The spontaneity of the Cr(VI) adsorption was evaluated from the Gibbs free energy change ([DELTA][G.sup.0]), calculated at equilibrium conditions as
The negative values of the Gibbs free energy change confirm the feasibility and the spontaneity of the Cr(VI) adsorption.
[DELTA]G denotes the Gibbs free energy change, and [DELTA]G = [DELTA]H - T[DELTA]S.
Table 1 elaborates the standard Gibbs free energy change when using glucose as the fermentation substrate and bacteria for hydrolysis, acid production, and fermentation [20, 21].
From Table-1, it also can be clearly seen that enthalpy change at high-affinity sites H1 is - 10.88 kJ/mol and that at low-affinity sites H2 is - 60.49 kJ/mol; Gibbs free energy change
at high- affinity sites G1 is -30.97 kJ/mol and that at low- affinity sites G2 is -20.42 kJ/mol.
hermodynamic parameters consisting of Gibbs free energy change
([DELTA][G.sup.[omicron]]), enthalpy change ([DELTA][H.sup.[omicron]]), and entropy change ([DELTA][S.sup.[omicron]]) were calculated from the following equation: