Modeling for mean ion activity coefficient of strong electrolyte system with new boundary conditions and ion-size parameters

doi:10.1016/j.cjche.2015.04.010

Chinese Journal of Chemical Engineering ›› 2015, Vol. 23 ›› Issue (7): 1169-1177.DOI: 10.1016/j.cjche.2015.04.010

Modeling for mean ion activity coefficient of strong electrolyte system with new boundary conditions and ion-size parameters

Miyi Li¹, Tao Fang²

1 School of Chemical Engineering and the Environment, Beijing Institute of Technology, Beijing 100081, China;
2 Beijing Institute of Aerospace Testing Technology, Beijing 100074, China

收稿日期:2014-11-18 修回日期:2015-03-06 出版日期:2015-07-28 发布日期:2015-08-21
通讯作者: Miyi Li
基金资助:
Supported by the National Natural Science Foundation of China (21206010).

Modeling for mean ion activity coefficient of strong electrolyte system with new boundary conditions and ion-size parameters

Miyi Li¹, Tao Fang²

1 School of Chemical Engineering and the Environment, Beijing Institute of Technology, Beijing 100081, China;
2 Beijing Institute of Aerospace Testing Technology, Beijing 100074, China

Received:2014-11-18 Revised:2015-03-06 Online:2015-07-28 Published:2015-08-21
Contact: Miyi Li
Supported by:
Supported by the National Natural Science Foundation of China (21206010).

摘要/Abstract

摘要： A rigorous approach is proposed to model the mean ion activity coefficient for strong electrolyte systems using the Poisson-Boltzmann equation. An effective screening radius similar to the Debye decay length is introduced to define the local composition and new boundary conditions for the central ion. The crystallographic ion size is also considered in the activity coefficient expressions derived and non-electrostatic contributions are neglected. Themodel is presented for aqueous strong electrolytes and compared with the classical Debye-Hückel (DH) limiting lawfor dilute solutions. The radial distribution function is compared with the DH andMonte Carlo studies. Themean ion activity coefficients are calculated for 1:1 aqueous solutions containing strong electrolytes composed of alkali halides. The individual ion activity coefficients andmean ion activity coefficients in mixed solvents are predicted with the new equations.

关键词: Activity coefficient, Electrolyte, Ion size, Poisson-Boltzmann equation

Abstract: A rigorous approach is proposed to model the mean ion activity coefficient for strong electrolyte systems using the Poisson-Boltzmann equation. An effective screening radius similar to the Debye decay length is introduced to define the local composition and new boundary conditions for the central ion. The crystallographic ion size is also considered in the activity coefficient expressions derived and non-electrostatic contributions are neglected. Themodel is presented for aqueous strong electrolytes and compared with the classical Debye-Hückel (DH) limiting lawfor dilute solutions. The radial distribution function is compared with the DH andMonte Carlo studies. Themean ion activity coefficients are calculated for 1:1 aqueous solutions containing strong electrolytes composed of alkali halides. The individual ion activity coefficients andmean ion activity coefficients in mixed solvents are predicted with the new equations.

Key words: Activity coefficient, Electrolyte, Ion size, Poisson-Boltzmann equation

Miyi Li, Tao Fang. Modeling for mean ion activity coefficient of strong electrolyte system with new boundary conditions and ion-size parameters[J]. Chinese Journal of Chemical Engineering, 2015, 23(7): 1169-1177.

Miyi Li, Tao Fang. Modeling for mean ion activity coefficient of strong electrolyte system with new boundary conditions and ion-size parameters[J]. Chin.J.Chem.Eng., 2015, 23(7): 1169-1177.

参考文献

[1] P. Debye, E. Hückel, Zur Theorie der Electrolyte. I. Gefrierpunkt-serniedrigung und Verwandte Erscheinungen. Physikalische Zeitschrift, Phys. Z. 24 (1923) 185-206.

[2] R.H. Fowler, E.A. Guggenheim, Statistical Thermodynamics, Cambridge University Press, Cambridge, U.K., 1956

[3] L.A. Bromley, Approximate individual ion value of β (or B) in extended Debye-Hückel theory for uni-univalent aqueous solutions at 298.15 K, J. Chem. Thermodyn. 4 (1972) 669-673.

[4] J.E. Mayer, The theory of ionic solutions, J. Chem. Phys. 18 (1950) 1426-1436.

[5] R.A. Robinson, R.H. Stokes, Electrolyte Solutions, 2nd ed. Butterworths, London, 1959.

[6] J.L. Lebowitz, J.K. Percus, Mean spherical model for lattice gases with extended hard cores and continuum fluids, Phys. Rev. 144 (1966) 251-258.

[7] L. Blum, Mean spherical model for asymmetric electrolytes, Mol. Phys. 30 (1975) 1529-1535.

[8] R. Triolo, L. Blum, M.A. Floriano, Simple electrolytes in the mean spherical approximation. III. A workable model for aqueous solutions, J. Chem. Phys. 67 (1977) 5956-5959.

[9] R. Triolo, J.R. Grigera, L. Blum, Simple electrolytes in the mean spherical approximation, J. Phys. Chem. 80 (1976) 1858-1861.

[10] J.F. Lu, Y.X. Yu, Y.G. Li, Modification and application of the mean spherical approximation method, Fluid Phase Equilib. 85 (1993) 81-100.

[11] J.P. Simonin, L. Blum, P. Turq, Real ionic solutions in the mean spherical approximation. 2. Pure strong electrolytes up to very high concentrations, and mixtures, in the primitive model, J. Phys. Chem. 100 (1996) 7704-7709.

[12] J.P. Simonin, Real ionic solutions in the mean spherical approximation. 1. Simple salts in the primitive model, J. Phys. Chem. B 101 (1997) 4313-4320.

[13] A.C. Tikanen, W.R. Fawcett, Application of the mean spherical approximation and ion association to describe the activity coefficients of aqueous 1:1 electrolytes, J. Electroanal. Chem. 439 (1997) 107-113.

[14] N. Papaiconomou, J.P. Simonin, O. Bernard, W. Kunz, MSA-NRTL model for the description of the thermodynamic properties of electrolyte solutions, Phys. Chem. Chem. Phys. 4 (2002) 4435-4443.

[15] C.W. Outhwaite, Extension of the Debye-Hückel theory of electrolyte solutions, J. Chem. Phys. 50 (1969) 2277-2288.

[16] C.W. Outhwaite, Symmetrical radial distribution functions in the potentially theory of electrolyte solutions, Chem. Phys. Lett. 53 (1978) 599-601.

[17] C.W. Outhwaite, Numerical solution of a Poisson-Boltzmann theory for a primitive model electrolyte with size and charge asymmetric ions, J. Chem. Soc. Faraday Trans. 83 (1987) 949-959.

[18] M. Molero, C.W. Outhwaite, L.B. Bhuiyan, Individual ionic activity coefficients from a symmetrical Poisson-Boltzmann theory, J. Chem. Soc. Faraday Trans. 88 (1992) 1541-1547.

[19] R. Kjellander, D.J. Mitchell, An exact but linear and Poisson-Boltzmann-like theory for electrolytes and colloid dispersions in the primitive model, Chem. Phys. Lett. 200 (1992) 76-82.

[20] L.M. Varela, M.P. Rodriguez, M. Garcia, F. Sarmiento, V. Mosquera, Static structure of electrolyte systems and the linear response function on the basis of a dressed-ion theory, J. Chem. Phys. 109 (1998) 1930-1938.

[21] S. Abbas, S. Nordholm, Simple estimation of surface tension of single-component fluids, J. Colloid Interface Sci. 166 (1994) 481.

[22] D. Fraenkel, Simplified electrostatic model for the thermodynamic excess potentials of binary strong electrolyte solutionswith size-dissimilar ions, Mol. Phys. 108 (2010) 1435-1466.

[23] H. David, R. Resnick, J.Walker, Fundamentals of Physics, 7th ed. JohnWiley and Sons Inc., USA, 2005.

[24] J. Barthel, H. Krienke,W. Kunz, Physical Chemistry of Electrolyte Solutions: Modern Aspects, Steinkopff/Springer, Darmstadt/New York, 1998.

[25] R.D. Shannon, Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides, Acta Crystallogr. A 32 (1976) 751-767.

[26] J. O'Connell, A.E. GeGane, Thermodynamic properties of strong electrolyte solutions from correlation functions, J. Solut. Chem. 4 (1975) 763-778.

[27] Z. Abbas, E. Ahlberg, S. Nordholm, Monte Carlo simulations of salt solutions: exploring the validity of primitive models, J. Phys. Chem. B 113 (2009) 5905-5916.

[28] D.N. Card, J.P. Valleau,Monte Carlo study of the thermodynamics of electrolyte solutions, J. Chem. Phys. 52 (1970) 6232-6240.

[29] W.J. Hamer, Y.C. Wu, Osmotic coefficients and mean activity coefficients of uniunivalent electrolytes in water at 25 ℃, J. Phys. Chem. Ref. Data 4 (1972) 1047-1100.

[30] J. Kiepe, A.K. Rodrigues, S. Horstmann, J. Gmehling, Experimental determination and correlation of liquid density data of electrolyte mixtures containing water or methanol, Ind. Eng. Chem. Res. 42 (2003) 2022-2029.

[31] B.Y. Dan, D. Andelman, R. Podgornik, Dielectric decrement as a source of ion-specific effects, J. Chem. Phys. 134 (2011) 704-705.

[32] G.W. Vera, J.H. Vera, On the measurement of individual ion activities, Fluid Phase Equilib. 236 (2005) 96-110.

[33] G.W. Vera, E. Rodil, J.H. Vera, Towards accurate values of individual ion activities additional data for NaCl, NaBr and KCl, and new data for NH₄Cl, Fluid Phase Equilib. 241 (2006) 59-69.

[34] W.D. Yan, Y.J. Xu, S.J. Han, Activity coefficients of sodium chloride in methanol-water mixed solvents at 298.15 K, Acta Chim. Sin. 52 (1994) 937-946.

[35] M.A. Esteso, D.O.M. Gonzalez, L.F. Hernandez, Activity coefficients for NaCl in ethanol-water mixtures at 25 ℃, J. Solut. Chem. 18 (1989) 277-288.

[36] D.O.M. Gonzalez, M.L. Fernandez, M.L.F. Hernandez, M.A. Esteso, Activity coefficients for NaBr in ethanol-water mixtures at 25 ℃, J. Solut. Chem. 24 (1995) 551-563.

[37] L. Malahias, O. Popovych, Activity coefficients and transfer free energies of potassium chloride in methanol-water solvents at 25 ℃, J. Chem. Eng. Data 27 (1982) 105-109.

Modeling for mean ion activity coefficient of strong electrolyte system with new boundary conditions and ion-size parameters

Modeling for mean ion activity coefficient of strong electrolyte system with new boundary conditions and ion-size parameters

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	Jiahao Lu, Zhimeng Wang, Qi Zhang, Cheng Sun, Yanyan Zhou, Sijia Wang, Xiangyun Qiu, Shoudong Xu, Rentian Chen, Tao Wei. The effects of amino groups and open metal sites of MOFs on polymer-based electrolytes for all-solid-state lithium metal batteries[J]. 中国化学工程学报, 2023, 60(8): 80-89.
[2]	Hae-Kyun Park, Dong-Hyuk Park, Bum-Jin Chung. Influence of the electrolyte conductivity on the critical current density and the breakdown voltage[J]. 中国化学工程学报, 2023, 59(7): 169-175.
[3]	Shaojun Niu, Guobin Zhu, Kai Wu, Honghe Zheng. The feasibility for natural graphite to replace artificial graphite in organic electrolyte with different film-forming additives[J]. 中国化学工程学报, 2023, 56(4): 58-69.
[4]	Qiongna Xiao, Yuyan Jiang, Weiqiang Yuan, Jingjing Chen, Haohong Li, Huidong Zheng. Styrene epoxidation catalyzed by polyoxometalate/quaternary ammonium phase transfer catalysts: The effect of cation size and catalyst deactivation mechanism[J]. 中国化学工程学报, 2023, 55(3): 192-201.
[5]	Qingyue Han, Suqing Wang, Wenhan Kong, Bing Ji, Haihui Wang. Composite polymer electrolyte reinforced by graphitic carbon nitride nanosheets for room-temperature all-solid-state lithium batteries[J]. 中国化学工程学报, 2023, 54(2): 257-263.
[6]	Wei Hong, Xinran Shen, Jian Wang, Xin Feng, Wenjing Zhang, Jing Li, Zidong Wei. High-loading Pt-alloy catalysts for boosted oxygen reduction reaction performance[J]. 中国化学工程学报, 2022, 48(8): 30-35.
[7]	Deen Yan, Huangwang Mai, Wen Chen, Wei Yang, Hanbo Zou, Shengzhou Chen. Enhanced electrochemical performance of garnet-based solid-state lithium metal battery with modified anodic and cathodic interfaces[J]. 中国化学工程学报, 2022, 44(4): 140-147.
[8]	Q. Yang, A. Wang, J. Luo, W. Tang. Improving ionic conductivity of polymer-based solid electrolytes for lithium metal batteries[J]. 中国化学工程学报, 2022, 43(3): 202-215.
[9]	Haotian Lu, Jinghong Zhou, Yueqiang Cao, Tongxin Shang, Guanghua Ye, Quan-Hong Yang, Xinggui Zhou. Understanding the effects of electrode meso-macropore structure and solvent polarity on electric double layer capacitors based on a continuum model[J]. 中国化学工程学报, 2022, 50(10): 423-434.
[10]	He Liu, Tao Li, Xiangqun Xu, Peng Shi, Xueqiang Zhang, Rui Xu, Xinbing Cheng, Jiaqi Huang. Stable interfaces constructed by concentrated ether electrolytes to render robust lithium metal batteries[J]. 中国化学工程学报, 2021, 37(9): 152-158.
[11]	Huan Zhou, Peng Wu, Wenxuan Li, Xingfan Wang, Kuo Zhou, Qing Hao. Thermodynamic modeling and phase diagram prediction of salt lake brine systems II. Aqueous Li⁺-Na⁺-K⁺-SO₄^2- and its subsystems[J]. 中国化学工程学报, 2021, 34(6): 134-149.
[12]	Yingfei Hou, Lin Jiang, Yaoyao Zhang, Zhiwen Qin, Chi Jiang, Ming Wang. A design of Nafion-coated bilayered quasi-solid electrolyte for lithium-O₂ batteries with high performance[J]. 中国化学工程学报, 2021, 34(6): 208-216.
[13]	Xianming Zhang, Mengchen Li, Yufeng Hu, Zhichang Liu, Shuqin Mo. Experimental results for the vapor-liquid equilibria of (formaldehyde + 1,3,5-trioxane + methanol + salt + water) systems and comparison with predictions[J]. 中国化学工程学报, 2021, 32(4): 291-300.
[14]	Fangfang Li, Francesca Mocci, Xiangping Zhang, Xiaoyan Ji, Aatto Laaksonen. Ionic liquids for CO₂ electrochemical reduction[J]. 中国化学工程学报, 2021, 29(3): 75-93.
[15]	Jie Yang, Alejandro Gallegos, Cheng Lian, Shengwei Deng, Honglai Liu, Jianzhong Wu. Curvature effects on electric-double-layer capacitance[J]. 中国化学工程学报, 2021, 29(3): 145-152.