Thermodynamic parameters of cadmium adsorption onto orange peel calculated from various methods: A comparison study Hai Nguyen Tran a,b, *, Sheng-Jie You b, *, Huan-Ping Chao b, * a Department of Civil Engineering, Chung Yuan Christian University, Chungli 320, Taiwan b Department of Environmental Engineering, Chung Yuan Christian University, Chungli 320, Taiwan A R T I C L E I N F O Article history: Received 3 March 2016 Received in revised form 6 May 2016 Accepted 7 May 2016 Available online 9 May 2016 Keywords: Equilibrium constant Thermodynamic parameters Physical adsorption Electrostatic attraction Cadmium Orange peel A B S T R A C T Thermodynamic adsorption investigation plays a key role in estimating adsorptive mechanisms (i.e., physical or chemical). Accuracy estimation of the thermodynamic parameters is directly dependent on the equilibrium constant between two phases (K C ; dimensionless). In this study, the thermodynamic parameters were calculated from the K C constants derived from the adsorption isotherm constants (i.e., Langmuir, Freundlich, and Henry) and partition coefficient, with and without dimensionality consideration. Results showed that the optimal selection of K C is strongly dependent on: the adsorption characteristics (i.e., Henry, Freundlich, and Langmuir) where equilibrium data are actually located; and the correlation coefficient of the van’t Hoff equation. Both the Langmuir and Freundlich constants (dimensionless) are appropriate to calculate the thermodynamic parameters. The Langmuir constants from its four linear forms can be applied to calculate the thermodynamic parameters without significant difference. The Cd(II) biosorption process onto the orange peel (OP) occurred spontaneously (DG  ), in an exothermic nature (DH  ), and with increased randomness (+DS  ). The biosorption process involved physical adsorption with minimal activation energy (E a ) and adsorption energy (E). The biosorption phenomenon reached fast equilibrium and reversibility. The negatively charged carboxylic groups (–COO  ) on the OP’s surface play an important role (approximately 90%) in Cd 2+ biosorption through electrostatic attractions (out-sphere complexes). ã 2016 Elsevier Ltd. All rights reserved. 1. Introduction Isotherms, kinetics, and thermodynamics studies play an important role in thoroughly understanding the adsorption process of organic and inorganic compounds in water solutions. In the three studies, the thermodynamic adsorption is essential in consideration of the types and mechanisms of the adsorption process under variations of the solution temperature. The thermodynamics can effectively exhibit adsorption mechanisms through a series of the adsorptive equilibrium experiments under different temperatures and various initial adsorbate concentra- tions as well as fixed optimal conditions (i.e., pH of the solution, the adsorbent’s particle size, ionic strength, and solid/liquid ratio). When the adsorption phenomenon reaches equilibrium, the thermodynamic parameters can be calculated. These parameters comprise the Gibbs energy change (DG  ), the enthalpy change (DH  ), and the entropy change (DS  ). It is noticeable that the estimation of DG  , DH  , and DS  is directly affected by the thermodynamic equilibrium constant (K C ; dimensionless). In adsorption thermodynamics, the equilibrium constant K C can derive from the constants of various adsorption isotherms (i.e., Langmuir, Freundlich, Brunauer-Emmett-Teller (BET), Henry, Frumkin, Flory–Huggins, and Redlich–Petersone) or the partition coefficient. The different estimation approaches might lead to great variations in the thermodynamic parameters; therefore, the most appropriate approaches should be recommended. Several researchers presented the thermodynamic parameters of adsorption phenomena by employing the equilibrium constants derived from the constants of various adsorption isotherms or the partition coefficient. For example, Lyubchik et al. [1] compared the thermodynamic parameters of the adsorption process of the metals from liquid phase on activated carbons, estimated from the various equilibrium constants derived from the constants of Henry, Langmuir, Freundlich, and BET isotherms. Roth et al. [2] applied the constants of Langmuir isotherm, distribution (the Henry’s constant), and partition for computing the thermodynam- ic parameters of cadmium accumulation process onto different * Corresponding author. E-mail addresses: trannguyenhai2512@gmail.com, tnhai120723@yahoo.com.vn (H.N. Tran), sjyou@cycu.edu.tw (S.-J. You), hpchao@cycu.edu.tw (H.-P. Chao). http://dx.doi.org/10.1016/j.jece.2016.05.009 2213-3437/ã 2016 Elsevier Ltd. All rights reserved. Journal of Environmental Chemical Engineering 4 (2016) 2671–2682 Contents lists available at ScienceDirect Journal of Environmental Chemical Engineering journal homepage: www.else vie r.com/locat e/jece