# Tempkin Isotherm Essay

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Tempkin isotherm contains a factor that explicitly takes into account adsorbing species-adsorbate interactions . This isotherm assumes that the heat of adsorption of all molecules in the layer decreases linearly with coverage due to adsorbate-adsorbate interaction and adsorption was characterized by a uniform distribution of binding energies, up to some maximum binding energy. Tempkin isotherm has generally been used in the linearized and rearranged form as following: Q_e⁡〖=β lnK_T+ β ln⁡〖C_e 〗 〗.............................6 where, KT is an equilibrium constant of binding corresponding to the maximum energy of binding (mg L-1) and the β is related to the heat of adsorption. Figure 9. shows a plot of Qe versus …show more content…
Lagergren’s first-order kinetic model
The pseudo-first-order kinetic model of Lagergren is more suitable for lower concentration of solute and its linear form is: log⁡〖(Q_e-Q_t )=log⁡〖Q_e- k_1/2.303 t〗 〗 .................................7
Where, Qt (mg g-1) is the amount of adsorbate adsorbed at time t (min); Qe (mg g-1) is the adsorption capacity in the equilibrium; k1 (min-1) is the rate constant of pseudo-first-order
The values of k2 for removal of iron by Tribulus Terrestris adsorbents was calculated from the slopes of the respective linear plots of t/Qt vs. t (Figure.10).The correlation coefficients, R2 was 0.994 for Tribulus Terrestris respectively suggest a strong relationship between the parameters and also explain that the process follows pseudo second order kinetics (Table 6 ).
Elovich kinetic model
Elovich model suggests that the chemisorptions, i.e. a chemical reaction, is probably the
Mechanism that controls the rate of adsorption. This model can be applied with success in liquid solution and the linear form of the Elovich equation is: Q_t= 1/β ln⁡αβ+ 1/β ln⁡t ..................................8
Where, α (mg g-1) is the initial sorption rate and β (g mg-1) is the desorption constant. The values of α and β can be calculated from the slope and intercept of the plot of Qt versus ln t

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