Critical Review and Discussion of the Nonlinear Form of Radke–Prausnitz Model in Adsorption Solid–Liquid Phases

Tran, Hai Nguyen; Bollinger, Jean-Claude; Salvestrini, Stefano; Chu, Khim Hoong; Juang, Ruey-Shin

doi:10.1061/JOEEDU.EEENG-7074

State-of-the-Art Reviews

Dec 21, 2022

Critical Review and Discussion of the Nonlinear Form of Radke–Prausnitz Model in Adsorption Solid–Liquid Phases

Authors: Hai Nguyen Tran https://orcid.org/0000-0001-8361-2616 [email protected], Jean-Claude Bollinger https://orcid.org/0000-0003-4059-5793, Stefano Salvestrini https://orcid.org/0000-0002-9392-9358, Khim Hoong Chu https://orcid.org/0000-0003-4012-0667, and Ruey-Shin Juang https://orcid.org/0000-0002-6373-9668Author Affiliations

Publication: Journal of Environmental Engineering

Volume 149, Issue 3

https://doi.org/10.1061/JOEEDU.EEENG-7074

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Abstract

The Radke–Prausnitz model, a typical three-parameter model belonging to the Langmuir–Freundlich-type equation, is increasingly being used to correlate the equilibrium data of various adsorption processes. However, very few published works provide the correct information on (1) the nonlinear form of this model, (2) the units of its parameters, and (3) its original citation. This work provides a critical analysis of the Radke–Prausnitz model with special emphasis on promoting its proper application in adsorption research. The correct expression and citation of the models used in adsorption studies are provided. The correct units of its parameters

a_{RP}

,

b_{RP}

, and

β

are

L / kg

,

({mol / kg) / (mol / L)}^{β}

, and unitless when the solution phase concentration

C_{e}

is given in

mol / L

and the adsorbed phase concentration

q_{e}

is defined in

mol / kg

. The Radke–Prausnitz model can be reduced to the Henry, Freundlich, Langmuir, or Redlich–Peterson model in some special cases. The Radke—Prausnitz model is valid when the exponent

β

is in the range of

0 \leq β \leq 1

. A new adsorption equilibrium constant of this model is introduced. The feasibility of using the new equilibrium constant to calculate the thermodynamic parameters (

Δ G °

,

Δ H °

, and

Δ S °

) of adsorption processes is discussed herein.

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Data Availability Statement

All data, models, and code generated or used during the study appear in the published article.

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Journal of Environmental Engineering

Volume 149 • Issue 3 • March 2023

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Published online: Dec 21, 2022

Published in print: Mar 1, 2023

Discussion open until: May 21, 2023

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Hai Nguyen Tran https://orcid.org/0000-0001-8361-2616 [email protected]

Director, Center for Energy and Environmental Materials, Institute of Fundamental and Applied Sciences, Duy Tan Univ., Ho Chi Minh 700000, Viet Nam; Faculty of Environmental and Chemical Engineering, Duy Tan Univ., Da Nang City, Viet Nam; Faculty of Environmental and Chemical Engineering, Duy Tan Univ., Da Nang 550000, Viet Nam (corresponding author). ORCID: https://orcid.org/0000-0001-8361-2616. Email: [email protected]; [email protected]

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Jean-Claude Bollinger https://orcid.org/0000-0003-4059-5793

Professor, Faculy of Sciences and Technology, Univ. of Limoges, Laboratory E2Lim, Limoges 87060, France. ORCID: https://orcid.org/0000-0003-4059-5793

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Stefano Salvestrini https://orcid.org/0000-0002-9392-9358

Professor, Dept. of Environmental, Biological, and Pharmaceutical Sciences and Technologies, Univ. of Campania Luigi Vanvitelli, via Vivaldi 43, Caserta 81100, Italy; Environmental Technologies, Univ. Spin-Off of Univ. of Campania Luigi Vanvitelli, via Vivaldi 43, Caserta 81100, Italy. ORCID: https://orcid.org/0000-0002-9392-9358

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Khim Hoong Chu https://orcid.org/0000-0003-4012-0667

Director, R&D Dept., Honeychem Research, Newtown, Wellington 6021, New Zealand. ORCID: https://orcid.org/0000-0003-4012-0667

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Ruey-Shin Juang https://orcid.org/0000-0002-6373-9668

Professor, Dept. of Chemical and Materials Engineering, Chang Gung Univ., Guishan, Taoyuan 33302, Taiwan; Div. of Nephrology, Dept. of Internal Medicine, Chang Gung Memorial Hospital, Linkou, Taoyuan 33305, Taiwan. ORCID: https://orcid.org/0000-0002-6373-9668

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Khim Hoong Chu, Mohd Ali Hashim, Modeling of aqueous phase adsorption: Is it time to bid adieu to the Harkins–Jura isotherm?, Journal of Molecular Liquids, 10.1016/j.molliq.2022.121122, 371, (121122), (2023).
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