I have 2 work, one is varying concentration of heavy metal and one is varying dosage of adsorbent. How to find the absorption capacity respectively with calculations?
For varying concentration of heavy metal is it find Kf instead of absorption capacity, and for varying absorbent dose is it find absorption capacity (q) and Adsorbate concentration (Se) is it use fixed concentration.
q=KfSe^(1/n)
q: Adsorption capacity
Se: Adsorbate conc
Kf: Freundlich exponent
1/n: Freundlich slope
Hello,
if you want to determine the Freundlich maximum adsorption capacity qm , it is necessary to operate with constant initial concentration C0 and variable weights of adsorbent (Adsorbnet dose) ; thus ln (qm) is the extrapolated value of ln (q) for C=C0.
And the Freundlich exponent KF is equal to
KF =qm/(C0)1/n
where C0 is the initial concentration of the solute in the bulk solution(mg.L−1)and qm is the Freundlich maximum adsorption capacity (mg.g−1)
Finally i think that this paper will be helpful :
O. Hamdaoui, E. Naffrechoux « Modeling of adsorption isotherms of phenol and chlorophenols onto granular activated carbon Part I. Two-parameter models and equations allowing determination of thermodynamic parameters » Journal of Hazardous Materials 147 (2007) 381–394
Good Luck
Kf of Freundlich equation gives maximum adsorption capacity. Please refer adsorption paper.
No, that is the maximum adsorption capacity qm(determined by the variation of the mass of adsorbent at constant initial concentration C0) which gives KF.
The original paper is : G.D. Halsey, The role of surface heterogeneity, Adv. Catal. 4 (1952) 259–269.
I dont have the original paper but this information is referd by many others such as:
O. Hamdaoui, E. Naffrechoux « Modeling of adsorption isotherms of phenol and chlorophenols onto granular activated carbon Part I. Two-parameter models and equations allowing determination of thermodynamic parameters » Journal of Hazardous Materials 147 (2007) 381–394
Shahryari, Z., Goharrizi, A. S., & Azadi, M. (2010). Experimental study of methylene blue adsorption from aqueous solutions onto carbon nano tubes. International Journal of Water Resources and Environmental Engineering, 2147483647(2), 016-028.
Hu, X. J., Wang, J. S., Liu, Y. G., Li, X., Zeng, G. M., Bao, Z. L., ... & Long, F. (2011). Adsorption of chromium (VI) by ethylenediamine-modified cross-linked magnetic chitosan resin: isotherms, kinetics and thermodynamics. Journal of hazardous materials, 185(1), 306-314.
Baccar, R., Sarrà, M., Bouzid, J., Feki, M., & Blánquez, P. (2012). Removal of pharmaceutical compounds by activated carbon prepared from agricultural by-product. Chemical Engineering Journal, 211, 310-317.
Dear Salim Bousba,
Do you feel that Kf is not equal to qm?
Refer the below link:
http://www.unilorin.edu.ng/publications/okeolafo/FILE3%20%20LANGMUIR%20AND%20FREUNDLICH%20CF%208A-ANAS,%20DEC%202010.pdf
If by "adsorption capacity", you mean "adsorption maximum", the answer is that the Freundlich does not predict an adsorption maximum. However, the Langmuir model does include the adsorption maximum:
q = (b*K*C) / (1+K*C)
where q = concentration on the solid, C = equilibrium concentration in solution, K = a measure of the intensity of adsorption, and b = adsorption maximum.
To linearize, plot C/q on the y-axis against C on the x-axis. The slope of the equation for that linear relationship is1/b and the y-intercept will be 1/b*K. Calculate b and K from that.
you can make experiments varying the mass of adsorbent or initial concentration since in both cases the equilibrium will be achieved. Once equilibrium was attained you need make a mass balance to estimate the q value. For both systems
q= (C0-Ce)*V/m
After obtain q, it is necessary make a graph of q versus Ce and interprete the expermental data with langmuir or freundlich model to obtain the isotherms´s parameters. Thus with the matematical model you can obtain the adsorption capacity at any equilibrium concentration.
Thank you for the advice given .
you all really help me a lot
but now i have a new problem
If i want to find kf
The unit of kf = L/g
from equation KF =qm / (C0)1/n
qm = mg/g, Co =mg/l
*then if i want to apply my kf(adsorption capacity) with wastewater
where as my kf = 5 L/g
wastewater have 10 mg/l of lead, volume 100 ml of solution. Then my Question is how many adsorbent does i should use. i must use L/g. dont need to think about concentration is it ? mean i should use 0.02 g of adsorbent ?
you are wrong, the units of Kf depend of value of n. Kf = mg^(1-1/n)*L^(1/n)/g
I would just like to add that, in my opinion, you shouldn't refer to q as "adsorption capacity". This term is reserved for the maximum amount that can be adsorbed, at infinite Se. Also, Kf is the Freundlich constant, which is clearly not an exponent, and Se is the solute concentration, not adsorbate.
Salim Bousba explained very well how to estimate maximum adsorbate concentration from the parameters of the Freundlich equation. The paper he mentioned in his original post uses several equations to estimate qm. This seems to me to be the best approach, in order to best assess the most reasonable values.
If you just want to find Kf, I suggest you should just work directly with the original equation, forget about qm.
May any one help on how to fix Ce on the X-axis when plotting isotherms of different adsorbents on the same set. I seen a lot of publications having different adsorbents however, they are able to plot qe vs Ce on the same axis, how possible is this because different adsorbents attain different Ce? I have managed to calculate both Ce and qe of each of my 10 different adsorbents however, I find it difficult on how to manipulate their isotherms on the same plot since both Ce and qe are different for each adsorbent.
dear Nyiko Mauric.
simply paste one set of Ce values on the A(X)-axis in originlab and paste their respective qe values on the B(Y) axis. similarly paste the next Ce set of values on the A(X) axis (below the first Ce values), and paste their respective qe values (in front of it) on the C(Y) axis and so on. the originlab will automatically arrange the all the values in ascending order and will give you the required graph.
the attached figure may help you.
You can use this equation KF =qm/(C0)1/n as Dr Salim Bousba mentioned to estimate the Freundlich maximum adsorption capacity.
Please check the following papers:
Journal of Molecular Liquids 225 (2017) 730–740
RSC Adv., 2016, 6, 42180.
RSC Adv., 2016, 6, 84050–84067,
RSC Adv., 2016, 6, 79688–79705.
Good luck.
I am working on adsorption process.
Can we draw the freundlich isotherm at different-2 adsorbate concentration where we have fixed the dose of adsorbent.
I ma varun, working in adsorption process using an activated carbon. Can we do the adsorption study at the different-2 adsorbate where adsorbent conc. is constant
Based on Freundlich equation one can not determine the qemax value. Power function is an increasing function. Regards,
I fully agree with Grzesik, the adsorption capacity can't be obtained with the Freundlich isotherm. When you are confinced that the surface is fully occupied with at least a monolayer of adsorbate, then you could usethe BET equation. Alternatively you could try to use the Langmuir Freundlich or Sips equation, but this is a three parameter eq.
Of the four commonly used two-parameter functions: hyperbolic, exponential, logarithmic and power, only the hyperbolic and exponential functions meet boundary conditions both in zero and in infinity. The first of them is eg. the Langmuir isotherm, based on theoretical foundations and having a long tradition. The second one is sometimes called the Jovanovic isotherm, and in the case of adsorption it is difficult to find any theoretical basis. Regards,
Carry out the sorption at a constant initial concentration and various sorbent dosages for all initial concentrations used in your work (5 or 7). Apply the expression:
In qe = In Kf + 1/n In Ce
Get the Kf and 1/n values from the various initial concentrations and apply them to the equation:
In Kf = In qm - 1/n In Co
A plot of In Kf against In Co gives a straight line that gives an intercept In qm. qm (maximum adsorption capacity) can then be obtained.
It should be stressed again that the Freundlich eq. cannot be used to find the adsorption capacity.
We may write the equation as Q=Kf.C^n
Q is the measured adsorption, say in mg/g(sorbent) or mmol/g (sorbent), C the equilibrium concentration in dimensionless units (obtained using a standard state concentration)
The parameter n (dimensionless) is a non-ideality parameter accounting for interactions that are not considered explicitly ( heterogeneity, electrostatic interactions or binding stoichiometry).
The parameter Kf( same units as Q) is the product of the adsorption affinity (Ka dimensionless) and maximum adsorption (Qmax in units of Q). However, we have no information available to separate Kf into Qmax and Ka. Therefore, Qmax cannot be found without further information.
You can use Freundlich equation . The Freundlich exponent KF is equal to KF =qm/(C0)1/n
Where C0 is the initial concentration of the solute in the bulk solution (mg.L−1)and qm is the Freundlich maximum adsorption capacity (mg.g−1)
ce/qe = 1/qm KL + ce/qm , where ce is the equilibrium concentration of the adsorbate and qe is the adsorption capacity adsorbed at equilibrium, qm is maximum adsorption capacity and KL is the Langmuir adsorption constant.
Sami Guiza, Do not spread false information. Freundlich isotherm is a power function. This function has no upper limit.
At low concentration and in a well determined area we can determine qmax
The parameters in an equilibrium adsorption equation should relate to equilibrium . Therefore the use of an initial concentration in the Freundlich eq. is wrong. Just as the idea that the maximum adsorbed amount can be found.
Any advice that states this differently is WRONG.
Sami Guiza, The Freundlich equation is an empirical equation mainly used in the gas-solid system. There is no parameter in this equation that can be associated with maximum adsorption capacity. What is this "low concentration" you are writing about - initial or equilibrium? It seems that you have read something, somewhere and misinterpreted.
Nagy, M. Experimental Study of Adsorption from Dilute
Aqueous Solutions of a Nonelectrolyte: 1-Propanol on Activated
Carbon. Langmuir 1991, 7, 344−349.
Nagy, M. Study of Adsorption from Dilute Solutions:
Thermodynamic Analysis of Experimental Data. Langmuir 1994, 10,
563−569.
Nagy, M.; Siegl, Z.; Szili, K.; Fábos, V.; Kántor, K. Sorbent
Mass Variation Method: A New Possibility for the Determination of
Binding Isotherms. Langmuir 2016, 32, 6409−6418.
(25) Paria, S.; Khilar, K. C. A Review on Experimental Studies
Dear Dr. Saiy, Please read carefully this papers so you will find a well-proven answer to the problem of adsorption capacity
Best wishes: Dr.M. Nagy
Freundlich model cannot give info about maximum capacity it only tell the equilibrium constant and degree of heterogeneity. However its better to use other models like Langmuir or Elovich to estimate adsorption capacity.
Magori Nyangi Based on the value of the parameters of the empirical equation, can we conclude about the "degree of heterogeneity" and "equilibrium constant"? Where did you read it? By the way. Is Elovich equation not a logarithmic function? Is it not an increasing function? Think before you write anything.
The KF and n values of Freundlich isotherm can tell the affinity/degree of heterogeneity, I read several articles about it as long as the experimental data agree with the model equation.
To get parameters of the elovich equation then a linear equation is preferable and by that case, the functions must be logarithm, but from it the qm can also be deduced
Magori Nyangi You have read - well - a lot of crap one can read. Much worse when they are repeated. And the logarithmic function is going to what? - to infinity - so it is only suitable for local approximation. Moreover, there is no linear Elovich equation. This is another repeated rubbish.
This review paper published by Hindawi have such information, so may be it is misleading but we rely on published papers.
Magori Nyangi In a word, those who wrote this review do not really know what an empirical function is. Many do not know. You probably too. It is sad. Think it over. A lot of time ahead of you.
Thank you for a constructive info, However I am humbly requesting for a paper or any trusted reference that give a detailed description about Elovich isotherm that can be helpful to me and many other in this discussion..
Magori Nyangi It is nice that you thanked me. As for the Elovich equation, it is used to describe kinetic data, not equilibrium data. The original form is a differential equation that, when integrated, gives a logarithmic function with respect to time. This function satisfies the boundary condition at zero, but not in infinity. Hence, the interpretation of the parameters of this function for equilibrium processes is impossible.
Dear Magori, there is a difference between an equation that runs through the data like a trendline in excel and an equation that is mathematically derived from a clear physical view of what is happening. The first is an empirical model , and the second is a physical model. By using the words "empirical model", we mean any equation used that seems to fit the data. Much to the surprise of many, the Freundich isotherm is just a trendline. It has no meaning other than that is what the data looks like. There are attempts to make it more physical, but ultimately, it is a trendline. In addition to this, there is no concept of capacity in the Freundlich isotherm. As the concentration is solution increases, the amount adsorbed on the surface increases without limit. This means there is no limit to the amount adsorbed, and hence no "capacity". I hope that this answers some of your concerns, and expresses more clear what others have said above. See the equations in the reply from Luuk K Koopal . Good luck.
The Freundlich isotherm is actually an empirical power function and nothing else. The use of the term "trend line" here is, in my opinion, a misunderstanding.
You can use CHB SSSAJ spreadsheet to calculate sorption parameters. It is written by Carl H. Bolster (2007). As far as I know it free of charge. You can download from "https://www.ars.usda.gov/research/software/download/?softwareid=201&modecode=50-40-05-00#downloadForm"
Please, read paper by Sasha Jiang et al. : Langmuir, 2018 34 12802 - 12808.
Here a method is suggested and experimentally controlled to determine the adsorption capacity and other important quantities. The Freundlich tratment is simly an empirical one.
Dear Muhammad Akram
You can find some information in the enclosed article how the sorption isotherm are constructed and the estimation of their parameters. You should obtaine a plot of ln(𝐶𝑒/𝑞𝑒) versus ln 𝐶𝑒 that enables the determination of Redlich-Peterson constants, where 𝛽 is slope and 𝐴 is intercept. This is actually matter of fact obtaning the regression line and its parameters. This isotherm model has a linear dependence on concentration in the numerator and an exponential function in the denomination which altogether represent adsorption equilibrium over a wide range of concentration of adsorbate which is applicable in either homogenous or heterogeneous systems because of its versatility.
The sips model is a bitmore complicated. See J. Toth, “State equation of the solid gas interface layer,” Acta
Chimica (Academiae Scientiarum) Hungaricae, vol. 69, pp. 311–317, 1971 for better description.
Muhammad Akram There is a lot of software available where e.g. the Marquardt-Levenberg method is built in. These include Statistica, Mathlab and Origin. But it's called black boxes. They count something, but it is not known how. Learn one of the programming languages and you will free yourself from many problems. In addition, avoid R-P isotherm, because it has non-interpretable parameters and you can not use it to determine the value of the maximum adsorption capacity or equilibrium constant.
The question is, how is it possible that many people think otherwise, that is, that this quantity can be determined using the Freundlich isotherm?
Please, read paper by Sasha Jiang et al. : Langmuir, 2018 34 12802 - 12808.
Here a method is suggested and experimentally controlled to determine the adsorption capacity and other important quantities. The Freundlich tratment is simply an empirical one.
Solution of the so-called inverse the problem for a power function (Freundlich isotherm) is a deceptively simple task. Both lumped parameters are numerically correlated and their value is also affected by the measure of fit used.
If the adsorbed mass could increase to infinity then the use of the Freundlich isotherm would be justified. Since this is impossible, the Freundich isotherm, i.e. a power function, can only be used for local approximation of equilibrium curve.
As far as I am correct, the question is about the Freundlich isotherm, and not Langmuir one.
Dear Sand Saiy, you must know that One cant predict maximum adsorption capacity on the basis of Freundlich model. For that mostly we use Langmuir model to calculated tested material maximum adsorption capacity.
Yes, totally agree with you Mirosław Grzesik, as the question is about Langmuir rather than Freundlich.
I will write again. The question concerns the possibility of using the Freundlich isotherm to estimate the value of the maximum adsorption capaciy, which is impossible. Instead of an increasing function, which is a power function, it is better to use a non-decreasing function, e.g. an exponential (Jovanovic isotherm) or a hyperbolic (Langmuir isotherm) function. Composition of hyperbolic and power functions (L-F isotherm) can also be used, but only for local approximation, due to the inflection point.
