In batch study, langmuir isotherm parameters can be calculated by a plot between 1/qe vs 1/Ce, what changes in the procedure occur when we do the same calculation for fixed bed column where we have data at various time..do we have to generate the data for different concentration until they reach to the breakthrough time?
Isotherms are generated from equilibrium studies. When you have a fixed bed columns study, it is a flow system and changes with time become zero under steady state and not due to equilibrium condicitons necessarily. So what you have is a kinetic study. Now, if the kinetics is adsorption is equilibrium controlled, then one may be able to extract Langmuir parameters if it follows Langmuir kinetics, which it may or may not.
I have a note to add to the statement from @K Mondal. A reaction step is either at equilibrium or it is not. In the former case, a different reaction step controls the kinetics of the process. In the latter case, a different reaction step may or the given reaction step may control the kinetics of the process. IOW, Langmuir isotherms are NOT kinetic models, they are equilibrium models, as you rightly state in your first sentence.
To determine kinetic parameters from reactor systems, you must first establish the reactions to model the chemistry. This is an exercise equivalent to what is done in a first year general chemistry course. Then, you must convolve the kinetic equations for the reactions on to an equation of the reactor itself (fixed bed or CSTR for example). This is an exercise equivalent to what is done in a senior-level chemical engineering reactor design course.
In reality it is very difficult and not very common for anyone to thoroughly examine the catalyst surface under actual reaction conditions. Langmuir-like kinetic expressions are usually just a more sophisticated curve fit that is used when kinetics fail to fit inerger or half integer order very well. If you get new data outside of the range of the original data and it fits you can feel good about the model and it may even be correct - or it could just be a good curve fit. There are many reaction systems that have been studied thoughly (like Fischer-Tropsch) that have many different kinetic models that fit the data pretty well. If you get additional information outside of the original data set that doesn't fit and is reproducible you may need to amend your model.
It is possible to determine the equilibrium adsorption isotherm from breakthrough curves experiment but indeed, you will need experiment for each concentration. And you can do that regardless the kinetics of the adsorption.
Knowing the molar input flow (Q_mol), you have to determine the time it takes to fully saturate your column. You have to integrate (1-C/Ce) to determine this time T_b (see http://facstaff.cbu.edu/rprice/lectures/adsorb.html). Finally, you divide by the mass of adsorbent in your column (m_ads).
qe = Q_mol x T_b / m_ads
Sebastien,
Yes I agree. It can be done. But usually it isn't because it is difficult and it isn't necessary if all you want is a good data fit of kinetic data. A research scientist might do this in order to get a better understanding of the fundamental science but it is a dfficult task and it may have to be repeated many times as conditions change and catalyst ages.
Dear Rick,
I agree, usually, adsorbed amount are measured by equilibrium methods and breakthrough curves are used to study the kinetics of the adsorption. However, it is a good way to check if the breakthrough curves are consistent with the isotherms.
Regards
Sebastian
I have to disagree . The qe value you obtain is that of the amount adsorbedand is the bed capacity and I do not have any arguments there except that one has to consider diffusion characteristics to determine the true bed capacity. Secondly, once breakthrough occurs, what is the value of the equilibrium concentration to be used for plotting the isotherm?
Jeffrey
I completely I agree with you and my response was not meant to overlook these finer aspects. Thanks for your addition.
Kanchan has raised two very valid questions above. The composite Ce may be an approximation. Otherwise if all you want is to use conventional thinking you will require a circular system where the composite solution (Ce) is channeled back to the column bed until you get uniform Ce.
- Badges
- Science topic
- Similar topics
- Analytical Chemistry
- Column