I am not sure if the answer may be given so easily without examining actual experimental data; typically, one tests various models starting from simplest, i.e., Langmuir model, Freundlich model, various types of Dubinin-Polyani models etc, with independent sorption sites or different pore distribution or with accounting for lateral  interactions - quite typical work on evaluating models, requiring a proper use of statistical methods, and what is important, the sorption isotherm containing as more points as possible (and not limiting the criteria by correlation coefficients). One may suppose that Freundlich model will be enough flexible for modeling sorption on soil and sand (but, unfortunately, Freundlich exponent becomes dependent on concentration range of a solute). For GAC, both Freundlich model or Dubinin_Radushkebich (Poluani) models may work. Yet, if to recall that sorption is to be studied also from wastewater, the story becomes complicated with the complexes formed often between pollutants and DOM and/or competitive or clogging effect of DOM on sorption.  

Thanks Mikhail. The content is informative and helpful. I have a little question, while performing adsorption studies on real wastewater as you said story becomes complicated due to formation of complexes. Can this complex/clogging may assist in multilayer adsorption of further solutes, thereby favoring the Langmuir adsorption. And is it possible to compare the adsorption of a particular compound using different isotherms but present in wastewater and in synthetic water?

Dear Kshitiz, the questions are difficult:-). I suppose you are talking about adsorption of a particular compound but not of dissolved organic matter (DOM). I would start from the second question. Yes, it is possible to compare the adsorption isotherms of a particular compound from (actual) wastewater and synthetic (waste?)water. The difference (or lack of it) will be informative whether synthetic water simulates real wastewater. For example, it may be relatively simply to mimick wastewater in terms of ionic strengths and major ions. But is not trivial to mimick organic matter present in wastewater. Whether  DOM is important or not, one may learn based on comparing isotherms measured from synthetic and (real?) wastewater.  Regarding the first question, I am not sure if there are straighforward relations between complex formation of a sorbing compound and, for example, DOM, and multilayer adsorption of this compound. Let me say that complex formation of a sorbing compound with DOM or DOM-induced clogging of pores may have no any relations with multilayer adsorption of this particular compound.

Thank you Mikhail. Yes, I am surely agree with you as it is very difficult to replicate all the physico-chemical characteristics of real wastewater into synthetic wastewater. I am focusing on the adsorption of a particular compound, but while working with real wastewaters, it is very important to take into account all the DOM and other compounds present in wastewater also, as many compounds can play an inhibitory role in adsorption of a particular compound based on their solubility. In case of simulated/synthetic wastewater, I have a question, can we ideally follow Freundlich adsorption isotherm?

Yes, it certainly may happen. A similar example: sorption of many organic compounds by soil follows Freundlich model, despite soil solution may be quite rich by dissolved organic matter and ions (e.g., Ca2+, Na+). However, what should be carefully tested, whether it is INDEED Freundlich model-trend...very often, the statistical verification is non-satisffactory. Also, Freundlich model (with non-unit exponent) cannot be extrapolated to infinitely low state, and, generally, this exponent is concentration-dependent. In short, a careful evaluation of the fitting is needed.

Dear Mikhail, Thank you for the valuable suggestion. It is very difficult to work at lower concentrations and/or with compounds having poor solubility in water. The adsorption as you mentioned is a concentration-dependent process. The adsorption of such compounds at many times follow unpredictable adsorption behaviour and equilibrium concentration also vary unusually. What precautions can be taken for the study of such compounds and can you help me with any reference regarding fitting of the freundlich curve for adsorption of such compounds.