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Ionic exchange and statistical thermodynamics I. Equilibria in simple exchange systems
Affiliation:1. Advanced Ceramics Research Center, Nagoya Institute of Technology, Tajimi, 507-0071, Japan;2. WPI, International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, Fukuoka, 819-0395, Japan;1. Widhoc Smart Solutions S.L. Parque Tecnológico de Fuente Álamo, CEDIT, Carretera del Estrecho-Lobosillo Km 2, 30320 Fuente Álamo. (Murcia), Spain;2. The Institute of Electronics, Communications and Information Technology (ECIT), Queens University of Belfast, Belfast BT3 9DT, UK;3. Producción Vegetal Department, Universidad Politécnica de Cartagena, Paseo Alfonso XIII, 48, 30203 Cartagena (Murcia), Spain;4. Tecnología Electrónica Department, Universidad Politécnica de Cartagena, Campus Muralla del Mar, Doctor Fleming, s/n, 30202 Cartagena (Murcia), Spain;5. Ingeniería de Sistemas y Automática Department, Universidad Politécnica de Cartagena, Campus Muralla del Mar, Doctor Fleming, s/n, 30202 Cartagena (Murcia), Spain;1. MATS School of Sciences, MATS University, Pagaria Complex, Raipur, Chhattisgarh, India;2. School of Studies in Chemistry, Pt. Ravishankar Shukla University, Raipur, Chhattisgarh, India;3. Department of Chemistry, University of Allahabad, Prayagraj, Uttar Pradesh, India;4. Department of Chemistry (MSET), MATS University, Gullu Campus, Raipur, Chhattisgarh, India;5. Department of Chemistry, Indian Institute of Technology Delhi, New Delhi, Delhi, India;1. Agronomy, Universidade Estadual de Londrina, Centro de Ciências Agrárias, Rodovia Celso Garcia Sid, s/n, CEP:86057970, Londrina PR, Brazil;2. Embrapa Soja, Centro Nacional de Pesquisa em Soja, Rodovia Carlos João Strass, s/n, Acesso Orlando Amaral, Distrito de Warta Caixa Postal: 231 CEP: 86001-970 Londrina PR, Brazil;3. Centro de Ciências Agrárias da Universidade Estadual de Londrina, Rodovia Celso Garcia Sid, s/n, CEP: 86057970 Londrina PR, Brazil
Abstract:
  • 1.1. The conditions for ionic exchange equilibria are derived by an application of classical thermodynamics. Only thermodynamically defined terms are used.
  • 2.2. The appropriate ionic concentration terms are derived by a modification of a statistical theory of localized monolayers due to Fowler and Guggenheim.
  • 3.3. The theory is first applied to a uni-univalent exchange. The resultant equation is of the simple mass action type.
  • 4.4. Unsymmetrical exchanges are treated by combining a method first presented by Guggenheim with an analysis of the problem of mutual ionic interaction in a monolayer of mixed valence types. Equilibrium exchange equations of a mass action type are developed.
  • 5.5. Vanselow's well known equation is an approximate form of the equations derived in this paper.
Keywords:
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