##### The equilibrium data estimated from the sorption isotherms are required to understand the mechanism of sorption

The equilibrium data estimated from the sorption isotherms are required to understand the mechanism of sorption. The experimental data were analyzed using models of Freundlich (9), Langmuir (10) and Dubinin-Radushkevich (11).

(9)

(10)

(11)

Where Qe (mg/g) is the adsorbed amount of dyes at equilibrium, Ce (mg/L) is the equilibrium concentration of dyes, Qm (mg/g) and Kl (L/mg) are Langmuir constants, and n are Freundlich constants, is the maximum amount of dyes conserved in the [email protected], ? is a constant related to the energy of transfer of dyes from the bulk aqueous solution onto the [email protected] and ? is Polanyi potential.

The relation between log Qe versus log Ce was linear with R2 values of 0.919, 0.722 and 0.991 for Br.G, To.B and Tr.B dyes, respectively (Fig.2a). The Freundlich constants (1/n) are 0.53, 0.64 and 0.49 for Br.G, To.B and Tr.B dyes which reveal a higher probability of multilayer adsorption (Nassar et el.,2012; Auta and Hameed, 2012, 2013) of Br.G, To.B and Tr.B on the active heterogeneous sites of [email protected] gives n values more than one indicates the desirable adsorption process (Table 5).

Plots of Ce/Qe vs. Ce of the experimental data according to the Langmuir model were linear with R2 values of 0.941, 0.935 and 0.908 for Br.G, Tr.B and To.B, respectively (Fig.2b). The separation factor RL was calculated according to equation (Hall, 1966) where C? is the highest initial concentration of dye, to explain the favorability of the adsorption process. The values of RL were found to be 0.016, 0.023 and 0.053 for Br.G, To.B and Tr.B. The values of RL between 0 and 1 which indicate the adsorption of Br.G, To.B and Tr.B dyes on [email protected] is a favorable process.

Table 5

The D–R isotherm represents a single uniform pore adsorption. The D–R isotherm is a general form of the Langmuir type because it does not suppose a surface was homogeneous or adsorption potential was constant (Kilislioglu and Bilgin, 2003; Ünlü and Ersoz, 2006). Plot the relation ln Q vs. ?2 (), where R is the universal gas constant (8.314×10?3 KJ./K/mol) and T is the absolute temperature in K give a straight line (R2 = 0.963, 0.936 and 0.874) for Br.G, To.B and Tr.B dyes (Fig.2c). E (KJ/mol) is the mean free energy of adsorption of one mole of the adsorbate when transferred to the surface of adsorbent (Ergene et el., 2009) was calculated with the help of equation (Hobson, 1969): . The values of E were 2.78, 2.96 and 2.39 KJ/mol, proving that adsorption was not dominated by the chemical ion exchange mechanism as E is not in the range of 8–16 KJ/mol and E smaller than 8 KJ/mol, the physical forces dominate (Rafatullah et el., 2009).