Vapor Pressures and Osmotic Coefficients of Aqueous LiOH Solutions

The investigated range of LiOH solution molality was from 0.07 to 4.77 mol‚kg-1. ... with Archer's extension and of the mean spherical approximation...
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Ind. Eng. Chem. Res. 2005, 44, 3807-3814

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Vapor Pressures and Osmotic Coefficients of Aqueous LiOH Solutions at Temperatures Ranging from 298.15 to 363.15 K Karamat Nasirzadeh,†,‡ Roland Neueder,† and Werner Kunz*,† Institut fu¨ r Physikalische and Theoretische Chemie, Universita¨ t Regensburg, D-93040 Regensburg, Germany, and Department of Chemistry, Azarbaijan University of Tarbiat Moallem, Tabriz, Iran

Precise vapor-pressure data for solutions of lithium hydroxide in water from temperatures of 298.15-363.15 K have been measured by a procedure and equipment known to yield data of high precision. The investigated range of LiOH solution molality was from 0.07 to 4.77 mol‚kg-1. The values of the osmotic coefficient have been calculated, taking into account the second virial coefficient in the equation for the water vapor pressure. Adjustable parameters of Pitzer’s model with Archer’s extension and of the mean spherical approximation of a nonrandom two-liquid model were evaluated. The new experimental data are compared to literature values, which exhibit a surprising scattering. 1. Introduction Aqueous electrolyte solutions play a dominant role in the chemistry of the Earth’s biosphere as well as in many industrial processes. Lithium and hydroxide ions are important components of natural fluids, such as sea and river water, and most natural brines. LiOH plays a role in solvolysis reactions such as hydrolysis and acid-base processes such as buffering and ionizations. Thermodynamic properties of an aqueous LiOH solution are required, for instance, in understanding various geochemical processes, such as those related to vapor formation and subsurface brines. In industry, lithium hydroxide is being used as an agent for control of the pH in the primary coolant-water circuits of pressurized nuclear reactors. The resistance of steel against caustic corrosion in concentrated LiOH solutions is still a problem.1 Here, basic information on the properties of lithium hydroxide solutions such as vapor-pressure data at elevated temperatures is important to establish the appropriate conditions. While the standard-state thermodynamic properties of these solutions have been extensively tabulated at 298.15 K, the temperature dependences, especially as functions of concentration, have not been widely evaluated by any self-consistent technique. Surprisingly, even at room temperature, there is a significant scattering in the literature data, as will be further discussed in this paper. To contribute to a better knowledge of the thermodynamic properties of aqueous electrolyte solutions, we report here on the values of osmotic coefficients for aqueous lithium hydroxide solutions that have been derived from the results of static vapor-pressure measurements within a temperature range T ) 298.15363.15 K. For comparison, we found in the literature only the following reported data for vapor pressures or osmotic coefficients of aqueous solutions of lithium hydroxide: values at T ) 298.15 K3 and at T ) 383.25, 413.12, and 443.09 K.4 There are some vapor-pressure * To whom correspondence should be addressed. Fax: +49 941 943 4532. E-mail: Werner.Kunz@ chemie.uni-regensburg.de. † Universita¨t Regensburg. ‡ Azarbaijan University of Tarbiat Moallem.

reports2 for this system above 363 K also. Some activity coefficients are also deduced from electromotoric force (emf) measurements at T ) 298.15 K.5 From the adjusted parameters of the Pitzer6 and mean spherical approximation of a nonrandom twoliquid (MSA-NRTL)7 models, we compute activity coefficients for wide temperature and concentration ranges. 2. Experimental Section 2.1. Chemicals. Water from the Millipore purification system with a specific conductivity of less than 2 × 10-7 S‚m-1 was used. Lithium hydroxide monohydrate (Aldrich, min 99.95%) was used without further purification. 2.2. Vapor-Pressure Measurements. The vaporpressure measurements were executed with a highly precise vapor-pressure apparatus that yields the total vapor pressures of the solutions. The apparatus was designed especially for vapor-pressure measurements of pure fluids and of electrolyte solutions over a wide temperature range from T ) 278.15 to 473.15 K with an uncertainty of (0.002% in the concentration and of 0.003 K in the temperature. The uncertainty of the pressure is about 0.01% (at low pressures, at least 1 Pa). Additionally, the uncertainty in the temperature leads to an uncertainty of the pure solvent vapor pressure of about 1 Pa at 298.15 K. The apparatus and the measuring method as well as the degassing procedure of the solution and pure solvent are described in detail elsewhere.8 3. Results 3.1. Experimental Results. The vapor pressures of aqueous solutions of lithium hydroxide were measured from 298.15 to 363.15 K in 5 K intervals and the molalities between 0.07 and 4.77 mol‚kg-1. The salt is not volatile so that the total measured pressure at equilibrium p is the vapor pressure of water. The experimental vapor-pressure data are given in Table 1. Osmotic coefficients of the aqueous solutions of lithium hydroxide as a function of molality m were calculated

10.1021/ie0489148 CCC: $30.25 © 2005 American Chemical Society Published on Web 04/14/2005

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Ind. Eng. Chem. Res., Vol. 44, No. 10, 2005

Table 1. Measured Vapor-Pressure Data, p, of Aqueous Solutions of Lithium Hydroxide at Temperatures T (K) and Molalities m (mol‚kg-1) p/kPa m

298.15

303.15

308.15

313.15

318.15

323.15

328.15

333.15

338.15

343.15

348.15

353.15

358.15

363.15

0.0000 0.0749 0.1239 0.1750 0.3439 0.4017 0.7404 0.8675 1.0143 1.0229 1.4307 1.5921 1.9050 1.9897 2.1177 2.3096 2.4074 2.5787 2.6682 3.1062 3.5105 4.2824 4.7722

3.167 3.157 3.152 3.147 3.130 3.124 3.091 3.078 3.064 3.063 3.023 3.007 2.977 2.969 2.957 2.938 2.929 2.912 2.904 2.862 2.824 2.752 2.706

4.243 4.232 4.225 4.218 4.195 4.187 4.143 4.126 4.107 4.106 4.053 4.032 3.992 3.981 3.964 3.940 3.928 3.906 3.895 3.840 3.789 3.694 3.635

5.626 5.612 5.602 5.593 5.563 5.553 5.494 5.472 5.446 5.445 5.374 5.347 5.294 5.280 5.258 5.226 5.210 5.182 5.167 5.095 5.030 4.908 4.832

7.381 7.362 7.350 7.338 7.299 7.286 7.209 7.180 7.147 7.145 7.054 7.018 6.949 6.931 6.903 6.861 6.840 6.803 6.784 6.691 6.607 6.448 6.350

9.588 9.563 9.547 9.532 9.482 9.465 9.365 9.328 9.285 9.283 9.165 9.119 9.031 9.007 8.971 8.918 8.891 8.844 8.819 8.700 8.591 8.389 8.263

12.329 12.298 12.278 12.258 12.194 12.172 12.045 11.997 11.943 11.940 11.790 11.731 11.618 11.588 11.542 11.474 11.440 11.380 11.349 11.198 11.060 10.805 10.646

15.753 15.712 15.687 15.663 15.581 15.553 15.392 15.332 15.263 15.259 15.069 14.994 14.851 14.813 14.755 14.669 14.625 14.549 14.510 14.318 14.144 13.819 13.618

19.931 19.882 19.851 19.819 19.718 19.683 19.483 19.408 19.322 19.317 19.080 18.987 18.808 18.760 18.687 18.579 18.524 18.428 18.379 18.137 17.916 17.503 17.247

25.024 24.960 24.923 24.885 24.761 24.718 24.470 24.377 24.271 24.265 23.972 23.857 23.636 23.577 23.487 23.354 23.286 23.168 23.106 22.808 22.537 22.029 21.713

31.178 31.100 31.052 31.005 30.851 30.799 30.494 30.380 30.250 30.242 29.883 29.742 29.472 29.399 29.290 29.127 29.044 28.900 28.825 28.463 28.133 27.519 27.138

38.561 38.461 38.406 38.349 38.160 38.096 37.721 37.582 37.422 37.413 36.973 36.801 36.471 36.382 36.248 36.049 35.948 35.773 35.681 35.239 34.838 34.091 33.629

47.375 47.256 47.188 47.118 46.887 46.808 46.351 46.181 45.986 45.974 45.438 45.228 44.826 44.718 44.556 44.314 44.192 43.978 43.868 43.332 42.847 41.946 41.392

57.817 57.669 57.589 57.503 57.223 57.128 56.576 56.371 56.136 56.122 55.476 55.223 54.738 54.608 54.412 54.121 53.974 53.717 53.583 52.938 52.354 51.270 50.603

70.139 69.965 69.857 69.756 69.423 69.310 68.651 68.407 68.126 68.110 67.339 67.038 66.461 66.306 66.073 65.727 65.551 65.246 65.087 64.321 63.658 62.353 61.558

Table 2. Calculated Osmotic Coefficients for Aqueous Lithium Hydroxide Solutions as a Function of Temperature (K) and Solution Molality (mol‚kg-1) φ m

298.15

303.15

308.15

313.15

318.15

323.15

328.15

333.15

338.15

343.15

348.15

353.15

358.15

363.15

0.0749 0.1239 0.1750 0.3439 0.4017 0.7404 0.8675 1.0143 1.0229 1.4307 1.5921 1.9050 1.9897 2.1177 2.3096 2.4074 2.5787 2.6682 3.1062 3.5105 4.2824 4.7722

0.973 0.964 0.945 0.915 0.910 0.896 0.895 0.894 0.894 0.893 0.893 0.894 0.894 0.895 0.895 0.896 0.897 0.897 0.900 0.903 0.908 0.911

0.979 0.952 0.945 0.920 0.913 0.898 0.895 0.893 0.893 0.891 0.890 0.890 0.890 0.890 0.891 0.891 0.891 0.891 0.893 0.894 0.897 0.899

0.976 0.966 0.939 0.910 0.906 0.895 0.893 0.892 0.891 0.889 0.888 0.887 0.887 0.887 0.887 0.887 0.887 0.886 0.886 0.886 0.885 0.885

0.970 0.961 0.935 0.905 0.900 0.887 0.885 0.883 0.883 0.880 0.880 0.879 0.878 0.878 0.878 0.878 0.877 0.877 0.877 0.876 0.876 0.875

0.960 0.946 0.922 0.896 0.891 0.880 0.878 0.876 0.876 0.873 0.873 0.871 0.871 0.871 0.870 0.870 0.869 0.869 0.868 0.867 0.866 0.865

0.954 0.938 0.916 0.890 0.887 0.875 0.873 0.872 0.871 0.868 0.867 0.865 0.865 0.864 0.864 0.863 0.862 0.862 0.860 0.859 0.856 0.854

0.952 0.935 0.912 0.884 0.881 0.869 0.867 0.865 0.865 0.861 0.860 0.859 0.858 0.857 0.857 0.856 0.856 0.855 0.853 0.852 0.849 0.847

0.942 0.901 0.890 0.869 0.864 0.853 0.851 0.849 0.849 0.847 0.846 0.845 0.845 0.844 0.844 0.844 0.844 0.843 0.843 0.843 0.842 0.841

0.936 0.899 0.878 0.853 0.849 0.839 0.837 0.836 0.835 0.833 0.832 0.831 0.831 0.830 0.830 0.830 0.829 0.829 0.828 0.828 0.826 0.825

0.934 0.909 0.883 0.851 0.846 0.832 0.830 0.828 0.827 0.823 0.822 0.820 0.820 0.819 0.818 0.817 0.817 0.816 0.814 0.813 0.809 0.807

0.927 0.899 0.874 0.843 0.838 0.825 0.822 0.820 0.820 0.815 0.814 0.812 0.811 0.810 0.809 0.809 0.808 0.807 0.805 0.803 0.799 0.796

0.924 0.885 0.862 0.835 0.831 0.819 0.817 0.814 0.814 0.810 0.808 0.806 0.805 0.804 0.803 0.802 0.801 0.800 0.797 0.794 0.789 0.785

0.921 0.887 0.864 0.833 0.828 0.813 0.810 0.807 0.807 0.802 0.800 0.797 0.796 0.795 0.794 0.793 0.792 0.791 0.788 0.785 0.779 0.775

0.919 0.892 0.868 0.828 0.821 0.803 0.800 0.797 0.796 0.790 0.788 0.785 0.784 0.783 0.781 0.780 0.778 0.777 0.774 0.766 0.763 0.759

from the measured quantities p using the following relations:

ln as ) ln(p/p*) + (Bs - V/s )(p - p*)/RT

(1)

φ ) -ln as/νmMs

(2)

In these equations as is the activity of the solvent, ν is the stoichiometric number of the salt, Ms is the molecular weight of the solvent, T is the absolute temperature, p is the vapor pressure of the solution, and p* is the vapor pressure of the pure solvent. Bs is the second virial coefficient, and V/s is the molar volume of the pure solvent. The second term on the right-hand side of eq 2 is the correction for nonideality of the solvent vapor through the virial equation. The calculated values of osmotic coefficients are shown in Table 2, and the

second virial coefficients9 and molar volumes10 of pure water from T ) 298.15 to 363.15 K are presented in Table 3. Kangro and Groeneveld reported the results of vapor pressure measurements for concentrations from 1 to 5 mol‚kg-1 at 298.15 K. A comparison of our vapor pressures to their data is shown in Figure 1. 3.2. Correlation of Osmotic Coefficient Data. 3.2.1. Pitzer’s Ion-Interaction Model and Its Extension Proposed by Archer. We have used Pitzer’s ion-interaction model11 and its extension proposed by Archer6 that includes the ionic strength dependence of the third virial coefficient to improve the representation of the experimental results. This model was used for aqueous electrolytes6,12-14 and in a few cases for nonaqueous electrolytes15,16 with better significance.

Ind. Eng. Chem. Res., Vol. 44, No. 10, 2005 3809 Table 3. Second Virial Coefficient, Bs, Molar Volume, V/s, Density, ds, Relative Permittivity, E, of Water and the Debye-Hu 1 ckel Constant, AO, for 1:1 Electrolytes in Water at Different Temperatures 104Bsa/ 106V/s b/ dsb/ (m3‚mol-1) (m3‚mol-1) (kg‚m-3)

T/ K 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 a

-12.369 -11.373 -10.489 -9.701 -8.997 -8.367 -7.800 -7.290 -6.828 -6.410 -6.030 -5.684 -5.368 -5.078

Poling et al.9

18.069 18.094 18.124 18.157 18.193 18.234 18.277 18.323 18.373 18.425 18.480 18.538 18.599 18.663 b

997.04 995.64 994.02 992.21 990.21 988.04 985.71 983.22 980.58 977.80 974.88 971.82 968.64 965.33

Keenan et al.10

c

c

Aφ/ (kg1/2‚mol-1/2)

78.37 76.60 74.87 73.18 71.52 69.91 68.33 66.78 65.28 63.80 62.36 60.95 59.57 58.23

0.392 0.395 0.398 0.402 0.406 0.410 0.414 0.418 0.423 0.428 0.432 0.437 0.442 0.447

Figure 1. Comparison of vapor pressures for aqueous solutions of lithium hydroxide at 298.15 K: Kangro et a1.3 (2); this work (O).

Ellison et al.18

For 1:1 electrolytes, this model has the following form:

φ - 1 ) f φ + mBφ + m2C φ

(3)

f φ ) -AφI1/2/(1 + bI1/2)

(4)

Aφ ) (1/3)(2πNAds)1/2(e2/4π0kT)3/2

(5)

Aφ values were calculated from temperatures of 298.15363.15 K with 5 K intervals and are also presented in Table 3. The parameters b ) 1.2 kg1/2‚mol-1/2 and R1 ) 1.4 kg1/2‚mol-1/2 were fixed according to Pitzer and Mayorga.17 From the analysis of the experimental data, we found that R2 ) 14 kg1/2‚mol-1/2 and R3 ) 10 kg1/2‚mol-1/2 yielded reliable fits for all temperatures. The values of the Pitzer parameters estimated by fitting our experimental results are shown in Table 4, along with the standard deviation of the fit. 3.2.2. MSA-NRTL Model. The MSA-NRTL model7 describes the Gibbs energy of the electrolyte solution as the sum of two parts. The long-range part corresponds to the electrostatic interactions of ions and their contributions to the excess Gibbs energy. The second contribution describes all nonelectrostatic short-range interactions existing between ions and solvent molecules. The long-range contribution is modeled with the help of the restricted version of the MSA model19 adapted to the Gibbs energy formalism. The activity coefficients in the mole fraction scale are written as follows:

where

Bφ ) β(0) + β(1) exp(-R1I1/2) + β(2) exp(-R2I1/2) (6) and

C φ ) C (0) + C (1) exp(-R3I1/2)

(7)

In these equations, β(0), β(1), β(2), C (0), and C (1) are Pitzer’s ion-interaction parameters that are dependent on the temperature and pressure, R1, R2, R3, and b are adjustable parameters, and Aφ is the Debye-Hu¨ckel constant for the osmotic coefficient in the molal system. The term I is the ionic strength, I ) 1/2Σmjzj2, where mj is the molality of the ions of type j and zj is their valency. The remaining symbols have their usual meaning. With the help of density ds and relative permittivity  of pure water at different temperatures (see Table 3),

ln fMSA-NRTL ) ln fNRTL + ln fMSA

(8)

The short-range contribution is calculated with the help of the NRTL model, as described elsewhere,7,20,21

Table 4. Parameters of the Extended Pitzer Model for Aqueous Lithium Hydroxide Solutionsa

a

T/K

β(0)

β(1)

β(2)

103C (0)

C (1)

SD(φ)

298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15

0.030 151 0.021 823 0.026 132 0.026 960 0.025 441 0.024 510 0.025 519 0.025 610 0.029 796 0.031 469 0.031 100 0.028 895 0.030 350 0.033 300

0.161 763 0.201 484 0.184 343 0.155 993 0.146 464 0.140 477 0.119 270 0.075 174 0.014 504 -0.020 244 -0.037 501 -0.035 269 -0.063 120 -0.110 487

17.366 38 19.041 95 19.186 85 20.747 93 19.488 51 18.047 18 18.981 72 21.370 56 23.264 24 20.396 89 19.628 33 22.673 31 19.570 80 17.889 35

-1.466 06 -0.518 94 -1.819 51 -2.052 23 -1.980 09 -2.097 20 -2.304 91 -2.003 29 -2.905 46 -3.613 51 -3.712 16 -3.617 21 -3.962 05 -4.729 10

50.579 22 42.885 38 39.966 17 37.962 07 16.634 42 8.277 41 4.471 59 -36.690 46 -48.290 58 -25.538 63 -37.742 80 -62.661 83 -48.147 30 -30.945 57

0.002 0.001 0.003 0.003 0.001 0.002 0.002 0.002 0.001 0.002 0.001 0.001 0.001 0.003

b ) 1.2; R1 ) 1.4; R2 ) 14; R3 ) 10 (all in kg1/2‚mol-1/2).

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so that only the main results will be given here.

ln fNRTL ) β∆G h NRTL + s s

∑ s′

Table 5. Parameters of the MSA-NRTL Model for Aqueous Lithium Hydroxide Solutionsa

xs′Pss′ (τss′ - β∆G h s′NRTL) + Hs′

T/ K

xcPsc,ac (τsc,ac - β∆G h NRTL )+ c Hac xaPsa,ca ∂β∆G h NRTL (2) (τsa,ca - β∆G h NRTL ) + τ a sc,ac Hca ∂τsc,ac

∑ s′

(2) xs′τs′c,ac

∂β∆G h NRTL

(9)

∂τs′c,ac

s′ in the summations represents a solvent, xi is the mole fraction of species i, and

β∆G h

NRTL

)

∑s [xcXscτsc,ac + xaXsaτsa,ca + xs∑j τjsXjs]

(1) τmc,ac

(2) τmc,ac / (kg‚mol-1)

τam

τ cm

SD(φ)

298.15 12.595 567 -4.549 251 -4.549 242 -3.300 053 0.003 303.15 12.889 764 -4.562 812 -4.562 807 -3.541 181 0.004 308.15 10.571 472 -4.238 254 -4.238 257 -1.982 920 0.001 313.15 8.628 922 -3.965 864 -3.965 857 -0.693 874 0.004 318.15 5.599 347 -4.754 522 -1.444 592 -0.611 333 0.007 323.15 5.722 820 -4.788 553 -1.459 051 -0.666 171 0.007 328.15 6.103 280 -4.899 487 -1.460 362 -0.846 046 0.007 333.15 6.782 359 -5.136 165 -1.446 599 -1.209 948 0.008 338.15 6.875 343 -5.166 557 -1.394 545 -1.269 799 0.009 343.15 6.889 881 -5.158 536 -1.362 331 -1.277 475 0.009 348.15 6.996 790 -5.188 026 -1.335 583 -1.341 267 0.010 353.15 7.013 211 -5.186 161 -1.313 808 -1.351 486 0.011 358.15 7.107 686 -5.212 214 -1.285 433 -1.410 172 0.010 363.15 7.108 551 -5.197 506 -1.257 882 -1.406 265 0.010 a

σ ) 4.82 Å; R ) 0.2.

(10) The probability Pji of finding a particle of species j in the immediate neighborhood of a central particle of species i is assumed to obey a Boltzmann distribution

Pji ) exp(-Rτji)

(11)

Pji,ki ) exp(-Rτji,ki)

(12)

Hs )

∑k xkPks

(13)

Hji )

∑k xkPki,ji

(14)

Xji )

xjPji

(15)

∑k xkPki

The adjusted NRTL parameters are τas, τcs, τsc,ac, and R. τsa,ca is related to the other parameters by

τsa,ca ) τsc,ac + τas - τcs

(16)

An extra concentration dependence has been introduced in τsc,ac. (1) (2) τsc,ac ) τsc,ac + τsc,ac xs

(17)

The MSA term is given by

Γ ) -λzi2 ln f/,MSA i 1 + Γσ Γ)

with i ) ions

1 (x1 + 2κσ - 1) 2σ

∑Fizi2

κ ) x4πλ

(18) (19) (20)

so that 2Γ ) κ at vanishing ionic concentration and

λ)

e2 4πkT0

(21)

Γ is the MSA screening parameter, in the same way as κ is the screening parameter in the Debye-Hu¨ckel theory, and σ is the mean ionic diameter of the ions. To

Figure 2. Osmotic coefficient of aqueous solutions of lithium hydroxide. This work: (3) 298.15 K, (O) 303.15 K, (4) 308.15 K, (]) 313.15 K, ([) 318.15 K, (right rotated 4) 323.15 K, (5) 328.15 K, (+) 333.15 K, () 363.15 K. Holmes and Mesmer: (1) 383.15 K, (left rotated 4) 413.12 K, and (b) 443.09 K. Values of this work extrapolated with the help of Apelblat’s expression for (f) 383.15 K, (2) 413.12 K, and (g) 443.09 K.

keep a physical meaning, one can assume that the lithium cation is surrounded by one or more solvent layers. The σ parameter is calculated as the sum of the ionic radii of cation a+, anion a-, and the length of an orientated solvent molecule: a+(Li+) ) 0.69 Å, a-(OH-) ) 1.33 Å (taken from Kunz et al.19), and s(water) ) 2.8 Å (taken from Barthel et al.23). In all fits, σ was fixed to these values. In this version of the model,  is the permittivity of the pure solvent. A commonly accepted value for R is 0.2 in aqueous solutions,21 even though it can be adjusted.7 In this work we used this value for the R parameter at different temperatures. The results are given in Table 5. All of our osmotic coefficients are plotted in Figure 2 as a function of molality. The values at temperatures 383.29, 413.12, and 443.09 K were taken from Holmes and Mesmer4 and are limited to the maximum molality in their work. The lines through the points were generated using Archer’s extended Pitzer model6 for our experimental values, and for the work of Holmes and Mesmer,4 the values of the ion-interaction model of Pitzer were used. The overall trend in our results is the

Ind. Eng. Chem. Res., Vol. 44, No. 10, 2005 3811

equation used for 1:1 electrolytes is

Table 6. Calculated Parameters of Apelblat’s Expression [ln(∆p/kPa) ) A + B/T + C(ln T - T/2Tc)] at Different Molalities m m/(mol‚kg-1)

A

B

C

δrmsa/kPa

1.5921 1.9897 2.3096 2.4074 2.6682 3.5105 4.2824 4.7722

106.217 119.953 112.414 113.315 122.936 168.717 133.244 134.762

-8498.548 -9024.322 -8717.590 -8750.071 -9120.653 -10902.460 -9484.412 -9534.340

-14.549 -16.701 -15.493 -15.620 -17.135 -24.371 -18.716 -18.944

4.1955 × 10-3 5.9318 × 10-3 3.9552 × 10-3 5.6447 × 10-3 6.9912 × 10-3 8.2900 × 10-3 9.9701 × 10-3 5.9150 × 10-3

ln γ( ) -Aφ

]

2 m1/2 + ln(1 + bm1/2) + m(2β(0) + 1 + bm1/2 b m2 A1 + A2) + (3C(0) + A2) (23) 2

in which

[ (

)

]

[ (

)

]

R12m 2β(1) 1/2 exp(-R1m1/2) A1 ) 2 1 - 1 + R1m 2 R1 m (24)

δrms ) [∑(p - pcalc)2/n]0.5, where n is the number of experimental data points. a

monotonic decrease in the osmotic coefficients with increasing temperature. For comparison with the values given by Holmes and Mesmer,4 our results are regressed for different compositions using the empirical relation given by Apelblat.24 This expression can be used to extrapolate the pressure lowering to high temperatures with a good precision for nondilute solutions:

(

[

A2 )

R22m 2β(2) 1/2 1 1 + R m exp(-R2m1/2) 2 2 R22m (25)

{[ (

A3 ) 4C(1) 6 - 6 + 6R3m1/2 + 3R32m + R33m3/2 R34

)

B T ln ∆p ) A + + C ln T T 2Tc (at constant composition) (22)

]/ }

)

m2 exp(-R3m1/2) R34m2 2

(26)

The validity of γ( calculations depends on how well the model describes the osmotic coefficients in the dilute region. Activity coefficient values are reported in Table 7.

where ∆p ) p* - p, Tc is the critical temperature of pure water (Tc ) 647.096 K), T is the temperature in Kelvin, and A, B, and C are adjustable parameters. The calculated parameters for different concentrations are given in Table 6. From the calculated vapor pressures, the osmotic coefficients were calculated with the help of eq 1 and the vapor-pressure values of water taken from Wagner and Pruβ25 for the different temperatures. The extrapolated osmotic coefficients, together with the Holmes and Mesmer4 data at temperatures 383.29, 413.12, and 443.09 K, are shown also in Figure 2. 3.3. Calculation of the Mean Activity Coefficient. The mean molal activity coefficients were calculated using the Pitzer equation with the Archer extension; the corresponding parameters are given in Table 4. The

4. Discussion 4.1. Osmotic Coefficients. Figure 3 shows the osmotic coefficients of the alkaline hydroxides vs molality at 298.15 K. The osmotic coefficients of lithium hydroxides have been taken from Table 2 of this paper and those of sodium, potassium, and cesium hydroxides from Hamer and Wu.26 At a given concentration, it can be seen that the osmotic coefficients of these four hydroxides increase in the order lithium, sodium, potassium, and cesium. It is well-known that, at room temperature, the order of osmotic coefficients for aqueous solutions of the alkali-metal hydroxides is opposite

Table 7. Mean Molal Activity Coefficient of Aqueous Solutions of Lithium Hydroxide Calculated from the Archer Extension of the Pitzer Model γ( m

298.15

303.15

308.15

313.15

318.15

323.15

328.15

333.15

338.15

343.15

348.15

353.15

358.15

363.15

0.0749 0.1239 0.1750 0.3439 0.4017 0.7404 0.8675 1.0143 1.0229 1.4307 1.5921 1.9050 1.9897 2.1177 2.3096 2.4074 2.5787 2.6682 3.1062 3.5105 4.2824 4.7722

0.980 0.946 0.917 0.853 0.838 0.777 0.763 0.749 0.748 0.721 0.713 0.700 0.697 0.693 0.688 0.685 0.681 0.679 0.671 0.664 0.655 0.650

0.993 0.957 0.927 0.863 0.848 0.787 0.773 0.759 0.758 0.729 0.720 0.706 0.703 0.698 0.692 0.689 0.684 0.681 0.671 0.663 0.651 0.646

0.989 0.951 0.920 0.854 0.839 0.778 0.763 0.749 0.748 0.719 0.710 0.695 0.692 0.687 0.680 0.677 0.672 0.669 0.658 0.649 0.633 0.625

0.998 0.958 0.925 0.854 0.837 0.772 0.756 0.741 0.740 0.709 0.699 0.684 0.680 0.675 0.668 0.664 0.659 0.656 0.644 0.634 0.618 0.609

0.966 0.920 0.884 0.812 0.795 0.732 0.716 0.701 0.700 0.669 0.659 0.644 0.640 0.635 0.627 0.624 0.618 0.615 0.603 0.593 0.576 0.567

0.942 0.894 0.858 0.785 0.768 0.705 0.690 0.675 0.674 0.642 0.633 0.617 0.613 0.608 0.600 0.596 0.591 0.588 0.575 0.564 0.546 0.536

0.945 0.893 0.855 0.779 0.762 0.696 0.680 0.665 0.664 0.631 0.621 0.605 0.601 0.595 0.588 0.584 0.578 0.575 0.562 0.551 0.533 0.523

0.934 0.869 0.824 0.740 0.722 0.656 0.640 0.624 0.623 0.590 0.580 0.564 0.560 0.554 0.547 0.543 0.537 0.534 0.521 0.511 0.495 0.486

0.937 0.866 0.815 0.725 0.706 0.636 0.619 0.602 0.601 0.566 0.556 0.539 0.535 0.529 0.521 0.517 0.511 0.508 0.495 0.484 0.467 0.457

0.917 0.851 0.804 0.714 0.694 0.620 0.602 0.584 0.583 0.547 0.536 0.518 0.514 0.508 0.499 0.496 0.489 0.486 0.472 0.461 0.442 0.431

0.897 0.828 0.779 0.688 0.668 0.595 0.576 0.559 0.558 0.522 0.511 0.493 0.489 0.483 0.474 0.470 0.464 0.461 0.447 0.436 0.417 0.406

0.907 0.831 0.777 0.682 0.662 0.589 0.570 0.553 0.552 0.515 0.504 0.485 0.481 0.475 0.466 0.462 0.455 0.452 0.438 0.426 0.406 0.395

0.881 0.809 0.757 0.663 0.643 0.568 0.550 0.532 0.531 0.494 0.482 0.464 0.459 0.453 0.445 0.441 0.434 0.431 0.416 0.404 0.385 0.373

0.870 0.800 0.750 0.654 0.633 0.554 0.534 0.516 0.515 0.476 0.465 0.446 0.441 0.435 0.426 0.422 0.415 0.412 0.397 0.385 0.364 0.352

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Figure 3. Comparison of the osmotic coefficients of aqueous solutions of alkali-metal hydroxides at 298.15 K: (3) cesium hydroxide;26 (b) potassium hydroxide;26 (2) sodium hydroxide;28 (O) lithium hydroxide.

to that observed for alkali-metal chlorides, bromides, iodides, nitrates, chlorates, and perchlorates26-28 (cf. Figure 3). For lithium hydroxide, the osmotic coefficients were computed from the ion-interaction parameters of Table 4. For alkali-metal chlorides and other alkalimetal hydroxides, ion-interaction parameters were taken from Hamer and Wu26 and Holmes and Mesmer.28 The activity coefficients of these two families are also in the opposite order, at least above molalities of 1 mol‚kg-1 and at elevated temperatures.27,28 Hamer and Wu26 inferred the osmotic coefficients from the activity coefficients of emf measurements by Harned and Swindells5 at 298.15 K. The discrepancy between these osmotic coefficient values and our data is up to 8% at 298.15 K. Pitzer and Mayorga,29 in their extensive and thorough compilation of thermodynamic data for aqueous electrolyte solutions, concluded that “there are small but troublesome conflicts among data for LiOH and further experiments are needed to resolve them.” Corti et al.33 reported the 6% discrepancy for the activity coefficient of several authors for 0.1 mol‚kg-1 LiOH solutions at 298.15 K. The Pitzer ion-interaction model parameters reported by Covington et al.34 even produce an undue change in the osmotic coefficient at high molalities. One error source for this system may be the dissolved CO2, which reacts with LiOH to yield the corresponding carbonate. In our measurements, we carefully degassed several times to remove the trace amount of dissolved gases. A comparison of our osmotic coefficient data to available literature values for 298.15 K is shown in Figure 4. It can be seen from Figure 2 that, at every concentration, the osmotic coefficients decrease with increasing temperature, which indicates increasing ion association. There is, indeed, evidence for strong ion pairing and an increasing association constant with increasing temperature for aqueous solutions of LiOH from conductivity measurements.33 This ion pairing is more pronounced for LiOH than for the other alkali-metal hydroxide solution. The ion association increases from cesium to lithium hydroxide, and it is reversed for chlorides, bromides, iodides, nitrates, chlorates, perchlorates, etc.30 In the case of lithium hydroxide, the cation is strongly hydrated and hence too large to permit

Figure 4. Comparison of the osmotic coefficients of aqueous lithium hydroxide solutions at 298.15 K: (O) this work; (3) Hamer and Wu;26 (2) Pitzer and Mayorga;29 (b) Covington et al.34 Pitzer and Mayorga29 concluded that the osmotic coefficient data for aqueous solutions of LiOH are contradictory and require further experiments.

contact ion pairing. Therefore, the low osmotic coefficients are assumed to come from a high amount of solvent-separated ion pairs. The process of this type of ion pairing is referred to as ‘‘localized hydrolysis”.30,31 Its impact on the osmotic coefficient values is expected to decrease with increasing cation size. In the hydration shell around a cation, a water molecule must be highly polarized, with the positive charge directed away from the cation, which can be very roughly represented as follows:

Li+‚‚‚‚‚‚OH-‚‚‚‚‚‚H+ Related with the polarization of a water molecule by the interaction with the cation, there is cooperative hydrogen bonding of the water molecule with the anion (hydroxide):

Li+‚‚‚‚‚‚OH-‚‚‚‚‚‚H+‚‚‚‚‚‚OHThe smaller the cation, the more polarized will be the solvent molecules, so that the effect decreases from lithium to cesium.30 Such a bridging mechanism stabilizes the solvent-separated ion pair, particularly in the case of LiOH. As a consequence, this strong ion pairing leads to reduced osmotic and activity coefficients and explains why lithium hydroxide has low and cesium hydroxide high osmotic and activity coefficients at the same salt concentrations. Concerning the anion dependence, the osmotic coefficients of aqueous lithium solutions at a given concentration increase in the following order: LiOH < LiNO3 < LiCl < LiBr < LiI < LiClO4. Lithium hydroxide has the lowest osmotic coefficient and highest ion association. Quantum chemical studies of an aqueous lithium hydroxide solution also yield the highest association for this system.30 4.2. Extended Pitzer Model of Archer. This extended ion-interaction Pitzer model of Archer is capable of representing experimental values of the osmotic and activity coefficients of most aqueous and nonaqueous electrolytes more accurately over a wide range of ionic strengths than the original model of Pitzer. It gives

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reasonable quality fits for aqueous electrolyte solutions from the freezing temperatures up to 423.15 K12 with nine parameters: four fixed ones, b, R1, R2, and R3, and five temperature-dependent adjustable parameters, β(0), β(1), β(2), C (1), and C (2). From the analysis of the experimental osmotic coefficient data for our studied systems, we found that the values of R1 ) 1.4 kg1/2‚ mol-1/2, R2 ) 14 kg1/2‚mol-1/2, R3 ) 10 kg1/2‚mol-1/2, and b ) 1.2 kg1/2‚mol-1/2 were satisfactory in the investigated temperature range. 4.3. MSA-NRTL Model. The MSA-NRTL model turned out to be an accurate model for the description of the thermodynamics of electrolyte solutions.7 Its big advantage compared to Pitzer-based models is 2-fold: first, it seems that with less parameter comparably good data descriptions can be achieved and, second, the parameters have a physical meaning. This is not the case for the Pitzer models although some attempts have been made to interpret the possible meaning of some Pitzer parameters. However, the number of systems described with MSANRTL is still small so that final conclusions cannot yet be drawn. There are six parameters for the MSA-NRTL model: the mean ionic solvated diameter σ, the nonrandomness factor R, and four parameters (τas, τcs, (2) τ(1) sc,ac, and τsc,ac) that have to be adjusted by fitting the model to the experimental data. In the present paper, MSA-NRTL parameters were obtained from the fitting of experimental osmotic coefficient data for the investigated system at different temperatures. Their values are given in Table 5. 5. Conclusions The vapor-pressure and osmotic coefficients of aqueous solutions of lithium hydroxide were determined over a temperature range from 298.15 to 363.15 K using a precise vapor-pressure apparatus. Experimental data of the investigated systems are satisfactorily correlated using the extended Pitzer ion-interaction model of Archer and the MSA-NRTL model. The description of the experimental data with the MSA-NRTL model is as good as that with the extended Pitzer model. The given values for this system should help to solve the problem of various conflicting data sets known from the literature. Acknowledgment We thank the Arbeitsgemeinschaft industrieller Forschung AiF “Otto von Guericke e.V.” (AiF) for financial support. K.N. is grateful to the Iran Ministry of Science, Research and Technology for a grant. List of Symbols A, B, and C ) adjustable parameters in Apelblat’s expression (eq 22) a-, a+ ) anion radius, cation radius (Å) as ) activity of the solvent Aφ ) Debye-Hu¨ckel constant for the osmotic coefficient in the molal scale Bs ) second virial coefficient of water b ) adjustable parameter in the Pitzer model Bφ ) second virial coefficient in Archer’s extended Pitzer model C (0), C (1) ) Pitzer ion-interaction parameter in Archer’s extended Pitzer model Cφ ) third virial coefficient in the Pitzer model

ds ) density (kg‚m-3) e ) electronic charge f ) activity coefficient in the mole fraction scale I ) ionic strength in the molality scale k ) Boltzmann constant m ) molality of the solution (mol‚kg-1) Ms ) molar mass of the solvent (mol‚kg-1) NA ) Avogadro’s number p*, p ) vapor pressures of the pure solvent and electrolyte solution (kPa) R ) gas constant s ) solvent radius SD(L) ) standard deviation of property L T ) absolute temperature Tc ) critical temperature V/s ) molar volume of the solvent x ) mole fraction of compound i in the liquid phase Xij ) local molar fraction of compound i around the central molecule j Greek Letters R ) nonrandomness MSA-NRTL model adjustable parameters R0, R1, R2 ) adjustable parameters in the Pitzer model β(0), β(1), β(2) ) Pitzer ion-interaction parameters  ) dielectric constant of the solvent 0 ) vacuum permittivity φ ) osmotic coefficient γ( ) mean molal activity coefficient λ ) Debye-Hu¨ckel screening parameter σ ) mean ionic diameter in the MSA-NRTL model τas, τcs, τsc,ac ) MSA-NRTL parameters Γ ) MSA screening parameter Subscripts s ) solvent s′ ) solvent in the summations c, a ) cation, anion ij ) paired state of particles i and j +, - ) cation, anion ( ) cation-anion paired state

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Received for review November 10, 2004 Revised manuscript received March 2, 2005 Accepted March 14, 2005 IE0489148