al.46 Deviations as a function of as a function of (lower box) temperature, T, and (upper box) molality, m.

and thus were not included in the overall fitting procedure or in Figure 6. The average characteristics of the deviations in Cpϕ of the individual data sets from the overall fitting equation (again, of the same form as eq 6 but with different parameters) are summarized in Table 8. As with Vϕ, the overall fitting equation of all (present and literature) Cpϕ values served to compare the various data sets obtained at different pressures. As the overall fits for both Vϕ and Cpϕ were used only for comparison purposes, no details of such equations are given here. Comparison of KOH(aq) with Other Alkali Metal Hydroxide Solutions. Comparison of the present results for KOH(aq) with those of the other alkali metal hydroxides is restricted by the limited availability of the latter at elevated temperatures. Density and heat capacity data for NaOH(aq) have been determined53,56 under similar conditions to the present study. In contrast, apart from some densities for LiOH(aq) solutions at close to saturation pressure,42 almost no reliable data have been reported under nonambient conditions for either volumes or heat capacities for the aqueous solutions of the other alkali metal hydroxides. Accordingly, to make such a comparison it was necessary to use unpublished data for LiOH(aq) and CsOH(aq) determined in our laboratory as part of a larger investigation of the properties of concentrated caustic solutions.63 For convenience the comparison was made in terms of differences in the apparent molar quantities between KOH(aq) and the other MOH(aq) solutions. The results so obtained are illustrated in Figures 7 and 8 for the standard (infinite dilution; m = 0) values and for a moderately concentrated (at the arbitrary value of m = 4 mol·kg−1) set of solutions. With regard to Vϕ (Figure 7), the most striking feature of the data is the almost constant differences between KOH(aq)

Table 7. Summary of Deviations of Literature and Present Apparent Molar Volumes from the Overall Fitting Equation ref Akerlof and Bender Mashovets et al.39 Tham et al.40 Roux et al.45 Herrington et al.41 Corti et al.42 Sipos et al.43 Patterson et al.46 Salavera et al.44 this work

37

biasa

scatterb

0.01 0.11 −0.50 0.12 −0.10 0.24 −0.01 −0.17 2.24 0.00

0.06 0.36 0.50 0.17 0.12 0.58 0.07 0.39 2.24 0.02

Bias/(cm3·mol−1) = mean(Vexp − Vfit ϕ ϕ ). exp fit mean(|Vϕ − Vϕ |). a

b

Scatter/(cm3·mol−1) =

The high temperature data of both Mashovets et al.39 and Corti et al.,42 obtained at close-to-saturation pressure, are reasonably consistent with the present values. At low temperatures (≤373 K) all of the available data are broadly consistent with the exception of the results reported by Salavera et al.44 For heat capacities, there are few data available in the literature, mainly at low temperatures and only at atmospheric 2967



Article

Figure 7. Differences between the apparent molar volumes, Vϕ, of KOH(aq) and other alkali metal hydroxide solutions, MOH(aq), as functions of temperature, T. Open symbols and dashed lines correspond to infinite dilution (m = 0) values; full symbols and solid lines correspond to molality m = 4 mol·kg−1: red ○●, M = Li;63 blue □■, M = Na;53 ◇◆, M = Cs.63

Figure 6. Deviations of present and literature apparent molar heat fit capacities from the overall fit, ΔCpϕ = Cexp pϕ − Cpϕ: ●, this work; □, Corti et al.;42 ○, Roux et al.;45 ◊, Patterson et al.;46 red +, Gucker and Schminke;47 blue ▲, Singh et al.48 Deviations as a function of as a function of (lower box) temperature, T, and (upper box) molality, m.

(represented by the zero line in the plot) and NaOH(aq) and CsOH(aq), at least up to 525 K and irrespective of concentration. These differences essentially reflect the differences in the hard-sphere volumes of the cations (r(Cs+) > r(K+) > r(Na+)). While the Vϕ values of LiOH(aq) follow this simple pattern at lower temperatures, they depart from it markedly at higher temperatures and exhibit a significant dependence on concentration (Figure 7). These departures are almost certainly a reflection of the much greater ion pairing in LiOH(aq) cf. the other alkali metal hydroxides, especially at higher temperatures.64−66 Similar trends are observed for the apparent molar heat capacities (Figure 8). At least up to ∼525 K, the differences Cpϕ(MOH(aq)) − Cpϕ(KOH(aq)) are more or less constant and are not much affected by the solute concentration, although at higher temperatures this constancy is lost somewhat. More importantly, LiOH(aq) is again the odd system out, with its differences from KOH(aq) showing a marked dependence on both temperature and concentration, even at low T. Volume and Heat Capacity Changes for the Ionization of Water. Beside the determination of accurate densities and heat capacities of KOH(aq) up to high concentrations, a major aim of this study was to obtain appropriate data for calculating ΔVo and ΔCop for the ionization of water (eq 7). This equilibrium is without doubt the most important occurring in aqueous solution, particularly for modeling the behavior of geochemical and engineering processes. Such data can be derived from neutralization reactions, as shown for example in eq 8:

Figure 8. Differences between apparent molar isobaric heat capacities, Cpϕ, of KOH(aq) and other alkali metal hydroxide solutions, MOH(aq), as functions of temperature, T. Open symbols and dashed lines correspond to infinite dilution (m = 0); full symbols and solid lines correspond to molality m = 4 mol·kg−1: red ○●, M = Li;63 blue □■, M = Na;53 ◇◆, M = Cs.63

2968



Article

Table 9. Present and Literature Values of the Standard Molar Volume Changes, ΔVo, and Standard Molar Isobaric Heat Capacity Changes, ΔCop, for the Ionization of Water (eq 7) T/K

323.15

373.15

423.15

473.15

523.15

573.15

p/MPaa

0.101

0.101

0.476

1.55

3.98

8.59

−71.7 ± 2 −76.7 −76.4 ± 5 −93.4 −87.8 −80.1 ± 3

−137.5 ± 6 −144.3

−34.1 −35.1

ΔVo/cm3·mol−1 ± 0.3 −43.9 ± 1 −48.8 ± 1.7 −48.5 ± 2.3 −52.4 −50.8 ± 1.1 −51.7 ± 2.2

−222 −233 −227 −230 −236

ΔCop/J·K−1·mol−1 ±5 −344 ± 13 −341 ±7 −341 −352 ± 14 −344

−531 −511 −545 −690 −547

−928 ± 70 −964 ± 93

ref this workb 56b,d 65 66 67 64 46c ref this workb 65 68 67 64 46c 55b 69

−20.9 ± 0.5 −21.6 −22.8 ± 1.7 −21.7 −22.2 −22.4 ± 0.5 −22.4

−23.4 ± 0.4 −25.5 −25.8 ± 1.6 −25.4 −25.8 −25.9 ± 0.8 −26.8

−194 ± −186 ± −183 ± −182 −185 ± −185.9 −186 ± −180

−167 ± −174 ± −167 ± −182 −183 ± −187.3 −182 ± −175.1

5 5 7 4 5

−29.9 −33.9 −34.0

4 5 5 5

−224 ± 10 −222.2

5

± 11 ± 30 ± 21 ± 25

−314 ± 26 −348.3

± 24 ± 45 ± 39

−2164 ± 46

−476 ± 34 −758.9

−984 ± 93

Atmospheric pressure (T ≤ 373 K) or saturation vapor pressure of pure water.59 bAt p = 10 MPa. cAt p = 0.35 MPa. dCalculated using Voϕ(NaOH),53Voϕ(NaCl),54Voϕ(HCl).68 a

H 2O(l) = OH−(aq) + H+(aq)

(7)

KOH(aq) + HCl(aq) = H 2O(l) + KCl(aq)

(8)

If the standard partial molar volumes and heat capacities, Voϕ and Copϕ, of KOH(aq), HCl(aq), and KCl(aq) are known under identical conditions, then ΔVo and ΔCop for the ionization process, eq 7, can be derived assuming electrolyte additivity: ΔV o = V ϕo(KOH) + V ϕo(HCl) − V ϕo(KCl) − V *(H 2O) (9)

ΔC po = C poϕ(KOH) + C poϕ(HCl) − C poϕ(KCl) − C*p (H 2O) (10)

where V*(H2O) is the molar volume of pure water and C*p (H2O) is its isobaric molar heat capacity. Both of these values are well established and were obtained from the IAPWS formulation.59 The Voϕ and Copϕ values for KCl were calculated for the present temperatures and pressure using the model of Pabalan and Pitzer;67 those for HCl(aq) were obtained from the data of Sharygin and Wood68 as described previously.56 The KOH(aq) values were taken from fitting eqs 3 and 6 by extrapolation to infinite dilution. All values were for a pressure of 10.0 MPa. The results for ΔVo and ΔCop calculated from the above data are summarized along with literature values in Table 9, and are plotted in Figures 9 and 10. Note that most of the literature data were reported at the saturation vapor pressure of pure water or, for T ≤ 373.15 K, at ambient pressure. Despite differences in pressure, at lower temperatures (T ≤ 425 K), the present values of ΔVo are in excellent agreement with all previous studies (Figure 9). As would be expected from the increasing compressibility of the solvent, the various studies diverge at higher temperatures. Thus, while there is good agreement among the present results and those obtained by Sweeton et al.69 and Sharygin and Wood,68 the results of Chen et al.71 and especially of Marshall and Franck70 are more negative. Above 523 K no data were available for comparison;

Figure 9. Standard molar volume change for the ionization of water, ΔVo, as a function of temperature, T: ●, this work; ×, Patterson et al.;46 green ◊, Sharygin and Wood;68 red □, Sweeton et al.;69 blue ▲, Marshall and Franck;70 violet +, Chen et al.;17 ○, Hnedkovsky et al.53 The dashed line was calculated by the present authors from the pressure derivative of the ionization constant of water57 at p = 10 MPa.

however, the present result at 573 K is in reasonable agreement with the value calculated by the present authors from the pressure derivative at 10 MPa of the ionization constant of water57 (dashed line in Figure 9). While derivatives of real equilibrium constant data are notoriously unreliable, such data have the advantage of being completely independent of density data. 2969



Article

tration. Apparent molar quantities derived from these data were fitted by an extended Redlich−Meyer equation to obtain the standard molar values at infinite dilution. Although no direct comparisons could be made the present results were broadly compatible with the available literature data. Comparison of the present results with those of the other alkali metal hydroxides showed LiOH(aq) to be quite different. The values at infinite dilution were used to calculate the changes in volume and heat capacity associated with the ionization of water.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00192. Densities (Table S1) and massic heat capacities (Table S2) of KOH(aq) at rounded temperatures, molalities, and at pressure p = 10 MPa calculated from fitted experimental data of the present work. Densities were calculated via eqs 2 and 3 using the parameters in Table 4; heat capacities were calculated via eqs 5 and 6 using the parameters in Table 6. All pure water properties were calculated via the IAPWS formulation.57,59 Standard molar volumes and standard molar heat capacities obtained by extrapolation to infinite dilution are also included in the Tables (PDF)

Figure 10. Standard molar heat capacity change for the ionization of water, ΔCpo, as a function of temperature, T: ●, this work; ×, Patterson et al.;46 green ▼, Schrödle et al.;56 green ◊, Sharygin and Wood;68 red □, Sweeton et al.;69 violet +, Chen et al.;71 blue ▲, Palmer and Drummond;72 ⧫, Djamali.73 The dashed line was calculated by the present authors from the second temperature derivative of the ionization constant of water57 at p = 10 MPa.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ΔCop

The present results for at lower temperatures (T ≤ 425 K), are also in excellent agreement with the literature data (Figure 10), again despite the pressure differences. At higher temperatures the agreement is still reasonable with respect to the values of Sweeton et al.,69 Palmer and Drummond,72 and Sharygin and Wood.68 On the other hand, the present results are rather less negative than those of Chen et al.71 and Djamali.73 Note that Chen et al.’s value of ΔCop at 573 K (Table 9) was omitted from Figure 10 as it was over 1000 J·K−1·mol−1 more negative than all other results. It should also be mentioned that the ΔCop values of Sweeton et al.69 and Palmer & Drummond72 were obtained from the second temperature derivative of the ionization constant of water (measured by potentiometry). While this means they are experimentally independent of any heat capacity data, the reliability of such derivatives is always questionable. Other estimates of ΔCop at high T and p, like those of Olofsson and Hepler74 or Chen et al.,71 are based on extrapolations and suffer from the large uncertainties in the thermodynamic data for NaOH(aq) at high temperatures that were available at the time. The good agreement with the values of Sharygin and Wood68 is unexpected because of the considerable difference in pressure. This is either fortuitous or it indicates that ΔCop is almost independent of pressure in the studied temperature range.

ORCID

Lubomir Hnedkovsky: 0000-0002-1928-6999 Present Address #

S.B.: Wacker Chemie AG, Friedrich von Heyden Platz, 01612 Nünchritz, Germany. Funding

This work was funded by Alcoa World Alumina, BHP Billiton/ Worsley Alumina, Hydro Aluminium Metal Products, Rio Tinto Alcan, and UC Rusal Aughinish through the AMIRA International Collaborative Research Project P507C, the Australian Research Council (via Linkage Grant No. LP0776541), and by Murdoch University. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Gratz, A. J.; Bird, P.; Quiro, G. B. Dissolution of quartz in aqueous basic solution, 106−236°C: Surface kinetics of ″perfect″ crystallographic faces. Geochim. Cosmochim. Acta 1990, 54, 2911− 2922. (2) Pascal, M. L.; Anderson, G. M. Speciation of Al, Si, and K in supercritical solutions: Experimental study and interpretation. Geochim. Cosmochim. Acta 1989, 53, 1843−1855. (3) Anderson, G. M. Is there alkali−aluminum complexing at high temperatures and pressures? Geochim. Cosmochim. Acta 1995, 59, 2155−2161. (4) Azaroual, M.; Pascal, M. L.; Roux, J. Corundum solubility and aluminum speciation in KOH aqueous solutions at 400°C from 0.5 to 2.0 kbar. Geochim. Cosmochim. Acta 1996, 60, 4601−4614. (5) Walther, J. V. Experimental determination and interpretation of the solubility of corundum in H2O between 350 and 600°C from 0.5 to 2.2 kbar. Geochim. Cosmochim. Acta 1997, 61, 4955−4964.

■

CONCLUSIONS Densities and massic heat capacities of aqueous solutions of potassium hydroxide, measured at 323.15 ≤ T/K ≤ 573.15, p = 10 MPa and concentrations up to m = 6 mol·kg−1 using a purpose-built vibrating-tube densimeter and a modified Setaram C80 calorimeter, respectively, were found to be well behaved and varied smoothly with temperature and concen2970



Article

(31) Kragness, R. C.; Waggener, H. A. Precise etching of semiconductors. U.S. Patent US3765969 A, 1970. (32) Walker, T. O.; Dearing, H. L.; Simpson, J. P. Potassium modified lime muds improve shale stability. World Oil 1983, 93−94 (96), 100. (33) Hemphill, T. Using potassium to stabilize Gulf of Mexico shales. World Oil 1989, 209 (81−88), 90. (34) Sutcu, H.; Dural, A. Effect of hydroxides on carbonization of bituminous coal. Coal Prep. 2006, 26, 201−208. (35) Ros, A.; Lillo-Ródenas, M. A.; Fuente, E.; Montes-Morán, M. A.; Martín, M. J.; Linares-Solano, A. High surface area materials prepared from sewage sludge−based precursors. Chemosphere 2006, 65, 132− 140. (36) Shie, J.−L.; Lin, J.−P.; Chang, C.−Y.; Lee, D.−J.; Wu, C.−H. Pyrolysis of oil sludge with additives of sodium and potassium compounds. Resour., Conserv. Recycl. 2003, 39, 51−64. (37) Akerlof, G.; Bender, P. The density of aqueous solutions of potassium hydroxide. J. Am. Chem. Soc. 1941, 63, 1085−1088. (38) Kelly, W. R.; Borza, P. F.; Harriger, R. D. Densities and viscosities of potassium hydroxide solutions at low temperatures. J. Chem. Eng. Data 1965, 10, 233−234. (39) Mashovets, V. P.; Dibrov, I. A.; Krumgalz, B. S.; Matveeva, R. P. Density of aqueous solutions of KOH at high temperatures in a wide range of concentrations. Zh. Prikl. Khim. 1965, 38, 2344−2347. (40) Tham, M. J.; Gubbins, K. E.; Walker, R. D. Densities of potassium hydroxide solutions. J. Chem. Eng. Data 1967, 12, 525−526. (41) Herrington, T. M.; Pethybridge, A. D.; Roffey, M. G. Densities of aqueous lithium, sodium and potassium hydroxides from 25 to 75 °C at 1 atm. J. Chem. Eng. Data 1986, 31, 31−34. (42) Corti, H. R.; Fernandez-Prini, R.; Svarc, F. Densities and partial molar volumes of aqueous solutions of lithium, sodium, and potassium hydroxides up to 250°C. J. Solution Chem. 1990, 19, 793−809. (43) Sipos, P. M.; Hefter, G.; May, P. M. Viscosities and Densities of Highly Concentrated Aqueous MOH Solutions (M+ = Na+, K+, Li+, Cs+, (CH3)4N+) at 25.0°C. J. Chem. Eng. Data 2000, 45, 613−617. (44) Salavera, D.; Libotean, S.; Patil, K. R.; Esteve, X.; Coronas, A. Densities and heat capacities of the ammonia + water + NaOH and ammonia + water + KOH solutions. J. Chem. Eng. Data 2006, 51, 1020−1025. (45) Roux, A. H.; Perron, G.; Desnoyers, J. E. Heat capacities, volumes, expansibilities, and compressibilities of concentrated aqueous solutions of lithium hydroxide, sodium hydroxide, and potassium hydroxide. Can. J. Chem. 1984, 62, 878−885. (46) Patterson, B. A.; Call, T. G.; Jardine, J. J.; Origlia-Luster, M. L.; Woolley, E. M. Thermodynamics for ionization of water at temperatures from 278.15 to 393.15 K and at the pressure 0.35 MPa: apparent molar volumes of aqueous KCl, KOH, and NaOH and apparent molar heat capacities of aqueous HCl, KCl, KOH, and NaOH. J. Chem. Thermodyn. 2001, 33, 1237−1262. (47) Gucker, F. T., Jr.; Schminke, K. H. A study of the heat capacity and related thermodynamic properties of aqueous solutions of lithium chloride, hydrochloric acid and potassium hydroxide at 25°C. J. Am. Chem. Soc. 1932, 54, 1358−1373. (48) Singh, P. P.; Woolley, E. M.; McCurdy, K. G.; Hepler, L. G. Heat capacities of aqueous electrolytes: eight 1:1 electrolytes and ΔCop for ionization of water at 298 K. Can. J. Chem. 1976, 54, 3315−3318. (49) Sipos, P.; May, P. M.; Hefter, G. T. Carbonate removal from concentrated hydroxide solutions. Analyst 2000, 125, 955−958. (50) Rudolph, W. W.; Hefter, G. T. Quantitative analysis in alkaline aluminate solutions by Raman spectroscopy. Anal. Methods 2009, 1, 132−138. (51) 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. (52) Jedelský, J.; Hnedkovsky, L.; Cibulka, I. Partial molar volumes of organic solutes in water. II. Dihydroxybenzenes at temperatures T = (298 to 473) K and pressures up to 30 MPa. J. Chem. Thermodyn. 1999, 31, 27−42.

(6) Wohlers, A.; Manning, C. E. Solubility of corundum in aqueous KOH solutions at 700 °C and 1 GPa. Chem. Geol. 2009, 262, 310− 317. (7) Bauer, A.; Berger, G. Kaolinite and smectite dissolution rate in high molar KOH solutions at 35° and 80°C. Appl. Geochem. 1998, 13, 905−916. (8) Mosser-Ruck, R.; Cathelineau, M.; Baronnet, A.; Trouiller, A. Hydrothermal reactivity of K−smectite at 300°C and 100 bar; dissolution−crystallization process and non−expandable dehydrated smectite formation. Clay Miner. 1999, 34, 275−290. (9) Bauer, A.; Velde, B. Smectite transformation in high molar KOH solutions. Clay Miner. 1999, 34, 259−273. (10) Nyamangara, J.; Munotengwa, S.; Nyamugafata, P.; Nyamadzawo, G. The effect of hydroxide solutions on the structural stability and saturated hydraulic conductivity of four tropical soils. S. Afr. J. Plant Soil 2007, 24, 1−7. (11) Sydansk, R. D. Stabilizing clays with potassium hydroxide. J. Pet. Technol. 1984, 36, 1366−1374. (12) Elert, K.; Sebastián, E.; Valverde, I.; Rodriguez-Navarro, C. Alkaline treatment of clay minerals from the Alhambra Formation: Implications for the conservation of earthen architecture. Appl. Clay Sci. 2008, 39, 122−132. (13) Pokrovskii, V. A.; Helgeson, H. C. Thermodynamic properties of aqueous species and the solubilities of minerals at high pressures and temperatures: The system Al2O3−H2O−KOH. Chem. Geol. 1997, 137, 221−242. (14) Christov, C.; Moller, H. C. A chemical equilibrium model of solution behavior and solubility in the H−Na−K−Ca−OH−Cl− HSO4−SO4−H2O system to high concentration and temperature. Geochim. Cosmochim. Acta 2004, 68, 3717−3739. (15) Sakagami, E.; Fujie, Y.; Katsui, Y. Alkaline Primary Batteries; Matsushita Electric Industrial Co., 1957. (16) Berndt, D.; Spahrbier, D. Batteries. in Ullmann’s Encyclopedia of Industrial Chemistry; Wiley−VCH Verlag, 2010; Vol. 7. (17) Hunger, H.; Wynn, J. E. Fuel cell; U.S. Dept. of the Army, 1964; p 3. (18) Elmore, G. V.; Tanner, H. A. Fuel cells with alkali metal hydroxide electrolyte and electrode containing fluorocarbon polymer. U.S. Patent US3419900 A, 1968. (19) Simons, E. L.; Cairns, E. J.; Surd, D. J. Performance of direct ammonia fuel cells. J. Electrochem. Soc. 1969, 116, 556−561. (20) Casado Gimenez, J.; Brillas Coso, E. Alkaline Fuel Cell for Cogeneration of Hydrogen Peroxide. ES Patent ES2126492B1, 1999. (21) Kleber, M.; Heitzer, W. Continuous production of a fatty acid alkyl ester mixture and its use as a fuel and/or motor fuel. DE Patent DE10043575 A1, 2002. (22) Vicente, G.; Martínez, M.; Aracil, J. Integrated biodiesel production: a comparison of different homogeneous catalysts systems. Bioresour. Technol. 2004, 92, 297−305. (23) Boehman, A. L. Biodiesel production and processing. Fuel Process. Technol. 2005, 86, 1057−1058. (24) Chang, W.-M. Method for refining biodiesel with high efficiency and at low costs, Patent 2008-10214318, Taiwan Wolmo Inc., 2008. (25) Potts, J. M.; Elder, H. W.; Anderson, Jr., J. F. Concentrated liquid fertilizers from superphosphoric acid and potassium hydroxide. U.S. Patent US3022154 A, 1962. (26) Asano, T. Manufacture of a potassium phosphate fertilizer, 1973, (Tekkosha Co., Ltd.). JP 71-90290. (27) Sugimoto, T. Two−step saponification of oils and fats in the presence of alcohols in the manufacture of liquid, skin−compatible bath soaps, 1995, (Samii Kk, Japan). JP. 94-67172, p 4 pp. (28) Shamanskaya, L. D.; Khabarov, S. N.; Zhukovskii, A. V. Production of liquid insecticide soap from neutral vegetable oils, 2004, (Russia). RU 2000-104190. No page numbers. (29) Isami, K.; Kimura, M.; Aoyama, T.; Tago, T. Anisotropic silicon etchant composition. US Patent US20090218542 A1, 2009. (30) Erdman, W. C.; Schmidt, P. F. Etching solutions for germanium and silicon. DE Patent DE2245809 A1, 1973. 2971



Article

(74) Olofsson, G.; Hepler, L. G. Thermodynamics of ionization of water over wide ranges of temperature and pressure. J. Solution Chem. 1975, 4, 127−143.

(53) Hnedkovsky, L.; Königsberger, E.; Cibulka, I.; Königsberger, L. C.; Schrödle, S.; May, P. M.; Hefter, G. Densities of NaOH(aq) at temperatures from (323 to 573) K and 10 MPa pressure. J. Chem. Eng. Data 2007, 52, 2237−2244. (54) Archer, D. G. Thermodynamic properties of the sodium chloride + water system. II. Thermodynamic properties of NaCl(aq), NaCl.2H2O(cr), and phase equilibria. J. Phys. Chem. Ref. Data 1992, 21, 793−829. (55) Hill, P. G.; MacMillan, R. D. C.; Lee, V. A fundamental equation of state for heavy water. J. Phys. Chem. Ref. Data 1982, 11, 1−14. (56) Schrödle, S.; Königsberger, E.; May, P. M.; Hefter, G. Heat capacities of aqueous solutions of sodium hydroxide and water ionization up to 300 °C at 10 MPa. Geochim. Cosmochim. Acta 2008, 72, 3124−3138. (57) Harvey, A. H.; Lemmon, E. W. NIST/ASME Steam Properties, Formulation for General and Scientific Use. NIST Standard Reference Database 10, version 3.0; NIST, 2013. (58) Jacobsen, R. T.; Penoncello, S. G.; Lemmon, E. W. Roland Span Multiparameter Equations of State; Elsevier: Amsterdam, 2000; Vol. 5, p 33. (59) 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. (60) Millero, F. J. The molal volumes of electrolytes. Chem. Rev. 1971, 71, 147−176. (61) Archer, D. G.; Wang, P. The dielectric constant of water and Debye−Hückel limiting law slopes. J. Phys. Chem. Ref. Data 1990, 19, 371−410. (62) Ginzburg, D. M.; Kochkalda, V. E.; Guba, N. I. Enthalpies and specific heats in the potassium hydroxide−water system. Zh. Fiz. Khim. 1973, 47, 2145−2146. (63) Hnedkovsky, L.; Bochmann, S.; Hefter, G. T.; May, P. M. Unpublished results. Murdoch University, 2010. (64) Ho, P. C.; Palmer, D. A.; Wood, R. H. Conductivity measurements of dilute aqueous LiOH, NaOH nad KOH solutions to high temperatures and pressures using a flow−through cell. J. Phys. Chem. B 2000, 104, 12084−12089. (65) Arcis, H.; Ferguson, J. P.; Zimmerman, G. H.; Tremaine, P. R. The limiting conductivity of the borate ion and its ion−pair formation constants with sodium and potassium under hydrothermal conditions. Phys. Chem. Chem. Phys. 2016, 18, 24081−24094. (66) Arcis, H.; Ferguson, J. P.; Applegarth, L.M.S.G.A.; Zimmerman, G. H.; Tremaine, P. R. Ionization of boric acid in water from 298 to 623 K by AC conductivity and Raman spectroscopy. J. Chem. Thermodyn. 2017, 106, 187−198. (67) Pabalan, R. T.; Pitzer, K. S. Apparent molar heat capacity and other thermodynamic properties of aqueous potassium chloride solutions to high temperatures and pressures. J. Chem. Eng. Data 1988, 33, 354−362. (68) Sharygin, A. V.; Wood, R. H. Volumes and heat capacities of aqueous solutions of hydrochloric acid at temperatures from 298.15 to 623 K and pressures to 28 MPa. J. Chem. Thermodyn. 1997, 29, 125− 148. (69) Sweeton, F. H.; Mesmer, R. E.; Baes, C. F. Acidity measurements at elevated temperatures. VII. Dissociation of water. J. Solution Chem. 1974, 3, 191−214. (70) Marshall, W. L.; Franck, E. U. Ion product of water substance, 0−−1000°C, 1−−10,000 bar New International Formulation and its background. J. Phys. Chem. Ref. Data 1981, 10, 295−304. (71) Chen, X.; Oscarson, J. L.; Gillespie, S. E.; Cao, H.; Izatt, R. M. Determination of enthalpy of ionization of water from 250 to 350 °C. J. Solution Chem. 1994, 23, 747−768. (72) Palmer, D. A.; Drummond, S. E. The molal dissociation quotients of water in sodium trifluoromethanesulfonate solutions to high temperatures. J. Solution Chem. 1988, 17, 153−164. (73) Djamali, E. The standard state thermodynamic properties for completely ionized hydrochloric acid and ionization of water up to 523 K. J. Chem. Thermodyn. 2009, 41, 872−879. 2972


Molar Volumes and Heat Capacities of Aqueous Solutions of

Recommend Documents