Studying different methods to determine the thermo kinetic constants in the adsorption of Pb²⁺ on an activated carbon from Bois carré seeds

The effect of temperature on the adsorption of lead by an activated carbon from Bois carré seeds is investigated. The pseudo second order equation is applied to the kinetic data obtained at different temperatures in order to determine the adsorption rate constants at these temperatures. Then, the Arrhenius equation is applied to these rate constants to determine the activation energy of the sorption reaction and the pre-exponential factor. They are equal to 37 kJ mol^-1 and 6.1 × 10³ mol ^-1 kg s^-1, respectively. By applying the Eyring equation to the rate constants, the standard thermodynamic activation parameters of the sorption reaction can also be calculated. In addition, the isotherms of lead adsorption on the activated carbon from Bois carré seeds, at different temperatures, are determined and fitted by the Freundlich equation. The Niwas and the classical methods are applied to the equilibrium data obtained at these different temperatures in order to determine the equilibrium constants. Then, the Van't Hoff equation is applied to the equilibrium constants in order to determine the standard enthalpy of the sorption reaction. The standard sorption enthalpy is also determined using a new method suggested by the authors, the value is equal to -53.2 kJ mol^-1. The other standard thermodynamic parameters (free standard enthalpy and standard entropy) are deduced. The thermodynamic study shows that rate sorption of the activated carbon from Bois carré seeds increases with the temperature contrarily to the quantity of lead sorbed at equilibrium.