where, ΔG is standard free energy change, R is universal gas constant, T is temperature in Kelvin. From the thermodynamics, KD can be equal to apparent equilibrium constant (KD) at infinite dilute condition. Therefore, KD can be obtained by calculating KD at a different temperature and initial metal concentration and extrapolating to zero. Also, if the reasonable fit obtained with the Langmuir isotherm, the Langmuir equation constants can be used to calculate the Gibbs free energy change by the following equation:
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