The kinetic data used further to know the slowness of adsorption step according to Bangham model (Nowak and Bangham, 1996). The double logarithmic plots against time doesn’t give perfect line with a correlation coefficient (R2= 0.69, 0.74 and 0.77) for sorption of Br.G, To.B and Tr.B dyes onto [email protected], respectively (Fig.1CS). This means that the film diffusion is not the sole rate-controlling step. The values of ? (Table 3) are 0.47, 0.55 and 0.40 for Br.G, To.B and Tr.B dyes which means ? value independent of the dye size.
The plot of Bt versus t is straight line do not pass through the origin (Fig.1DS) proving that mass transfer is involved the values of the effective diffusion coefficient (Di) by plot F VS. t0.5 1/2.The results show that Di values are 8.74 ×10-7, 1.15 ×10-7 and 1.36 ×10-7 cm/min for Br.G, To.B and Tr.B dyes, respectively and it is independent of the size of the dyes
Table 4 shows the kinetic parameters of pseudo first order (7) and pseudo second order (8) studies for the sorption of Br.G, To.B and Tr.B onto [email protected]
By checking R2 for three dyes (Fig.1ES and 1FS), we found that sorption of three dyes followed a pseudo second model (0.956, 0.933 and 0.991) rather than pseudo first order (0.369, 0.434 and 0.669) (Table 4) that means the pseudo second order is dominated which prove that rate limiting step may be chemical adsorption means chemisorption reaction which involves valence forces by sharing or electron exchange between the adsorbate and the adsorbent (Wang and Aiqin, 2008). The values of the rate constant of the sorption (k2), calculated from the slopes, are 0.28, 0.16 and 0.17 g/ mg/ min. The Half-life time (t1/2) of sorption for second order which it depends on the concentration and this time used to characterize how fast the reaction occurs, calculated by the following equations: (t1/2 = 1/ (k2 C?), t1/2 = 0.30 , 0.50 and 0.48 min for Br.G , To.B and Tr.B dyes. The initial rate constant (h = K2 Qe2) of Br.G, To.B and Tr.B dyes are 2.99, 2.09 and 1.94 min g/mg.