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Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Densities and Apparent Molar Volumes of Aqueous Solutions of K4Fe(CN)6, K3Fe(CN)6, K3Co(CN)6, K2Ni(CN)4, and KAg(CN)2 at 293 to 343 K Lubomir Hnedkovsky,* Yaser Kianinia, and Glenn Hefter Chemistry Department, Murdoch University, Murdoch, Western Australia 6150, Australia

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ABSTRACT: Densities of aqueous solutions of K4Fe(CN)6, K3Fe(CN)6, K3Co(CN)6, K2Ni(CN)4, and KAg(CN)2 have been measured with a vibrating-tube densimeter at temperatures from 293.15 to 343.15 at 5 K intervals over the approximate concentration range 0.02 to 0.4 mol·kg−1. Apparent molar volumes, Vϕ, calculated from these data were fitted with an extended form of the Redlich−Rosenfeld−Meyer equation to obtain the standard partial molar quantities, V°. The Vϕ and V° values for all the salts are in reasonable agreement with literature data at all temperatures. Deviations of the Vϕ values from the Debye− Hückel limiting law were found to increase considerably with increasing anion charge. Values of V° for the cyanometallate anions were obtained using an appropriate extrathermodynamic assumption and were found to increase with increasing crystallographic size or ionic charge except for Fe(CN)64−, which shows a remarkable contraction of more than 35 cm3·mol−1 relative to Fe(CN)63−. The origins of this anomaly are unclear. Isobaric expansivities, α, of all the salt solutions show the greatest increase with solute concentration, but the smallest dependence on the nature of the anion, at lower temperatures. These effects are consistent with the dissolved ions changing from water-structure breaking to net structure making with increasing temperature.

1. INTRODUCTION The physicochemical properties of solutions containing complex cyanometallate anions, [M(CN)x]y−, are of considerable importance from both fundamental and practical viewpoints. Scientific interest in these ions stems from their unusual thermodynamic and kinetic stabilities and their welldefined structures and charges. Some of the cyanometallate ions are pseudospherical and are therefore among the very few anions that can be used to test the roles of size and charge in the development of electrolyte solution theories, with a minimum of geometric or electronic complications. Cyanometallate salts also have numerous practical applications. For example, such compounds are utilized for mineral flotation,1 in the recovery of molybdenum,2 and in analytical chemistry.3 Other uses of cyanometallate compounds in the food industry, organic synthesis, photography, metallurgy, electrochemistry, health care, and chemistry in general have been summarized in a previous paper4 and so will not be repeated here. Of the various physicochemical characteristics of electrolyte solutions, volumetric properties are particularly important. Such quantities are used for unit conversions and for calculating the effects of pressure on thermodynamic properties such as activity and osmotic coefficients, which in turn are required for calculating solubilities, chemical speciation, and mass transport of © XXXX American Chemical Society

minerals under industrial, geochemical, and hydrometallurgical conditions.5 Not surprisingly, therefore, the densities and apparent molar volumes of cyanometallate salts have attracted significant attention over the years.6−13 The available data (Table 1) exhibit some interesting features. First, all of the studies to date have been made at 298.15 K, except for that of Curthoys and Mathieson,6 which reported volumes at 288.15 ≤ T/K ≤ 333.15. Second, there is an unusual preponderance of dilatometric data, frequently down to very low concentrations (Table 1). Dilatometry is generally regarded as being more sensitive and more accurate than other techniques (especially densimetry) for measuring apparent molar volumes at low concentrations and thus for determining standard state volumes at infinite dilution. Last, while a number of volumetric studies of hexacyanometallate salts have been reported, only one determination6 has appeared for both K2Ni(CN)4 and KAg(CN)2. This paper reports the densities and apparent molar volumes of aqueous solutions of five potassium salts containing complex cyanometallate anions, viz., K4Fe(CN)6, K3Fe(CN)6, Received: June 21, 2018 Accepted: September 6, 2018

A

DOI: 10.1021/acs.jced.8b00513 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Literature Investigations of the Apparent Molar Volumes of Aqueous Solutions of Potassium Cyanometallate Salts solute

concentration range/mmol·kg−1

T/K

method

ref

K4Fe(CN)6

1−500 10−500 0.3−230 471, 477 0.4−3 7−130 10−130 2−500 10−500 0.9−450 2−40 1−7 20−160 1−200 15−500 18−63 0.4−38 1−200 2−500

288.15−333.15 298.15 298.15 298.15 298.15 298.15 298.15 288.15−333.15 298.15 298.15 298.15 298.15 298.15 288.15−333.15 298.15 298.15 298.15 288.15−318.15 288.15−333.15

dilatometry, pycnometry vibrating tube densimetry dilatometry, pycnometry dilatometry dilatometry vibrating tube densimetry dilatometry dilatometry, pycnometry vibrating tube densimetry dilatometry, pycnometry dilatometry dilatometry vibrating tube densimetry dilatometry, pycnometry vibrating tube densimetry dilatometry dilatometry, pycnometry dilatometry, pycnometry dilatometry, pycnometry

6 7 8 9 10 11 12 6 7 8 9 10 11 6 7 12 13 6 6

K3Fe(CN)6

K3Co(CN)6

K2Ni(CN)4 KAg(CN)2

Table 2. Experimental Density Differences, Δρ, and Apparent Molar Volumes, Vϕ, for Aqueous Solutions of K4Fe(CN)6 at Molalities, m, Temperatures, T, and Pressure p = 0.1 MPaa m mol ·kg −1

0.02006 0.03010 0.04007 0.05003 0.05995 0.08023 0.09994 0.12019 0.14987 0.19988 0.24970 0.29983 0.39972

0.02006 0.03010 0.04007 0.05003 0.05995 0.08023 0.09994 0.12019 0.14987 0.19988 0.24970 0.29983 0.39972

0.02006 0.03010 0.04007 0.05003

Δρ kg·m−3

Vϕ cm 3·mol−1

T = 293.15 K ρw = 998.207 kg·m−3 4.992 118.68 7.445 119.92 9.855 120.97 12.252 121.74 14.615 122.56 19.406 123.84 24.005 124.94 28.686 125.85 35.457 127.05 46.663 128.70 57.543 130.22 68.259 131.54 88.925 133.82 T = 308.15 K ρw = 994.033 kg·m−3 4.900 122.74 7.308 123.98 9.670 125.10 12.021 125.87 14.334 126.77 19.046 127.85 23.562 128.88 28.169 129.68 34.822 130.82 45.845 132.33 56.573 133.66 67.115 134.91 87.539 136.87 T = 323.15 K ρw = 988.035 kg·m−3 4.846 124.70 7.224 126.09 9.564 127.06 11.890 127.82

Δρ kg·m−3

Vϕ cm 3·mol−1


B

Δρ kg·m−3

Vϕ cm 3·mol−1




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Table 2. continued m mol ·kg −1

Δρ kg·m−3

cm ·mol

Δρ kg·m−3

0.05995 0.08023 0.09994 0.12019 0.14987 0.19988 0.24970 0.29983 0.39972

14.180 18.839 23.310 27.867 34.456 45.376 56.001 66.462 86.690

128.69 129.79 130.79 131.58 132.66 134.10 135.39 136.56 138.49

14.149 18.796 23.257 27.805 34.381 45.277 55.878 66.324 86.502

0.02006 0.03010 0.04007 0.05003 0.05995 0.08023 0.09994 0.12019 0.14987 0.19988 0.24970 0.29983 0.39972

T = 338.15 K ρw = 980.551 kg·m−3 4.820 125.15 7.185 126.51 9.511 127.53 11.829 128.18 14.110 129.03 18.744 130.17 23.190 131.20 27.725 132.00 34.281 133.09 45.149 134.53 55.719 135.85 66.143 136.97 86.262 138.97

Vϕ −1

3

cm ·mol

Δρ kg·m−3

cm ·mol−1

128.94 130.08 131.07 131.86 132.94 134.38 135.68 136.81 138.78

14.126 18.763 23.217 27.757 34.321 45.201 55.782 66.220 86.357

129.05 130.21 131.21 132.01 133.09 134.52 135.84 136.95 138.95

Vϕ −1

3

Vϕ 3

T = 343.15 K ρw = 977.765 kg·m−3 4.816 124.98 7.180 126.32 9.508 127.29 11.820 128.04 14.103 128.81 18.729 130.04 23.175 131.05 27.706 131.86 34.258 132.96 45.118 134.42 55.677 135.76 66.095 136.89 86.204 138.90

Standard uncertainties: u(T) = 0.002 K, u(p) = 1 kPa, ur(m) = 0.0005, ur(Δρ) = 0.0005; combined total uncertainty: Uc(Vϕ) = 0.3 cm3·mol−1.

a

Table 3. Experimental Density Differences, Δρ, and Apparent Molar Volumes, Vϕ, for Aqueous Solutions of K3Fe(CN)6 at Molalities, m, Temperatures, T, and Pressure p = 0.1 MPaa m mol ·kg −1

0.01813 0.02721 0.03657 0.04528 0.05438 0.07277 0.09066 0.10848 0.13528 0.18087 0.22467 0.26903 0.39970

0.01813 0.02721 0.03657 0.04528 0.05438 0.07277 0.09066 0.10848 0.13528 0.18087 0.22467 0.26903

Δρ kg·m−3

Vϕ cm 3·mol−1

T = 293.15 K ρw = 998.207 kg·m−3 3.277 147.98 4.897 148.47 6.554 149.00 8.093 149.26 9.680 149.74 12.878 150.28 15.958 150.78 19.004 151.14 23.522 151.76 31.102 152.51 38.224 153.22 45.288 153.91 65.318 155.65 T = 308.15 K ρw = 994.033 kg·m−3 3.207 151.74 4.793 152.19 6.412 152.79 7.911 153.19 9.472 153.48 12.609 153.90 15.620 154.43 18.608 154.72 23.039 155.27 30.474 155.93 37.473 156.52 44.389 157.22

Δρ kg·m−3

Vϕ cm 3·mol−1

T = 298.15 K ρw = 997.047 kg·m−3 3.247 149.60 4.854 150.02 6.498 150.50 8.023 150.78 9.598 151.22 12.773 151.70 15.825 152.22 18.846 152.58 23.329 153.17 30.852 153.87 37.922 154.55 44.935 155.21 64.844 156.83 T = 313.15 K ρw = 992.216 kg·m−3 3.192 152.53 4.770 153.00 6.382 153.58 7.874 153.98 9.427 154.28 12.546 154.74 15.545 155.23 18.518 155.53 22.927 156.08 30.326 156.73 37.291 157.32 44.183 157.98 C

Δρ kg·m−3

Vϕ cm 3·mol−1

T = 303.15 K ρw = 995.649 kg·m−3 3.225 150.78 4.824 151.09 6.451 151.75 7.961 152.12 9.527 152.50 12.684 152.90 15.713 153.43 18.718 153.73 23.176 154.28 30.649 154.98 37.689 155.57 44.637 156.31 64.434 157.85 T = 318.15 K ρw = 990.213 kg·m−3 3.179 153.20 4.751 153.66 6.351 154.39 7.844 154.61 9.390 154.93 12.493 155.44 15.483 155.89 18.446 156.17 22.835 156.74 30.209 157.36 37.142 157.97 44.012 158.61



Article


Δρ kg·m−3

0.39970

64.090

0.01813 0.02721 0.03657 0.04528 0.05438 0.07277 0.09066 0.10848 0.13528 0.18087 0.22467 0.26903 0.39970

ρw 3.169 4.733 6.336 7.819 9.363 12.450 15.433 18.384 22.762 30.110 37.017 43.876 63.377

0.01813 0.02721 0.03657 0.04528 0.05438 0.07277 0.09066 0.10848 0.13528 0.18087 0.22467 0.26903 0.39970

ρw 3.152 4.707 6.304 7.780 9.310 12.383 15.352 18.285 22.636 29.943 36.799 43.638 63.042

Vϕ −1

3

cm ·mol

158.71 T = 323.15 K = 988.035 kg·m−3 153.71 154.29 154.76 155.12 155.39 156.00 156.42 156.72 157.26 157.89 158.52 159.10 160.51 T = 338.15 K = 980.551 kg·m−3 154.48 155.09 155.49 155.84 156.23 156.80 157.20 157.53 158.10 158.75 159.44 159.95 161.36

Δρ kg·m−3 63.803 ρw 3.162 4.718 6.320 7.797 9.337 12.419 15.398 18.338 22.706 30.033 36.921 43.770 63.228 ρw 3.150 4.706 6.302 7.781 9.304 12.382 15.346 18.272 22.625 29.927 36.774 43.610 62.999

Vϕ −1

3

cm ·mol

159.44 T = 328.15 K = 985.693 kg·m−3 154.05 154.80 155.16 155.57 155.83 156.39 156.77 157.11 157.65 158.30 158.93 159.49 160.89 T = 343.15 K = 977.765 kg·m−3 154.52 155.06 155.48 155.76 156.28 156.76 157.21 157.60 158.14 158.80 159.52 160.04 161.46

Δρ kg·m−3 63.563 ρw 3.156 4.713 6.311 7.787 9.323 12.396 15.369 18.306 22.663 29.979 36.847 43.691 63.118

Vϕ cm ·mol−1 3

160.04 T = 333.15 K = 983.196 kg·m−3 154.33 154.93 155.35 155.74 156.04 156.67 157.05 157.37 157.94 158.58 159.25 159.77 161.17


a

Table 4. Experimental Density Differences, Δρ, and Apparent Molar Volumes, Vϕ, for Aqueous Solutions of K3Co(CN)6 at Molalities, m, Temperatures, T, and Pressure p = 0.1 MPaa m mol ·kg −1

0.01504 0.02501 0.02953 0.04081 0.05018 0.06136 0.08045 0.10117 0.12010 0.15131 0.20130 0.25288 0.30235 0.35668

0.01504 0.02501

Δρ kg·m−3

Vϕ cm 3·mol−1

T = 293.15 K ρw = 998.207 kg·m−3 2.810 145.02 4.649 145.66 5.485 145.74 7.552 146.14 9.259 146.37 11.275 146.86 14.701 147.37 18.380 147.88 21.724 148.18 27.165 148.71 35.743 149.38 44.430 149.93 52.595 150.43 61.366 150.98 T = 308.15 K ρw = 994.033 kg·m−3 2.751 148.76 4.560 149.11

Δρ kg·m−3

Vϕ cm 3·mol−1

T = 298.15 K ρw = 997.047 kg·m−3 2.788 146.39 4.613 147.08 5.439 147.26 7.494 147.52 9.182 147.86 11.178 148.40 14.580 148.84 18.236 149.26 21.553 149.57 26.959 150.03 35.477 150.67 44.102 151.19 52.210 151.67 60.930 152.18 T = 313.15 K ρw = 992.216 kg·m−3 2.739 149.50 4.539 149.91 D

Δρ kg·m−3

Vϕ cm 3·mol−1

T = 303.15 K ρw = 995.649 kg·m−3 2.769 147.63 4.584 148.18 5.403 148.42 7.444 148.69 9.119 149.08 11.102 149.60 14.482 150.01 18.113 150.45 21.409 150.73 26.784 151.16 35.249 151.77 43.828 152.25 51.886 152.71 60.563 153.18 T = 318.15 K ρw = 990.213 kg·m−3 2.729 150.11 4.518 150.66 DOI: 10.1021/acs.jced.8b00513 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article


Δρ kg·m−3

0.02953 0.04081 0.05018 0.06136 0.08045 0.10117 0.12010 0.15131 0.20130 0.25288 0.30235 0.35668

5.372 7.401 9.069 11.041 14.401 18.013 21.290 26.636 35.057 43.595 51.619 60.256

0.01504 0.02501 0.02953 0.04081 0.05018 0.06136 0.08045 0.10117 0.12010 0.15131 0.20130 0.25288 0.30235 0.35668

0.01504 0.02501 0.02953 0.04081 0.05018 0.06136 0.08045 0.10117 0.12010 0.15131 0.20130 0.25288 0.30235 0.35668

cm ·mol

Δρ kg·m−3

149.44 149.71 150.05 150.55 150.98 151.39 151.68 152.10 152.69 153.14 153.57 154.02

5.348 7.366 9.026 10.991 14.334 17.929 21.192 26.513 34.896 43.401 51.394 60.000

Vϕ −1

3

T = 323.15 K ρw = 988.035 kg·m−3 2.720 150.66 4.503 151.22 5.312 151.30 7.316 151.61 8.964 151.97 10.918 152.40 14.238 152.87 17.805 153.32 21.050 153.55 26.326 154.03 34.666 154.53 43.109 154.97 51.063 155.33 59.620 155.73 T = 338.15 K ρw = 980.551 kg·m−3 2.711 151.04 4.483 151.79 5.287 151.90 7.282 152.24 8.921 152.61 10.871 152.96 14.167 153.55 17.717 154.00 20.948 154.22 26.187 154.79 34.497 155.23 42.897 155.68 50.818 156.03 59.330 156.45

cm ·mol

Δρ kg·m−3

cm ·mol−1

150.18 150.49 150.84 151.32 151.76 152.18 152.45 152.87 153.46 153.88 154.29 154.72

5.328 7.337 8.991 10.948 14.280 17.861 21.116 26.410 34.766 43.239 51.209 59.787

150.82 151.15 151.50 151.97 152.39 152.81 153.05 153.51 154.07 154.48 154.87 155.29

Vϕ −1

3

T = 328.15 K ρw = 985.693 kg·m−3 2.715 150.92 4.492 151.59 5.297 151.71 7.298 151.98 8.947 152.25 10.895 152.72 14.204 153.23 17.763 153.67 21.004 153.88 26.260 154.42 34.587 154.88 43.015 155.30 50.953 155.66 59.490 156.07 T = 343.15 K ρw = 977.765 kg·m−3 2.711 150.90 4.483 151.69 5.284 151.91 7.282 152.12 8.921 152.54 10.867 152.94 14.165 153.49 17.710 153.99 20.938 154.24 26.176 154.79 34.483 155.23 42.877 155.71 50.789 156.07 59.301 156.49

Vϕ 3

T = 333.15 K ρw = 983.196 kg·m−3 2.713 150.95 4.486 151.75 5.291 151.87 7.288 152.18 8.929 152.53 10.877 152.94 14.181 153.45 17.731 153.93 20.969 154.11 26.213 154.68 34.534 155.10 42.944 155.54 50.869 155.90 59.393 156.31


a

Table 5. Experimental Density Differences, Δρ, and Apparent Molar Volumes, Vϕ, for Aqueous Solutions of K2Ni(CN)4 at Molalities, m, Temperatures, T, and Pressure p = 0.1 MPaa m mol ·kg −1

Δρ kg·m−3

0.02009 0.03016 0.04015 0.05036 0.06049 0.08047 0.10052 0.12061

T = 293.15 K ρw = 998.207 kg·m−3 2.589 111.78 3.873 112.10 5.152 112.03 6.456 112.02 7.736 112.17 10.258 112.31 12.774 112.43 15.271 112.61

Vϕ 3

−1

cm ·mol

Δρ kg·m−3

Vϕ 3

−1

cm ·mol

T = 298.15 K ρw = 997.047 kg·m−3 2.561 113.14 3.837 113.25 5.103 113.25 6.385 113.42 7.654 113.52 10.144 113.71 12.635 113.79 15.107 113.95 E

Δρ kg·m−3

Vϕ cm ·mol−1 3

T = 303.15 K ρw = 995.649 kg·m−3 2.540 114.17 3.801 114.45 5.054 114.46 6.326 114.58 7.585 114.65 10.053 114.83 12.518 114.95 14.968 115.09 DOI: 10.1021/acs.jced.8b00513 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article


Δρ kg·m−3

0.15107 0.20044 0.25014 0.30041 0.34766 0.39726

19.033 25.074 31.054 37.001 42.518 48.252

0.02009 0.03016 0.04015 0.05036 0.06049 0.08047 0.10052 0.12061 0.15107 0.20044 0.25014 0.30041 0.34766 0.39726

0.02009 0.03016 0.04015 0.05036 0.06049 0.08047 0.10052 0.12061 0.15107 0.20044 0.25014 0.30041 0.34766 0.39726

0.02009 0.03016 0.04015 0.05036 0.06049 0.08047 0.10052 0.12061 0.15107 0.20044 0.25014 0.30041 0.34766 0.39726

cm ·mol

Δρ kg·m−3

112.80 113.02 113.28 113.57 113.81 113.98

18.831 24.812 30.728 36.616 42.081 47.756

Vϕ 3

−1

T = 308.15 K ρw = 994.033 kg·m−3 2.521 115.10 3.773 115.38 5.016 115.40 6.277 115.53 7.526 115.61 9.975 115.80 12.418 115.94 14.848 116.08 18.501 116.30 24.386 116.43 30.199 116.68 35.992 116.92 41.365 117.12 46.952 117.26 T = 323.15 K ρw = 988.035 kg·m−3 2.480 117.12 3.712 117.36 4.936 117.38 6.172 117.61 7.396 117.75 9.805 117.89 12.196 118.14 14.582 118.29 18.176 118.46 23.942 118.65 29.640 118.93 35.331 119.14 40.593 119.37 46.084 119.47 T = 338.15 K ρw = 980.551 kg·m−3 2.468 117.69 3.688 118.12 4.900 118.22 6.122 118.58 7.329 118.84 9.714 119.01 12.074 119.35 14.430 119.55 17.984 119.73 23.680 119.97 29.304 120.30 34.926 120.53 40.119 120.78 45.538 120.90

cm ·mol

Δρ kg·m−3

cm ·mol−1

114.13 114.31 114.57 114.85 115.06 115.23

18.655 24.583 30.446 36.281 41.700 47.327

115.28 115.45 115.70 115.96 116.16 116.31

Vϕ 3

−1

T = 313.15 K ρw = 992.216 kg·m−3 2.504 115.95 3.749 116.15 4.981 116.25 6.235 116.37 7.475 116.46 9.908 116.61 12.330 116.81 14.748 116.92 18.376 117.13 24.215 117.28 29.985 117.54 35.738 117.77 41.068 117.98 46.622 118.09 T = 328.15 K ρw = 985.693 kg·m−3 2.474 117.41 3.701 117.72 4.915 117.89 6.151 118.03 7.369 118.19 9.767 118.36 12.144 118.66 14.521 118.79 18.099 118.97 23.835 119.19 29.504 119.48 35.168 119.70 40.407 119.92 45.871 120.03 T = 343.15 K ρw = 977.765 kg·m−3 2.468 117.66 3.688 118.07 4.898 118.27 6.114 118.71 7.319 118.99 9.694 119.25 12.055 119.53 14.403 119.77 17.946 119.98 23.623 120.26 29.233 120.60 34.839 120.83 40.015 121.09 45.419 121.22

Vϕ 3

T = 318.15 K ρw = 990.213 kg·m−3 2.492 116.57 3.725 116.94 4.954 116.93 6.199 117.07 7.431 117.17 9.854 117.29 12.257 117.53 14.660 117.64 18.269 117.84 24.066 118.03 29.799 118.29 35.518 118.51 40.814 118.72 46.332 118.84 T = 333.15 K ρw = 983.196 kg·m−3 2.469 117.66 3.693 117.97 4.906 118.10 6.131 118.41 7.347 118.55 9.734 118.76 12.105 119.04 14.470 119.22 18.034 119.40 23.750 119.62 29.394 119.93 35.037 120.15 40.248 120.39 45.689 120.50


a

2. EXPERIMENTAL SECTION

K3Co(CN)6, K2Ni(CN)4, and KAg(CN)2. The measurements have been made at 5 K intervals over the temperature range 293.15 ≤ T/K ≤ 343.15 in the approximate concentration range 0.02 ≤ m/mol·kg−1 ≤ 0.4, using vibrating-tube densimetry.

2.1. Reagents. The reagents employed, their treatment, and the solutions prepared from them were identical to those reported previously.4 Briefly, the cyanometallate salts were the F



Article

Table 6. Experimental Density Differences, Δρ, and Apparent Molar Volumes, Vϕ, for Aqueous Solutions of KAg(CN)2 at Molalities, m, Temperatures, T, and Pressure p = 0.1 MPaa m mol ·kg −1

0.02005 0.03005 0.04021 0.05015 0.06026 0.08034 0.10063 0.12065 0.15054 0.19998 0.25068 0.29986 0.35032

0.02005 0.03005 0.04021 0.05015 0.06026 0.08034 0.10063 0.12065 0.15054 0.19998 0.25068 0.29986 0.35032

0.02005 0.03005 0.04021 0.05015 0.06026 0.08034 0.10063 0.12065 0.15054 0.19998 0.25068 0.29986 0.35032

0.02005 0.03005 0.04021 0.05015 0.06026 0.08034 0.10063 0.12065 0.15054 0.19998 0.25068 0.29986 0.35032

Δρ kg·m−3

Vϕ cm 3·mol−1

T = 293.15 K ρw = 998.207 kg·m−3 2.566 70.69 3.843 70.74 5.133 70.89 6.394 70.95 7.678 70.93 10.215 71.02 12.782 70.97 15.289 71.09 19.031 71.13 25.168 71.25 31.396 71.42 37.397 71.52 43.472 71.70 T = 308.15 K ρw = 994.033 kg·m−3 2.506 73.49 3.752 73.58 5.009 73.75 6.237 73.86 7.488 73.87 9.977 73.77 12.474 73.81 14.917 73.96 18.573 73.95 24.561 74.07 30.654 74.16 36.503 74.27 42.454 74.37 T = 323.15 K ρw = 988.035 kg·m−3 2.457 75.69 3.672 75.96 4.912 75.90 6.116 76.00 7.345 75.99 9.779 75.98 12.220 76.07 14.620 76.15 18.207 76.12 24.073 76.24 30.055 76.28 35.791 76.38 41.633 76.45 T = 338.15 K ρw = 980.551 kg·m−3 2.416 77.41 3.618 77.44 4.837 77.48 6.022 77.57 7.232 77.54 9.624 77.60 12.020 77.76 14.384 77.81 17.907 77.81 23.678 77.92 29.563 77.95 35.208 78.03 40.956 78.09

Δρ kg·m−3

Vϕ cm 3·mol−1

T = 298.15 K ρw = 997.047 kg·m−3 2.546 71.66 3.811 71.76 5.086 71.99 6.340 71.96 7.607 72.04 10.130 72.02 12.671 72.01 15.157 72.12 18.869 72.14 24.949 72.28 31.126 72.43 37.069 72.54 43.108 72.66 T = 313.15 K ρw = 992.216 kg·m−3 2.489 74.26 3.724 74.41 4.976 74.51 6.194 74.63 7.433 74.71 9.905 74.58 12.384 74.63 14.811 74.75 18.442 74.74 24.387 74.85 30.439 74.93 36.247 75.04 42.161 75.12 T = 328.15 K ρw = 985.693 kg·m−3 2.444 76.24 3.655 76.42 4.884 76.51 6.081 76.60 7.304 76.57 9.723 76.57 12.147 76.70 14.534 76.77 18.100 76.73 23.932 76.85 29.880 76.88 35.583 76.98 41.395 77.04 T = 343.15 K ρw = 977.765 kg·m−3 2.405 77.87 3.605 77.74 4.820 77.78 5.999 77.92 7.200 77.97 9.584 77.98 11.970 78.15 14.317 78.25 17.822 78.27 23.562 78.40 29.417 78.42 35.036 78.50 40.758 78.55

Δρ kg·m−3

Vϕ cm 3·mol−1

T = 303.15 K ρw = 995.649 kg·m−3 2.526 72.57 3.779 72.74 5.046 72.92 6.288 72.93 7.543 73.04 10.051 72.93 12.567 72.97 15.032 73.08 18.717 73.07 24.748 73.21 30.881 73.33 36.774 73.45 42.769 73.55 T = 318.15 K ρw = 990.213 kg·m−3 2.470 75.09 3.699 75.15 4.944 75.21 6.153 75.38 7.385 75.41 9.841 75.29 12.299 75.38 14.712 75.49 18.318 75.47 24.224 75.58 30.240 75.63 36.010 75.74 41.887 75.82 T = 333.15 K ρw = 983.196 kg·m−3 2.428 76.94 3.636 76.93 4.861 76.99 6.053 77.07 7.269 77.04 9.673 77.09 12.083 77.24 14.457 77.31 17.999 77.30 23.800 77.42 29.715 77.44 35.390 77.52 41.168 77.59


a

G



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Table 7. Debye−Hückel Limiting Slopes, AV, Standard Molar Volumes, V°, and Their Estimated Standard Uncertainties, σ(V°) (cm3·mol−1), for K4Fe(CN)6, K3Fe(CN)6, K3Co(CN)6, K2Ni(CN)4, and KAg(CN)2 at Experimental Temperatures, T, and Pressure p = 0.1 MPa V°/(cm3·mol−1) T

AV

K4Fe(CN)6

K3Fe(CN)6

K3Co(CN)6

K2Ni(CN)4

KAg(CN)2

K

cm3·kg0.5·mol−1.5)

σ(V°) = 0.5

σ(V°) = 0.4

σ(V°) = 0.4

σ(V°) = 0.3

σ(V°) = 0.2

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

1.8219 1.8979 1.9799 2.0685 2.1639 2.2666 2.3768 2.4951 2.6219 2.7576 2.9028

111.6 113.1 114.3 115.3 115.9 116.3 116.5 116.5 116.3 115.9 115.3

144.9 146.3 147.5 148.5 149.2 149.8 150.2 150.4 150.4 150.3 150.1

142.2 143.5 144.6 145.5 146.2 146.7 147.0 147.1 147.1 146.9 146.6

110.8 112.0 113.1 113.9 114.7 115.2 115.6 115.9 116.1 116.2 116.1

70.4 71.5 72.4 73.3 74.1 74.8 75.4 76.0 76.5 77.0 77.4

Table 8. Basis Functions, φi, and Fitting Parameters, ai, of Equation 2 for K4Fe(CN)6a

Table 10. Basis Functions, φi, and Fitting Parameters, ai, of Equation 2 for K3Co(CN)6a

φi(T, m)

ai

standard error

|t-statistic|

φi(T, m)

ai

standard error

|t-statistic|

1 τ2 1/τ3 mτ4 m/τ2 m1.5 m1.5τ3 m2/τ2 m2τ4

265.635 −846.51 −2.0485 −19552 7.002 −369.3 16593 10.970 −18420

0.841 4.92 0.0115 257 0.220 14.1 479 0.602 705

315 172 178 76.1 31.8 26.3 34.7 18.2 26.1

1 τ2 1/τ2 mτ3 m m1.5τ4 m2τ3

321.23 −799.40 −9.4807 −3102.6 34.07 7931 −1246

1.32 6.47 0.0671 86.2 1.22 530 156

243 124 141 36.0 28.0 15.0 8.01

τ = T/1000. Note that extra significant figures have been retained to avoid round-off errors. a

a τ = T/1000. Note that extra significant figures have been retained to avoid round-off errors.

Table 11. Basis Functions, φi, and Fitting Parameters, ai, of Equation 2 for K2Ni(CN)4a

Table 9. Basis Functions, φi, and Fitting Parameters, ai, of Equation 2 for K3Fe(CN)6a φi(T, m)

ai

standard error

|t-statistic|

1 1/τ4 τ4 mτ3 m/τ2 m1.5τ3 m1.5 m2τ3 m2τ2

192.934 −0.25974 −1738.6 −3439 4.450 7468 −149.4 −11500 3219

0.223 0.00143 10.8 126 0.408 659 21.5 1690 542

864 182 161 27.3 10.9 11.3 6.95 6.81 5.93

φi(T, m)

ai

standard error

|t-statistic|

3

−18.688 54.263 1.6334 −6.7435 0.27065 −0.12858

0.108 0.171 0.0170 0.0660 0.00772 0.00863

173 316 96.1 102 35.0 14.9

1/τ 1/τ2 1/τ4 m/τ m1.5/τ4 m2/τ4


and atmospheric pressure, p = (101 ± 1) kPa, using a vibrating tube densimeter (Anton Paar, Austria, Model DMA 5000 M). The operating protocol was that described in detail elsewhere.14 The uncertainty of the measured density differences between the sample and pure water was always within ±0.01 kg·m−3. The main contributor to the uncertainty of measured density differences is the uncertainty in the calibration constant of the vibrating tube, which was less than 0.03%. 2.3. Data Analysis. The measured differences in density, Δρ, between the solutions and pure water (at the same pressure and temperature) are recorded in Tables 2−6, along with the apparent molar volumes, Vϕ, calculated from them. Densities of pure water, ρw,15 are also included in Tables 2−6 to facilitate calculation of solution densities (ρ = ρw+Δρ). Values of Vϕ were obtained using the usual equation: ρ − ρw M Vϕ = s − ρ mρρw (1)


highest purity available commercially, recrystallized from water where necessary. Full specification of reagent sources and purity are exactly as given in Table 1 of the earlier publication.4 For convenience, this information is repeated as Table S1 in the Supporting Information for this paper. Solutions were prepared by weight using degassed high purity water (Ibis Technology, Australia) and were stored in the dark. Buoyancy corrections were applied throughout. All other details were as described previously.4 Based on the accuracy of the analytical balance and amounts of water and solutes used, the overall relative uncertainty in molality was ur(m) = u(m)/m = 0.0005. 2.2. Instrumentation. Densities were measured at 5 K intervals over the temperature range 293.15 ≤ T/K ≤ 343.15 H



Article

where Ms is the molar mass of the solute and m/mol·kg−1 is its concentration (molality) in the solution. Molar masses were calculated using the IUPAC-2015 atomic masses,16 which gave Ms/kg·mol−1 = 0.36833 for K4Fe(CN)6; 0.32923 for K3Fe(CN)6; 0.33232 for K3Co(CN)6); 0.24095 for K2Ni(CN)4; and 0.19869 for KAg(CN)2. The temperature and molality dependences of Vϕ were fitted using an extended form of the Redlich−Rosenfeld−Meyer (RRM) equation:17

Table 12. Basis Functions, φi, and Fitting Parameters, ai, of Equation 2 for KAg(CN)2a φi(T, m)

ai

standard error

|t-statistic|

1 τ2 1/τ3 m/τ4 m/τ3

107.225 −107.25 −0.69504 0.15587 −0.5215

0.660 3.86 0.00862 0.00812 0.0260

162.5 27.8 80.6 19.2 20.1


Figure 1. Apparent molar volumes, Vϕ, of potassium cyanometallate salts in aqueous solution as a function of solute concentration (√m) at p = 0.1 MPa and temperatures, T/K (bottom to top) = 293.15, 298.15, 303.15, 308.15, 313.15, 318.15, 323.15, 328.15, 333.15, 338.15, and 343.15 for (a) K4Fe(CN)6, (b) K3Fe(CN)6, (c) K3Co(CN)6, (d) K2Ni(CN)4, (e) KAg(CN)2. Lines were calculated via eq 2 using the relevant parameters in Tables 8−12. I



Article

n

Vϕ = ωAV m +

∑ aiφi(T , m) i

Vϕ values of K2Ni(CN)4(aq) and K3Fe(CN)6(aq). Similar effects have been reported for heat capacities and have been attributed tentatively to anion−anion interactions,4 although other factors may be at work. 3.2. Standard Molar Volumes. The standard-state (infinite dilution) molar volumes, V°, of the investigated solutes, obtained by fitting the data in Tables 2−6 with eq 2, are collected in Table 7. The dependence of V° on temperature is similar for all five salts (Figure 3). In particular, all of the hexacyanometallate salts show a flat maximum. While KAg(CN)2(aq) does not exhibit such a maximum, it will at higher T,

(2)

where AV is the theoretical (Debye−Hü ckel) slope for volumes.18 This quantity was calculated at the experimental temperatures and pressure using the equation of state of Wagner and Pruß15 and the NIST database No.10 (STEAM).19 In eq 2, ω is a valence factor (ω = [(z+ + z−)·z+·z−/2]1.5), having the value of 31.622 for K4Fe(CN)6, 14.697 for K3Fe(CN)6 and K3Co(CN)6, 5.196 for K2Ni(CN)6, and 1.000 for KAg(CN)2, while ai are empirical parameters obtained from least-squares fitting of the experimental data and φi(T,m) are basis functions of molality and temperature. The number of parameters for each fit was determined via the Bayesian information criterion (BIC)20 combined with a stepwise exclusion of all parameters or functions that were statistically insignificant at the 95% confidence level (i.e., with a |t-statistic| < 2). For convenience, the values of AV and the standard partial molar volumes at infinite dilution, V°, for the five investigated salts are listed as a function of temperature in Table 7, while the fitting (basis) functions with adjustable parameters are recorded in Tables 8 −12.

3. RESULTS AND DISCUSSION 3.1. Apparent Molar Volumes. The variations with concentration (√m) and temperature of the apparent molar volumes of the five salts studied are presented in Tables 2−6 and summarized in Figure 1. All salts show broadly similar trends, with Vϕ increasing more-or-less smoothly with increasing m and T, but there are also significant differences. Thus, the (veryapproximately linear) slopes of the Vϕ(√m) curves over most of the investigated concentration range increase, roughly in the ratio 1:2:7:15 with increasing anion charge, i.e., in going from 1:1 to 1:2 to 1:3 to 1:4 electrolyte types. These differences are seen more clearly in Figure 2, which plots the Vϕ values in terms

Figure 3. Standard molar volumes, V°, of potassium cyanometallate salts in aqueous solution as a function of temperature, T: (violet ▼) KAg(CN)2; (●) K2Ni(CN)4; (red ⧫) K4Fe(CN)6; (blue ■) K3Co(CN)6; (green ▲) K3Fe(CN)6.

Figure 2. Departures of apparent molar volumes from the Debye− Hückel limiting law (dashed line) for aqueous solutions of potassium cyanometallate salts as a function of solute concentration (√m) at (a) 298.15 K and (b) 343.15 K. From top to bottom: (purple) KAg(CN)2; (black) K2Ni(CN)4; (blue) K3Co(CN)6; (green) K3Fe(CN)6; (red) K4Fe(CN)6.

of their departure from the Debye−Hückel theory (DHT): those for KAg(CN)2(aq) show only small deviations while those for K4Fe(CN)6(aq) are particularly large. Surprisingly, at least at 298.15 K, there is a significant difference between the Vϕ values of K3Fe(CN)6(aq) and K3Co(CN)6(aq). As occurs for most electrolyte solutions, the departures from the DHT increase with increasing T (Figure 2). A minor feature of the data (Figure 1) is a barely discernible upward curvature at high m and low T for the

fit Figure 4. Deviations, δ(Vϕ) = Vlit ϕ − Vϕ , between literature and present values (fitted via eq 2, dashed line) of the apparent molar volumes of K4Fe(CN)6(aq) as a function of concentration at selected temperatures, T/K = (a) 298.15; (b) 308.15; (c) 313.15; and (d) 333.15. (●) Curthoys and Mathieson;6 (blue ▲) Lepori et al.;7 (green ▼) Johnstone et al.;9 (red ◆) Hepler et al.;10 (magenta +) Spitzer et al.;11 (◇) Bottomley et al.12 The shaded area represents the experimental concentration range of the present work.

J



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3.3. Comparisons with Literature Data. Overall comparisons of Vϕ with the literature data at various temperatures are given graphically as deviation plots for each salt as a function of concentration in Figures 4−8. Numerical comparison is,

fit Figure 7. Deviations, δ(Vϕ) = Vlit ϕ −Vϕ , between literature and present values (fitted via eq 2, dashed line) of the apparent molar volumes of K2Ni(CN)4 as a function of concentration at selected temperatures, T/K = (a) 298.15; (b) 308.15; and (c) 313.15. (●) Curthoys and Mathieson.6 The shaded area represents the experimental concentration range of the present work.

fit Figure 5. Deviations, δ(Vϕ) = Vlit ϕ − Vϕ , between literature and present values (fitted via eq 2, dashed line) of the apparent molar volumes of K3Fe(CN)6 as a function of concentration at selected temperatures, T/K = (a) 298.15; (b) 308.15; (c) 313.15; and (d) 333.15. (●) Curthoys and Mathieson;6 (blue ▲) Lepori et al.;7 (green ▼) Johnstone et al.;9 (red ◆) Hepler et al.;10 (magenta +) Spitzer et al.11 The shaded area represents the experimental concentration range of the present work.

fit Figure 8. Deviations, δ(Vϕ) = Vlit ϕ − Vϕ , between literature and present values (fitted via eq 2, dashed line) of the apparent molar volumes of KAg(CN)2 as a function of concentration at at selected temperatures, T/K = (a) 298.15; (b) 308.15; (c) 313.15; and (d) 333.15. (●) Curthoys and Mathieson.6 The shaded area represents the experimental concentration range of the present work.

fit Figure 6. Deviations, δ(Vϕ) = Vlit ϕ − Vϕ , between literature and present values (fitted via eq 2, dashed line) of the apparent molar volumes of K3Co(CN)6 as a function of concentration at selected temperatures, T/K = (a) 298.15; (b) 308.15; (c) 313.15; and (d) 333.15. (●) Curthoys and Mathieson;6 (blue ▲) Lepori et al.;7 (red ◆) Malatesta and Zamboni.13 The shaded area represents the experimental concentration range of the present work.

however, most conveniently made using the V° values at 298.15 K, which are listed in Table 13. Given the apparent high quality of many of the earlier investigations and the exceptional amount of dilatometric data down to very low concentrations, the agreement among independent studies is disappointingly modest. In particular, the V° values for K4Fe(CN)6(aq) appear to cluster into two groups differing by about 4 cm3·mol−1. This implies a problem with salt purity, although Curthoys and Mathieson6 have argued that such effects are due to ion association and anion hydrolysis at low concentrations, even of

as occurs for almost all salts in aqueous solution.21 It is also notable that the temperature of the maximum in V° appears to increase with decreasing anion charge (Figure S1 in the Supporting Information). This effect has been related to the ionic radius,5,6,22 although this quantity is somewhat indeterminate for lower-symmetry ions. The temperature dependences of Vϕ for all the investigated salts at finite concentrations are shown in Figures S2−S6 in the Supporting Information. K



Article

Table 13. Comparison of Present and Literature Standard Molar Volumes, V°, for K4Fe(CN)6, K3Fe(CN)6, K3Co(CN)6, K2Ni(CN)4, and KAg(CN)2 in Water at 298.15 K and 0.1 MPa V°/cm3·mol−1 ref

a

6 7 8 9 10 11 12 13 avg pw

K4Fe(CN)6

K3Fe(CN)6

K3Co(CN)6

K2Ni(CN)4

KAg(CN)2

112.3 113.09 108.5 109.2 110 113.3 110.65

146.2 146.71 146.4 147.3 147.8 146.6 -

111.0 ± 1.9 113.1 ± 0.5

146.8 ± 0.6 146.3 ± 0.4

142.5 143.66 144.75 143.3 143.6 ± 1.1 143.5 ± 0.4

113.3 113.3 ± 0.2b 112.0 ± 0.3

71.8 71.8 ± 0.1b 71.5 ± 0.2

a

Abbreviations: avg, average of literature values (±σ); pw, present work. bUncertainties from ref 6.

Table 15. Standard Molar Volumes, V°/cm3·mol−1, at T = 298.15 K of Potassium Cyanometallate Salts (KnY) and Their Constituent Ions, along with the Anionic Crystallographic Radii, r(Yn−)

such highly stable complex ions. As can be seen from the bottom two rows in Table 13, the present V° values overlap with the averages of the literature results within the estimated uncertainties for all salts except K2Ni(CN)4. At other temperatures (Figures 4−8) the Vϕ values of Curthoys and Mathieson6 are in good agreement with the present results, with differences typically

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