Good Morning all. Please i'm currently working on adsorption of heavy metals (Pb, Cr, Cd & Ni) by activated carbons derived from local plants. I have tested the effects of Contact time, adsorbent dose, pH and initial concentrations and have evaluated the Qe and %Removal for all the parameters. Now, i am at the stage of using isotherms (Langmuir and Freundlich). Since the Langmuir isotherm involves the plot of Ce/qe Vs. Ce, which of the Ce/Qe will i use in this case? (I have Ce/Qe for contact time, adsorbent dose, pH and initial concentrations)
Linearization of non-linear Langmuir equation will result in four different types (I, II, III and IV) of linear equations. But I can see that you are within the context of the Langmuir I plot.....use the Ce/We for initial concentrations.....You may jog through the article "Adsorption of Malachite green dye using orange peel" to guide you through the isotherms
You can use CAVS - adsorption evaluation to perform all regressions (Kinetcis, Isotherm and Fixed-bed).
The program uses non-linear regression, which is far more better than linear regression, and the equations are ready to be use.
The software is FREE to be used.
check the software here: http://bit.ly/CAVS_tutorials
You have so much data that you do not have to succumb to the so-called standards or nonsense of Ho and McKay. Just try to describe several kinetic curves together for different Co, not seperately. This way you can get ka, kd (rate constants) and mmax instead of some numbers k1 (PFO), k2 (PSO) etc.. No description of equilibrium data will be needed.
Babakura Babagana, You can have Ce/Qe for different pH, adsorbent dose, initial concentrations. You can not have it for contact time. Remove "contact time" and it will be OK.
Kingsley O. Iwuozor, Neither type I (L-B transformation) nor type II (H-W transformation) nor other types are linear functions. They are actually implicit forms of hyperbolic function. Read about linearization in any textbook on mathematics, and on this occasion you will recall Taylor's theorem.
Laith A. Naji thank you for your detailed answer, may I just ask, when you explain the Langmuir equation (A) step 2, do you mean draw a line from the Y-Axis at x=o and connect it to the point of Ce on the X-Axis at y=o as I am slightly confused how you will obtain the gradient/slope (m) from just 2 points without having the remaining parameters for the equation?
Dear Babakura Babagana
These kind of confusions come when you use the linearized isotherm equations which is misleading and errorsome. It can be learn from following manuscripts: Bioresource Technology 98 (2007) 1812–1821; Journal of Hazardous Materials 147 (2007) 381–394.
I recommend you to use the nonlinear curve fitting. Based on that calculate the R2 values which will help you to identify the good-fitting isotherm. I recommend you to refer the following articles for better clarification:
Balasubramani, K., N. Sivarajasekar, and Mu Naushad. "Effective adsorption of antidiabetic pharmaceutical (metformin) from aqueous medium using graphene oxide nanoparticles: Equilibrium and statistical modelling." Journal of Molecular Liquids 301 (2020): 112426.
Article Adsorption of Basic Magenta II onto H2SO4 activated immature...
Sivarajasekar, N., and R. Baskar. "Adsorption of basic red 9 on activated waste Gossypium hirsutum seeds: process modeling, analysis and optimization using statistical design." Journal of Industrial and Engineering Chemistry 20.5 (2014): 2699-2709.
Article Adsorption of basic red 9 onto activated carbon derived from...
I advise you to use the Langmuir and Freundlish equations in nonlinear forms. because the non-linear form reflects reality. however these models are very classic, in this last decade we use physical models for exemple see theses papers:
RSC advances 6(72), 67701-67714 (2016).;
Materials Chemistry and Physics 225, 111-121 (2019). ;
Sellaoui, L., Dotto, G.L., Lamine, A.B., Erto, A.: Interpretation of single and competitive adsorption of cadmium and zinc on activated carbon using monolayer and exclusive extended monolayer models. Environmental Science and Pollution Research 24(24), 19902-19908 (2017). etc.....
pls go through,
- Industrial & Engineering Chemistry Research 53(44):17454. DOI: 10.1021/ie502673m.
- Kinetics, thermodynamics and ion exchange characteristics of thorium phosphate: An inorganic ion exchanger . Indian J of Chemistry A 2014.
Hi. Choose the optimum pH and plot langmuir and freundlich at different initial concentrations.
I recommend you use Non-linear regression method as it gives a more accurate result than using Linear regression. You can as well use MS Excel SOLVER for the regression analysis. You need to use the non-linear Equations for the Models. Read through the attached paper.
As if it could be otherwise. Asif Ayub presents on RG, once again, links to commercial software presentations. I wonder if the recommenders of these posts actually get acquainted with these presentations.
Miroslaw it seems nonsense to criticize without logic. If u have better and logical alternative u should present people will follow that and will not recommend if these links are worthless. I often ignore your post because your post are not worthy to be replied. Hope next time you will be careful and will focus on your own job and will help researcher in a little better way.
Asif Ayub, You think RG is the right place to advertise commercial software, I don't think it is. So let it stay that way. I would like to add that combining graphical methods with calculating R2 on the basis of nonlinearly converted data and a straight line matched to them, may falsify the results, especially the conclusions drawn on their basis. If you believe that you are helping others by spreading such approach, I have my doubts.
You will use the qe, Ce from effect of contact time for the kinetics i.e. pseudo first order or pseudo second order kinetics order, while the effect of initial concentrations is use for the types of adsorption isotherms i.e. Langmuir, Freundlich isotherms. Thanks, my little submission.
These videos can answer your questions: https://www.youtube.com/channel/UC5MiS3nMoji95OZ7uE1V8qw/playlists?view=50&sort=dd&shelf_id=6
I don't know which time to repeat it. The equilibrium value, qe and the maximum value, qm do not depend on the contact time and time. Moreover, qm is independent of Ce. It's a material constant. Do not mislead the readers of the RG commentary.
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