I am doing adsorption isotherm studies. I have carried out kinetic modeling with Ce and qe values. However I am stuck in equilibrium studies. I have conducted the experiment for a run of 24 h, which is my equilibrium study time. How do I get the data for making the graph? Are we supposed to use the same data for Ce and qe for experimental study which we used for kinetic study?
Ce you can measure by an appropiate methode for metal e.g. ICP-OES, for mircopollutants HPCL.
Qe you can measure in case of metals after digestation of the adsorbent, and calculate that from the found concentraion.
Or you calculate Cstart - Ceq = Cadsorbed on adsorbent, now be sure that you know the volume, so that you can calculate to total amount of adsorbate. The total amount of adsorbate you divide by the amount of adsorbent.
If you do a kinetic analysis be sure that you collect enough data from the start of the reaction, if adsorption is fast, it could happend that you have near equilibrium data measured and this leads to a wrong conclusion on the kinetic model. The kinetic models have a big difference in the beginning.
An other point which you should keep in mind is the structure of your adsorbent, does the structure gives the the controling factor for the kinetic? If you got a porous systems the diffision to the adsorption sites will control the kinetic, due to the fact that is the slowest step. A chemisorption is a fast process.
If you look to the isotherm, you take a samples normally after the equilibrium is reached, which is mainyl after 24 h, in this case you change the starting concentration.
Ce is equivalente to the final concentration measured from your equilibrium test (after 24 h, or even more). Also you need to measure the initial concentration (Co).
with the mass balance qe = V*(Co - Ce)/m
qe in the y-axis
Ce in the x-axis
After that, you may try to fit the experimental data to the langmuir or freundlich model. This will tell you more about the physical interaction that is carried out.
Regards
The gas phase of adsorbate (c) needs to traverse a film around the particle where the mass transport is characterized by the film transfer coefficient (kf). At this point, the gas phase is in the particle (cp). This gas phase will diffuse (De) inside the particle until it contacts the surface of the particle (cp*). A certain amount of the adsorbate will be adsorbed on the surface (q). Each concentration (cp*) corresponds to an amount adsorbed (q) and each concentration (cp) is at amount equilibrium (qe). If you assume that these resistances are negligible (kf and De), so (c) arrives in an instantaneous way as (cp). This (cp) corresponds to an amount at equilibrium (qe). To establish the amount at equilibrium (qe), an infinite time is needed, which is supposed to be after 24h.
This video shows how to calculate Ce and qe in adsorption isotherm study easily: https://youtu.be/rdj058lMyHU