Hi, there are questions about applying the Langmuir equation for gas adsorption.
In one sentence, I wonder if it is okay to use C as the amount of gas supplied in the Langmuir equation.
q=q_sat * (KC/(1+KC))
Additional explanations are provided below.
When a certain concentration of gas is flowing, the amount of adsorbed gas is calculated.
The x-axis was set as the amount of gas supplied over time, and the y-axis was set as the total amount of adsorbed gas.
For example, if the gas concentration is set to 10 ppm at a flow rate of 10 liters per minute, it can be said that 0.1 ml of gas is supplied per minute.
The gas concentration after adsorption was measured every minute and converted into volume.
Therefore, the amount of adsorbed gas can be calculated with respect to the amount of supplied gas, and this is intended to be fitted to the Langmuir equation.
q=q_sat * (KC/(1+KC))
C is the concentration of applied gas. Here, 0.1 ml of gas is provided per minute, so the x values are 0.1, 0.2, 0.3, ... etc.
The q value is the total amount of adsorbed gas. If the gas concentration after adsorption is measured every minute, 47 ppm, 48 ppm, 49 ppm are measured, it is adsorbed by 3 ppm, 2 ppm, and 1 ppm.
Converting this to volume, 0.03 ml, 0.02 ml, and 0.01 ml each adsorbed.
Therefore, the total amount of adsorbed gas can be considered as 0.03 ml, 0.05 ml, and 0.06 ml.
Is it okay to fit these x and q values into the Langmuir equation?
I don't know the words that I want to say have been completely delivered because of my insufficient English skills.
Thanks for reading.
My impression from your description of the experimental setup is that the data are related to kinetics (rate) of adsorption while the Langmuir model is related to equilibrium between adsorbed and free gas. Thus, I would consider inappropriate to use your data for calculation of K and q_sat if there were no other experiments performed.
You would need data from at least two such experiments with different gas concentration. Both of these runs should be performed until equilibrium is achieved so that q and C are related to each other.
One of the derivations of the Langmuir equation is based on the quasi-kinetics consideration of adsorption as a reversible reaction:
A + Z = AZ with K as the equilibrium coefficient.
According to the law of acting masses K=[AZ]/[A][Z], where brackets [ ] mean concentration. Since [Z]+[AZ] = 1 in the Langmuir model, one can derive the Langmuir equation from the quation for K, where [A] is the concentration of the adsorptive.
Yes you can 100% vapor phase reactions also show Langmuir-Hinshelwood type inhibition by either feed and/or product components occupying/blocking active sites.
Tibor Dubaj Thank you for reminding me that the Langmuir equation is about equilibrium.
However, I have one more question.
When 0.1 ml of gas was added at the first time t_1, only 3 ppm of gas was adsorbed.
In addition, when 0.1 ml was added at time t_2 and a total of 0.2 ml of gas was added, total 5 ppm of gas was adsorbed by adsorbing 2 ppm additionally,
I think that it’s already in equilibrium at t_1 (Because, when 0.1 ml was added, it will not be able to adsorb more than 3 ppm) and also equilibrium at t_2 too.
So, can't I apply the Langmuir equation as I think the adsorption of the gas achieved equilibrium each time?
Maxim Mel'gunov Thanks for your answer!
I will find and read about the quasi-kinetics to understand this problem.
You're welcome. Planty of places in the internet you can find. See, e.g.
https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Book%3A_Surface_Science_(Nix)/03%3A_The_Langmuir_Isotherm/3.02%3A_Langmuir_Isotherm_-_derivation_from_equilibrium_considerations
To use the Langmuir equation you must have qe vs Ce equilibrium data or that you can convert to concentrations. And there are many ways to express concentrations. Also, start with a graph and see if it is an asymtotically increasing curve.
It is known how to derive the Langmuir equation/isotherm, but it is also known that later most people forget to use the equation, from which LE was obtained, to describe the kinetic data. Instead, various so-called PFO, PSO, PTO, FL-PSO etc., unrelated to are used.
Mirosław Grzesik Thanks for your answer!
Thanks to what you said, I seem to know something.
However, there are still questions, so I want to ask one more question.
You said that q_e vs c_e equilibrium is important, under the circumstances that I set, the gas is flowing in real time
Therefore, is there a problem if the amount injected at each time is set as c_e, and the total amount of adsorption until then is set as q_e?
Rick Manner Thanks for your answer!
I've never heard of Langmuir-Hinshelwood
I will find and read it with the opinions of others.
Jinwook Lee, The experiment you described is a flow-through kinetic test, and the data you get is kinetic data that you cannot substitute to the Langmuir isotherm. Obtaining equilibrium data in such a system is different than in the batch one. There, to get closer to equilibrium, we increase the time. Here, in turn, the contact time, which determines the relationship between the volume of the adsorbent and the volumetric flow rate, must be increased.
Jinwook Lee, Coming back to the data you obtained. As I mentioned above, these are kinetic data, so to describe it you can use a function where the independent variable is time. It can be an exponential or a hyperbolic function, it can be other functions. Unfortunately, this will be a description using empirical functions. You have three experimental points: (1.0.03), (2.0.05) and (3.0.06) (I hope you have more) so first you can try to describe them with the exponential function V=Ve (1-exp(-kt)). Of course, it will be difficult to see any physical meaning of the parameter k, while Ve is the upper limit of the function, i.e. the equilibrium volume here.
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