Based on my knowledge,Langmuir and Freundlich isotherms are not appropriate equations for estimating the heat of adsorption.The heat of adsorption can determined based on the theorem of dubinin radushkevich equation that can be accessed by these articles:
Rahimi, Safoora, Rozita M. Moattari, Laleh Rajabi, Ali Ashraf Derakhshan, and Mohammad Keyhani. "Iron oxide/hydroxide (α, γ-FeOOH) nanoparticles as high potential adsorbents for lead removal from polluted aquatic media." Journal of Industrial and Engineering Chemistry (2014).
and
Foo, KY, and B. H. Hameed. "Insights into the modeling of adsorption isotherm systems." Chemical Engineering Journal 156, no. 1 (2010): 2-10.
In an isotherm you have uptake (commonly in mmol/g) and pressure (commonly in bar) In Langmuir-Freundlich equation n=(a*b*p^1/c)+(1+b*p^1/c)
you have parameters a,b and c. In origin where you define the parameters for custom functions, you need to define n as dependent, p as independent parameter then a,b and c are your parameters that you will get from your fitting.
If you want to do dual site then you may want to add the parameters as a1,b1,c1, a2,b2,c2 then it is the same thing. After your fitting you will get 6 parameters instead of 3.
It is recommended to use dual site fitting when you have a steep increase in your isotherm at any region.
First: According to the text of your question you want to use the Langmuir isotherm -Freundlich to calculate the adsorption heat, which as explained by PhD Keyhani in the case of Langmuir and Freundlich isotherm it is not possible. In the case of the Langmuir-Freundlich combined model neither is possible to determine the adsorption heat starting from this model. To find the adsorption heats you can use other adsorption models or using these models to make the studies of adsorption at different temperatures and then applying the mathematical apparatus of adsorption thermodynamics do the calculations.
Second: To model the phenomenon adequately. For this you can use the MicrocalOrigin or other appropriate software for it. If you use the MicrocalOrigin, for example eight version, you should create a new function, that is, the mathematical function of the adsorption model that you are using. In this case you should go to Tools, select Fitting Function Organizer and when the corresponding dialog box appears, select New Function. You can now build your function, for which only minimal computer skills are needed.
yes I m using Origin 8 to build that function. I am able to give equation but the fitting is not converging further values it asks which I am using standard one then adj chi square is becoming negative in value.
If you don'T make an error in porgramming your fit function, then there might be problem with parameter initialisation. There are lots of possibilities to use for igood intialisation, however they require some knowledge of Origin C.