 # Langmuir Isotherm Essay

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Langmuir isotherm
The Langmuir adsorption model is established on the following hypotheses: (1) uniformly energetic adsorption sites, (2) monolayer coverage, and (3) no lateral interaction between adsorbed molecules . A mathematical expression of the Langmuir isotherm is given by the following equation:
Where qe (mg/g) is the amount of dye adsorbed on the solid adsorbent at equilibrium, qm (mg/g) is the maximum adsorption capacity, KL (L/mg) is the Langmuir equilibrium constant, and Ce (mg/L) is the EBT dye concentration at equilibrium. The essential characteristic of the Langmuir isotherm can be expressed by the dimensionless constant called equilibrium parameter, RL, defined by:
Where C0 is the initial EBT
Figure 8 shows the plot of Freundlich isotherm for EBT dye onto P – PAN and C – PAN adsorbents showing an acceptable linearity straight line. Values of n parameter are 1.7 for P – PAN and 2.22 for C – PAN suggesting values of 1/n comprised between 0 and 1 indicating a favorable adsorption of EBT dye onto both dyes.
Tempkin isotherm
Tempkin considered the effects of some indirect adsorbate/adsorbate interactions on adsorption isotherms and suggested that because of these interactions the heat of adsorption of all the molecules in the layer would decrease linearly with coverage. The Tempkin equation is given as described in the reference .
Where:
A plot of qe versus Ln (Ce) enables the determination of the isotherm constants BT and KT from the slope and the intercept, respectively. KT is the equilibrium binding constant (L/mol) corresponding to the maximum binding energy and constant BT is related to the heat of adsorption.
The isotherm constants of each model were calculated and presented in Table 2. Examination of the linear isotherm parameters show that the correlation coefficients (R2) obtained from the Freundlich isotherm model were higher in comparison with the others
The parameter KC can be calculated using the following equation as described in the reference :
Where Ce is the equilibrium EBT dye concentration on the adsorbent (mg/L) and qe is the solid phase concentration (mg/g).
The values of ΔH0 and ΔS0 were calculated from the slope of the linear plot of Ln (KC) versus 1/T (see Figure 9) and the free energy change ΔG0 was calculated at different temperatures and are given in Table 3.
We consider firstly the adsorption of EBT dye onto P – PAN adsorbent, the negative values of ΔG0 has decreased from - 2.72 to -7.48 kJ/mol with an increase in temperature from 298 K to 328 K. This behavior indicated that the spontaneous nature of adsorption and favorable at higher temperatures. In the other hand, the positive value of ΔH0 (44.514 kJ/mol) suggest that the process was endothermic nature. While the positive value of ΔS0 (158.51 J/mol K) indicating the entropy of the system increased during the

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