hi,
I plot a graph of langmuir isotherm with 1/qe vs 1/ce . It says theat from slope and intercept the langmuir constant is calculating . what is the calculation of kL from slope and intercept.
Dear Betty,
Langmuir isotherm equation is : 1/qe = 1/qm + 1/qm.KL
After the calculation of qe values, plot the graph of 1/qe vs. 1/ Ce using excel. The plot should give you a linear curve with an intercept and slop (an equation such as this: Y = mX + C). m=intercept=1/qe, hence qe=1/m. C=1/qm.KL. From the C value, we can calculate KL since the value of 1/qm is already calculated.
Another way which might be much easier is using the following equation:
1/qe = 1/Q0 + 1/KQ0. 1/Ce
From the plot of 1/qe vs.1/Ce you get a linear curve with intercept = 1/Q0 and slop = 1/KQ0. For examples with actual numbers, please see attached file.
http://mimoza.marmara.edu.tr/~zehra.can/ENVE401/4.%20Adsorption%20Equilibria%20Examples.pdf
Hoping this will be helpful,
Rafik
Unfortunately, linearizing a Langmuir isotherm gives wrong values for K and Qo. It also gives absolutely no measure of the true confidence we can have in these values. In essence, linearization is good only as a first estimate. For publication-level reports, the correct approach is to fit the data using non-linear regression with the exact form of the equation.
Attached is the analysis of the same data using Igor Pro. The next level of improvement would be to weight the data points according to values from propagations of their measurement uncertainties. This would fix the value at (0,0) to be exact for example.
Dear Jeffrey,
You are right. However, in the recent three years I have published 10 papers in good journals using the equation depicted in my first answer.
I appreciate the background and am aware of the acceptance of the linearization method in the literature. I intended foremost to point out its (serious) problems, not to admonish anyone personally for using it. I also hope to direct the future work to improve the method of analysis here. As an evangelist in this regard, I might note by analogy that, within my lifetime in the past, we could only linearize and graph this type of data by hand to get the slopes and intercepts. Only more recently have we created computer tools to do the linearized analysis for us. Now, we have computer tools that can do non-linear analysis faster than the time we need to linearize the data. It is really time to put such common tools to their proper use.
Dear Jeffrey,
I like the Langmuir Isotherm PDF.
Is that software public, I would wish to try it if its accessible.
Thanks.
Instead of a linear form, it is better to use the original nonlinear form and the measure of matching eg mean relative error. The graphic methods are inaccurate. Regards,
The graphical method can, on the other hand, be used to determine the starting point for a non-linear method, eg a non-linear regression. Regards
In case of graphical method the answer can be found above. However, it is better to use nonlinear regression, of course for explcit (with respect to qe) form of function. Regards,
@ Jeffrey J Weimer. I appreciate that you provided an attachment for guidance on calculating KL and other constants. Could you provide a step by step instructions including the suitable software for this analysis? It will be most helpful.
Dear Betty,
From the intercept you can get the value of qm (qm=1/intercept).
The slope=1/(qm.KL), then slope= intercept/Kl,
then KL=intercept/slope
Jeffrey J Weimer can you please guide me , how to find slope and intercept value from nonlinear fitting of langmuir and freundlich isotherms? how i can calculate the KL and KF from the nonlinear fitting ?