Tests for the Validity of Different Models Used for the Adsorption of Solutes on Activated Carbon
Analysis of the results of adsorption from aqueous liquid media onto activated carbon can be carried out by different models based on thermodynamic principles. Classically the Langmuir (eq. 1), Freundlich or Elovich (eq. 4) isotherms are used, which lead to the determination of an experimental maximum capacity, qm, and a constant K, characteristic of the adsorbate-adsorbent interactions. The following equations (Table I) have been transposed from the vapour phase to the liquid phase. With the Temkin relation: [Theta]=RT/[Delta]QlnK[inf]0C (eq. 6), it is possible to determine the variation of adsorption energy, [Delta]Q, between the adsorbed molecules and the solid phase, and the equilibrium constant K[inf]0 ([Theta] is the degree of surface covering of the solid phase [Theta]=q/qm, q is the adsorption capacity). The Fowler-Guggenheim equation: KC=[[Theta]/(1-[Theta])] Exp (2[Theta]W/RT) (eq. 7) gives the interaction energy, W, between the adsorbed molecules and an equilibrium constant, K. The Hill and De Boer relation: K[inf]1C=[Theta]/(1-[Theta])] Exp [[Theta]/(1-[Theta]) -K[inf]2[Theta]/RT] (eq. 8) yields an energetic interaction constant K[inf]2 (J.mol-1) characteristic of the interactions between the adsorbate molecules and an equilibrium constant, K[inf]1. In the Kiselev relation: K[inf]1C=([Theta]/[(1-[Theta]) (1 + K[inf]n[Theta]] (eq. 9), K[inf]n is a complex formation constant between adsorbed molecules and K[inf]1 is a constant relative to the adsorbate-adsorbent interaction. Linearization of the equations of Langmuir, and Elovich leads to qm and K values. For the Freundlich relation, if the experiments are made at constant Co and variable concentrations of adsorbent, the Freundlich relation can be transformed as relation (5): q=qm (C/Co)[sup]1/n). The value of qm and K are reported in the Table II. When the values obtained by the Elovich equation are very different from the Langmuir relation, they are not in concordance with the experimental adsorption isotherm as shown on the Figures 4, 5 and 6. A value of qm is necessary to calculate the ([Theta](=q/qm) of the Temkin, Hill-De Boer, Fowler- Guggenheim and Kiselev equations; [Theta] is calculated with the Langmuir value of qm: the linearized relations were tested for the following compounds: phenol, aniline, nitrobenzene, salicylic acid, 4-nitro phenol, 2-methyl-4,6 dinitro phenol, phenylalanine and tyrosine, studied at micromolar concentration. The results are shown in Table II. The Temkin linearization is of good quality for all the compounds; an example is given on the Figure 1. For the others (Figs. 2, 3), the linearization is not always verified (Hill-De Boer for phenylalanine: Fig. 3a) and the results are framed two times in the Table II. With the obtention of the two parameters [Delta][Theta], K K, W; K[inf]1, K[inf]2 and K[inf]1, K[inf]n, the isotherm can be recalculated. The results for some solutes are on Figures 4, 5, 6, 7, 8. Relatively poor results are obtained for Fowler-Guggenheim, Kiselev or Hill-De Boer models, where no association is present between the adsorbed molecules. The evolution of the variation of the adsorption energy ([Delta][Theta]) is reported on the Figure 9 for the different compounds. The greatest values are obtained for nitrobenzene and 4-nitro-phenol (+ 80, + 40 kJ.mol-1 probably due to the presence of the nitro group). All the values are positive (exothermic reaction ( [Delta][Theta]=-[Delta]H)) showing the affinity of molecules for the activated carbon.