Sulu çözeltiden Pb2+ iyonlarının kızılçam kabuğu (Pinus brutia ten) üzerinde adsorpsiyonundan elde edilen kinetik ve denge verilerinin doğrusal olmayan regresyon kullanılarak ileri düzeyde yorumlanması: Microsoft Excel Çözücü ile Pratik Bir Yaklaşım

Öz

Bu çalışma, kinetik ve denge verilerini değerlendirmek için doğrusal olmayan regresyon analizi kullanarak sulu çözeltilerden çam kabuğuna (Pinus brutia Ten.) Pb(II) iyonlarının adsorpsiyonunu araştırır. Adsorpsiyon deneyleri bir dizi başlangıç ​​konsantrasyonu üzerinde yürütüldü ve denge verileri Langmuir, Freundlich, Temkin ve Dubinin-Radushkevich (D-R) dahil olmak üzere çeşitli izoterm modellerine ve Tóth, Sips, Redlich-Peterson (R-P) ve Brouers-Sotolongo (B-S) gibi gelişmiş üç parametreli modellere uygulandı. Kinetik veriler, sözde birinci mertebeden (PFO), sözde ikinci mertebeden (PSO), Elovich, Avrami ve B-S modelleri kullanılarak analiz edildi. Microsoft Excel Solver tarafından kolaylaştırılan doğrusal olmayan regresyon, model parametrelerini optimize etmek için kullanıldı ve uyum iyiliği SSE, ARE, HYBRID, MPSD ve MAE dahil olmak üzere birden fazla hata fonksiyonu aracılığıyla değerlendirildi. Sonuçlar, Brouers-Sotolongo (B-S) modelinin hem kinetik hem de izoterm verileri için en iyi uyumu sağladığını ve adsorbanın heterojen yüzey özelliklerini yansıttığını göstermektedir. Adsorpsiyon sürecinin, kinetik sabitler (αBS ve nBS) ve yarı reaksiyon süresi (τ1/2) ile kanıtlandığı üzere, fiziksel ve kimyasal etkileşimlerin bir kombinasyonunu içerdiği bulunmuştur. Denge modelleri arasında, özellikle B-S, Tóth ve Sips modelleri olmak üzere üç parametreli izotermler, iki parametreli modellere göre üstün performans göstererek, bu sistemdeki adsorpsiyon mekanizmalarının karmaşık doğasını vurgulamıştır. Bu çalışma, çam kabuğunun ağır metal giderimi için düşük maliyetli ve çevre dostu bir adsorban olarak etkinliğini vurgulamakta ve adsorpsiyon çalışmalarında doğrusal olmayan regresyon ve gelişmiş hata analizinin faydasını göstermektedir. Bu yaklaşımın, model seçiminin hassasiyetini ve adsorpsiyon mekanizmalarının anlaşılmasını artırarak literatüre katkıda bulunacağı düşünülmektedir.

Anahtar Kelimeler

• Adsorpsiyon
• Hata fonksiyonu
• Excel Çözücü
• İzoterm
• Kinetik ve denge verileri
• Doğrusal olmayan regresyon

Advanced interpretation of kinetics and equilibrium data obtained from adsorption of Pb2+ ions from aqueous solution onto pine bark (Pinus brutia Ten.) using nonlinear regression: A practical approach with Microsoft Excel Solver

Öz

This study investigates the adsorption of Pb(II) ions from aqueous solutions onto pine bark (Pinus brutia Ten.) using nonlinear regression analysis to evaluate kinetic and equilibrium data. Adsorption experiments were conducted over a range of initial concentrations, and the equilibrium data were fitted to various isotherm models, including Langmuir, Freundlich, Temkin, and Dubinin-Radushkevich (D-R), as well as advanced three-parameter models like Tóth, Sips, Redlich-Peterson (R-P), and Brouers-Sotolongo (B-S). Kinetic data were analyzed using pseudo-first order (PFO), pseudo-second order (PSO), Elovich, Avrami, and B-S models. Nonlinear regression, facilitated by Microsoft Excel Solver, was used to optimize model parameters, and goodness-of-fit was assessed through multiple error functions, including SSE, ARE, HYBRID, MPSD, and MAE. Results indicate that the Brouers-Sotolongo (B-S) model provided the best fit for both kinetic and isotherm data, reflecting the heterogeneous surface characteristics of the adsorbent. The adsorption process was found to involve a combination of physical and chemical interactions, as evidenced by the kinetic constants (αBS and nBS) and the half-reaction time (τ1/2). Among the equilibrium models, three-parameter isotherms, particularly the B-S, Tóth, and Sips models, showed superior performance over two-parameter models, highlighting the complex nature of adsorption mechanisms in this system. This study underscores the efficacy of pine bark as a low-cost and eco-friendly adsorbent for heavy metal removal and demonstrates the utility of nonlinear regression and advanced error analysis in adsorption studies. This approach is thought to improve the precision of model selection and the understanding of adsorption mechanisms, contributing to the literature.

Anahtar Kelimeler

• Adsorption
• Error function
• Excel Solver
• Isotherm
• Kinetics and equilibrium data
• Non-linear regression

Kaynakça

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