As we all know that Langmuir adsorption isotherm is plotted by Ce/Qe Vs Ce and also some time 1/Qe Vs 1/Ce. (where “Qe” is the quantity of the adsorbed adsorbate at the time of equilibrium and “Ce” is the concentration of adsorbate remained at the time of equilibrium). what is the difference between these two? Also Freundlich adsorption isotherm is plotted as Log Qe Vs Log Ce.
Now when we apply function Log to Qe and Ce, we get plot of Freundlich and when we take reciprocal of both Qe and Ce (1/Qe and 1/Ce), then we get plot of Langmuir isotherm. so how does these two thing makes it different.
As in one case reciprocal of Qe and Ce is taken and in other case Log is applied, so how we expect linearity of spectra to be different ?
(You can take some random data, say one as Qe and other as Ce, then in one case apply reciprocal to both and in other apply Log to both. now plot both separately and compare the shape (linear or non linear), isn't it the same ?
You can easily draw both isotherms using origin pro software and selecting rectangular hyperbola and allometric function for Langmuir and Freundlich isotherm respectively.
The differences are determined by the fact that Langmuir isotherm model is a polynomial equation, while the Freundlich isotherm model is a logaritmic equation. Cannot be plotted together. But, it can be calculated qe values form both isotherm models and overlapped with the experimental isotherm.
Concerning the differences I would like to expand L. Bulagriu's answer a little:
1)The shape is mathematically different right from the beginning:
Langmuir: Kp=Q/(1-Q)
Freundlich: Kp^(1/n)=x/m
2)Freundlich is a purely empirical power series approach while Langmuir can be derived both from kinetics and from statistical thermodynamics (for the latter see Desjonqueres/Spanjaard, Concepts in surface physics, Chapter 6). Thus the applicability range of Langmuir is often somewhat larger than Freundlich, but once you get multilayers, both will fail.
The langmuir isotherm model is expressed in generalized and linear form as follws
qe=abCe/(a+bCe)
1/qe=1/a+1/abCe
Langmuir isotherm is plotted with 1/qe vs1/Ce
Where,
qe quantity fluoride adsorbed (mg/g)
Ce equilibrium concentration (mg/l)
Freundlich isotherm equation in generalized form and linear form is expressed as given:
qe=kf (ce)1/n
logqe=logkf+1/n(log Ce)
Freundlich isotherm is plotted with log qe vs log Ce
The langmuir isotherm model is expressed in generalized and linear form as follws
qe=abCe/(a+bCe)
1/qe=1/a+1/abCe
Langmuir isotherm is plotted with 1/qe vs1/Ce
Where,
qe quantity fluoride adsorbed (mg/g)
Ce equilibrium concentration (mg/l)
Freundlich isotherm equation in generalized form and linear form is expressed as given:
qe=kf (ce)1/n
logqe=logkf+1/n(log Ce)
Freundlich isotherm is plotted with log qe vs log Ce
Hi Ahlem, in the representation I wrote down both sides of the equation are dimensionless. Therefore, K has to "compensate" the pressure unit so it would be Pa^n.
Thanks prof Laura Bulgariu and prof. Jürgen Weippert for the explanation.
Langmuir isotherm model:
Monolayer adsorption taking place on homogenous sites
qe = (Qo *KL*Ce) / (1+KL*Ce)
Linearized form of Langmuir isotherm model (Y = mX + C):
1/qe = 1/(Qo *KL) * 1/Ce + 1/Qo
Where,
qe = equilibrium adsorption capacity (mg/g)
Ce = equilibrium concentration (mg/L)
Qo = adsorption capacity predicted by Langmuir model (mg/g)
KL = Langmuir constant
Plot a graph of 1/qe vs 1/Ce
Slope (m) gives KL
Intercept(C) gives Qo
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Freundlich isotherm model:
Multilayer adsorption taking place on heterogenous sites
qe = KF * Ce1/n
Linearized form of Freundlich isotherm model (Y = mX + C):
ln qe = 1/n * ln Ce + ln KF
Where,
qe = equilibrium adsorption capacity (mg/g)
Ce = equilibrium concentration (mg/L)
KF and n are Freundlich constants
Plot a graph of ln qe vs ln Ce
Slope (m) gives n
Intercept(C) gives KF
For more information regarding other isotherm models refer:
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U can plot both of them and both of them are linear plot. But if the R2 be higher the isotherm is fitted better than the other. If langmuier be fitted a mono layer formed but if freundlich be fitted a complex layer formed.
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