Toth T-Equation Isotherm

Another theoretical treatment that matches the experimental results for many adsorbents is the Toth [18] isotherms, referred to as the T-equation 

It is not clear how useful this equation is although it is claimed that the parameter yields the monolayer coverage value. The values obtained from this have been compared favorably with the BET values and, with some reservations, the same surface area value is obtained regardless of the adsorbent. 

One of the basic assumptions for the theory behind the T-equation is the validity of Henry s law and the notion that the virial equation is a thermodynamic requirement. This latter assumption is approximately correct for many situations but is strictly incorrect. 

Harkins and Jura [20] describe a method to obtain the absolute surface area of a solid by the following method. Firstly, the powder is exposed to a high vapor pressure of water. Indeed it is best to expose it in a high-sensitivity calorimeter over a reservoir of water. The powder is then allowed to fall into the reservoir and the amount of heat produced is measured. By doing so, one eliminates the outer surface of the adsorbed film releasing the energy associated with the liquid-gas interface surface tension. Since the liquid-gas surface tension energy is known one may then calculate from the amount of heat released the area of the powder (or at least the outer surface area of the adsorbed film before immersion). 

The principal problem with this technique is the difficulties involved experimentally. Assuming that these are overcome, there are still the following questions Are the particles well dispersed after immersion and Is there significant porosity or bed porosity in the sample that would lower the observed area due to capillary action Both of these questions were 

---