The DOI matches its Crossref record; 40 of the 40 references it cites were found in a registry or an index.
Derivation of Pseudo-First-Order, Pseudo-Second-Order and Modified Pseudo-First-Order rate equations from Langmuir and Freundlich isotherms for adsorption
Abstract
Abstract The kinetics of adsorption for Langmuir and Freundlich isotherms has been explored theoretically on the basis of Statistical Rate Theory (SRT). The Modified Pseudo-First-Order (MPFO) and Pseudo-First-Order (PFO) models were derived from Freundlich isotherm on the basis of Statistical Rate Theory at c 0 ≫ c e and at close to equilibrium respectively. Also, for a Langmuirian adsorption MPFO was derived at initial times of adsorption under condition c 0 ≫ c e and also Pseudo-First-Order (at close to equilibrium) and Pseudo-Second-Order (PSO) model (at close to equilibrium for c 0 ≫ c e and θ e ≅ 1 ) were obtained based on SRT. It has been proven that from Freundlich and Langmuir isotherms the fractional coverage is a linear function of t at very short initial times of adsorption. Also an useful rate equation was derived at condition c 0 ≅ c e from Freundlich isotherm. The theoretical obtained equations from Freundlich and Langmuir isotherms have been examined by several set of experimental data selected from literature.
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Cites
The adsorption of gases on plane surfaces of glass, mica and platinum
Langmuir, I. (1918) · Journal of the American Chemical Society · doi:10.1021/ja02242a004 · Cited by 23,242
Kinetic models of sorption: a theoretical analysis
Azizian, S. (2004) · Journal of Colloid and Interface Science · doi:10.1016/j.jcis.2004.03.048 · Cited by 2,315
Simonin, J.-P. (2016) · Chemical Engineering Journal · doi:10.1016/j.cej.2016.04.079 · Cited by 2,100
Chemical kinetics and dynamics
Steinfeld, J. I., Francisco, J. S., & Hase, W. L. (1989) · Cited by 1,418
Avrami, M. (1940) · Medical Entomology and Zoology · Cited by 1,085
Fan, S., Wang, Y., Wang, Z., Tang, J., Tang, J., & Li, X. (2017) · Journal of Environmental Chemical Engineering · doi:10.1016/j.jece.2016.12.019 · Cited by 699
A general kinetic model for adsorption: Theoretical analysis and modeling
Guo, X., & Wang, J. (2019) · Journal of Molecular Liquids · doi:10.1016/j.molliq.2019.111100 · Cited by 550
Characteristics of pseudo-second-order kinetic model for liquid-phase adsorption: A mini-review
Wu, F.-C., Tseng, R.-L., Huang, S.-C., & Juang, R.-S. (2009) · Chemical Engineering Journal · doi:10.1016/j.cej.2009.02.024 · Cited by 472
Kinetic modeling of liquid-phase adsorption of reactive dyes on activated carbon
Yang, X., & Al-Duri, B. (2005) · Journal of Colloid and Interface Science · doi:10.1016/j.jcis.2005.01.093 · Cited by 413
From Langmuir Kinetics to First- and Second-Order Rate Equations for Adsorption
Liu, Y., & Shen, L. (2008) · Langmuir · doi:10.1021/la801839b · Cited by 399
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Adsorption isotherm models: Classification, physical meaning, application and solving method
Wang, J., & Guo, X. (2020) · Chemosphere · doi:10.1016/j.chemosphere.2020.127279 · Cited by 2,289
Zhang, T., Wang, W., Zhao, Y., Bai, H., Wen, T., Kang, S., Song, G., Song, S., & Komarneni, S. (2021) · Chemical Engineering Journal · doi:10.1016/j.cej.2020.127574 · Cited by 513
Phosphorus adsorption by functionalized biochar: a review
Luo, D., Wang, L., Nan, H., Cao, Y., Wang, H., Kumar, T. V., & Wang, C. (2023) · Environmental Chemistry Letters · doi:10.1007/s10311-022-01519-5 · Cited by 387
On validity, physical meaning, mechanism insights and regression of adsorption kinetic models
Vareda, J. P. (2023) · Journal of Molecular Liquids · doi:10.1016/j.molliq.2023.121416 · Cited by 380
Metadata
- Authors
- Ezzati, R.
- Venue
- Chemical Engineering Journal
- Publisher
- Elsevier BV
- Published
- 2020-07
- Volume
- 392
- Pages
- 123705
- ISSN
- 1385-8947 (ISSN-L)
- OpenAlex
- W3016058779
- Cited by
- 482
- References
- 40
- FWCI
- 12.68
- Type
- journal article
- Language
- en
- Open access
- closed
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- Ezzati, R. (2020). Derivation of Pseudo-First-Order, Pseudo-Second-Order and Modified Pseudo-First-Order rate equations from Langmuir and Freundlich isotherms for adsorption. Chemical Engineering Journal. https://doi.org/10.1016/j.cej.2019.123705
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