The need to design low-cost adsorbents for the detoxification of industrial effluents has been a growing concern for most environmental researchers. So modelling of experimental data from adsorption processes is a very important means of predicting the mechanisms of various adsorption systems. Therefore, this paper presents an overall review of the applications of adsorption isotherms, the use of linear regression analysis, nonlinear regression analysis, and error functions for optimum adsorption data analysis.

A complete study of adsorption processes will be less complete if the structure and dynamics of its different elements and how they interact is not well captured. Therefore, the extensive study of adsorption thermodynamics in conjunction with adsorption kinetics is inevitable. Measurable thermodynamic properties such as temperature equilibrium constant and their non-measurable counterparts such as Gibbs free energy change, enthalpy, entropy etc. are very important design variables usually deployed for the evaluation and prediction of the mechanism of adsorption processes.

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The adsorption properties of layered double hydroxide (Mg/Al-CO3) for the removal of Congo Red (CR) dye from aqueous solution were studied. The layered double hydroxide was synthesized by co-precipitation method and characterized by X-ray diffraction (XRD), Fourier Transform Infrared spectroscopic (FTIR) and Energy-Dispersive X-ray Spectroscopic (EDX). The effects of various experimental parameters such as contact time, dye concentrations and temperature variation were investigated. The results show that the amount of Congo Red adsorbed increases with increase in temperature but decreases with increase in initial dye concentration and contact time. The data were also fitted to several kinetic models: zero-order kinetic model, first-order kinetic model, second-order kinetic model, pseudo-second-order kinetic model and third-order kinetic model respectively. The adsorption process was best defined by zero-order-kinetic model (R 2 = 1). Langmuir, Freundich, Temkin and Dubinin-kaganer-Radushkevich (DPK) adsorption isotherm models were applied to analyze adsorption data with Temkin isotherm being the most applicable to the adsorption process. Thermodynamic parameters e.g. ∆G o , ∆S o , ∆H o and ∆Hx of the adsorption process were found to be endothermic, spontaneous and feasible.

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