# Freundlich And Langmuir: An Analysis Of Absorption Isotherm Models

Langmuir Isotherm

Lamgmuir model is suitable for studying the monolayer adsorption, because the process is take place at homogeneous sites. Constant

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The Freundlich model can be expressed as [8]:

.................................................................................................... (6)

where qe mass of adsorbate is adsorbed per unit mass of adsorbent (mg/g), Ce is the equilibrium concentration of adsorbate (mg/l), Kf indicates adsorption capacity and n an intensity factor of the adsorption process , which varies with the heterogeneity of the adsorbent. The adsorption is better favorability when 1/n is to be grater. The fractional values of 1/n ranged between 0 and 1. The constants Kf and 1/n were calculated from the intercept and slope of the plot of ln qe versus ln Ce. Fig.10 shows the linear plot of Freundlich isotherm for adsorption of CV and MB onto fennel seeds. The calculated parameters are shown in table 2. The Freundlich isotherm model was found best fitted with experimental data as the value of R2 equal to 0.992 and 0.993 for CV and MB, table 2. Kf is a Freundlich constant that shows the adsorption capacity on heterogeneous sites level. The adsorption intensity given by the Freundlich coefficient (1/n) is smaller than unit indicating the favorable adsorption . These results indicate the Freundlich equation represents a better fit than Langmuir for CV and MB. The Langmuir equation is shown a homogeneous adsorption, while Freundlich equations is demonstrated a heterogeneous adsorption. The correlation

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the value of R2 is the indicator for the successful of the process. Whereas, R2 values are close to 1, high value, the best adsorption process[20,21]. The Pseudo first order is given in equation:. ......................................................................................(7)

Where

qe CV or MB amount that adsorbed onto unit weight of adsorbent at equilibrium (mg/gm). qt CV or MB amount that adsorbed onto unit weight of adsorbent at any time t (mg/g)

K1 is the rate constant for pseudo-first-order model (L/min).

The value of qe and K1 were found from slope and intercept of linear relation between log (qe- qt) with t at the given concentrations. The straight line between log (qe- qt) and the time emphasize the applicability of the equation (7) , fig. (11).

The pseudo second-order is given in equation: ........................................................................................................(8)

Where:

qe CV or MB amount that adsorbed onto unit weight of adsorbent at equilibrium (mg/gm). qt CV or MB amount that adsorbed onto unit weight of adsorbent at any time t