For my adsorption system I need to calculate thermodynamic parameters. For the study I used 3 equations
1. ∆G = −RT lnb (b is the Langmuir isotherm constant)
2. ∆G = ∆H −T∆S
3. ln b=- (∆H/RT)+(∆S/R)
When I plot the graph of ln b Vs 1/T. I got a positive gradient and a negative intercept. Giving a negative ∆H, ∆G, and negative ∆S.
Is it possible to have such values and a graph and is the graph acceptable with a positive gradient?.
Dear Rasika,
∆G = ∆H −T∆S ; I suggest that you plot the ∆G values versus the T values. In this case the slope of the line will give the value of ∆S and the intercept will give the ∆H value.
You can get the values of ∆G, to be used in the plot, from the following equation:
∆G = −RT lnKa
Generally in adsorption isotherms, the values for ∆H and ∆S are positive, whereas that for ∆G can be negative.
An example for such calculations is contained in the following link:
http://dns2.asia.edu.tw/~ysho/Water%20Research%20Centre/Publications/PDF/Fre%20Env%20Bul19,%202651.pdf
Hoping this will be helpful,
Rafik
Dear Mr. Rasika Eranda,
Thermodynamic study on adsorption is interesting one and it enables us to find whether the particular adsorption process is physical or chemical, spontaneous or non-spontaneous and also exothermic or endothermic.
The effect of temperature on the adsorption process is to be first analysed. The values of Gibbs free energy (ΔG°) for various temperatures can be calculated from the experimental data. The values of enthalpy change (ΔH°) and entropy change (ΔS°) can be estimated from the slope and intercept of the plot between ln KD and 1/T (where KD is distribution coefficient and T is absolute temperature).
From these thermodynamic parameters, we can determine thermodynamic feasibility, spontaneity and thermal effects of sorption.
I have herewith attached one of my research articles which is a thermodynamic study on adsorption. Hope you will get a clear idea to calculate various thermodynamic parameters.
Best wishes!
The fact that you get ∆H < 0 means that your adsorption is exothermic. This is the most common case - exothermic are, e.g., the adsorption of most gases onto a solid,the adsorption of surfactant dissolved in the oil at the water|oil interface etc. ∆H < 0 might not be the case for surfactant dissolved in the water adsorbing at water|gas (which is driven by entropy).
The fact that you get negative negative ∆G and ∆S means almost nothing, because the sign of these quantities depends on the choice of standard state in the bulk and at the surface. This is related to the fact that the adsorption constant under the logarithm is not dimensionless - i.e. lnb (and ∆G) will be positive if b is in angstroms and negative if b is in meters. If you want to say something more definite about ∆G and ∆S, you need to introduce a model for b, e.g., separate it into adsorption length and adsorption energy. An example with non-ionic surfactants:
https://www.researchgate.net/publication/259237417_Cohesive_and_Non-cohesive_Adsorption_of_Surfactants_at_Liquid_Interfaces
An example with ionic surfactants:
https://www.researchgate.net/publication/257942049_Ionic_surfactants_and_ion-specific_effects_adsorption_micellization_thin_liquid_films .
Chapter Cohesive and Non-cohesive Adsorption of Surfactants at Liqui...
Chapter Ionic surfactants and ion-specific effects: adsorption, mice...
Thank you very much for your help.
Dear Dr Radomir,
When we use ∆G = ∆H −T∆S and ln b=- (∆H/RT)+(∆S/R) slop/gradient should be negative but in my graph, the gradient is positive. Is it acceptable?
If you plot lnb vs. 1/T, and the slope -∆H/R is positive, it means ∆H < 0 - exothermic adsorption. It is not only acceptable, it is the usual case. You may worry if you consider a system that is a known case of endothermic adsorption, e.g., surfactants adsorbing from water solution to water|air surface.
The kind of a reaction whether it is exothermic or endothermic depends on the value of ∆G and NOT ∆H:
∆G < 0, Exothermic Reaction
∆G > 0, Endothermic Reaction
Rafik
Dear Radomir,
You are right. The right names are as follows:
∆G < 0, Exergonic reaction
∆G > 0, Endergonic reaction
Rafik
The chemical adsorption is a exothermic process, well DH is negative. The molecule when is free its entropy is a positve numbre, when the same molecule is adsorpbed its entropy is still positive but lower, well the change of entropy is negative, but the total entropy valoration includes the exothermic heat/T of sorrounders.
The following articles introduce the most correct manner for calculation of thermodynamic parameters and contain valuable explanations about this subject.
Journal of Molecular Liquids Volume 273, January 2019, Pages 425-434; Journal of Molecular Liquids Volume 280, 15 April 2019, Pages 298-300
Hello everyone,
Thank you for this precious informations. I would like to know how do we calculate the distribution coefficient KD because in some articles they just replace it with kL or kF depending on which model fits better the results of the experiment.
So can somebody clarify this to me.
Asif Ayub Your links are useful, thanks. Do you have a link or any reference to calculate the Thermodynamic parameters of GAS capture? KL?
@asif ayub , Your you tube links are very much informative.
You have calculated the value of K(L) by using the following formula.i.e. qe/ce..but in many recently published literatures, it was shown that it is a wrong way of calculating K(L).
I am confused why in some literature people are following Liu adsorption isotherm in place of Langmuir.
Though I have calculated the Kl as u have explained in your link. But confused whether it is a right way or not?
To all. There is no problem with the appropriate equations, by the way, known from the beginning of the last century, as well as with calculation algorithms. The problem is to determine reliable values of the equilibrium constants for different temperatures, and what is important, dimensionless. Without it, no plausible values for the state functions are possible.
This video shows how to calculate thermodynamic parameters (Enthalpy, Entropy and Gibb's free energy change) in adsorption process using OriginPro easily! #aminulcheminnovation #AminulSir #aminulchem #DrMdAminulIslam
https://youtu.be/g6t_Ze5tCAM
This video shows how to interpret thermodynamic parameters △G°, △H°, and △S° from experimental data. #aminulcheminnovation #AminulSir #aminulchem #DrMdAminulIslam #DMAI #MAI
https://youtu.be/LGuDshiNOmQ