We have developed two predictive methods for the heats of adsorption that stem from isotherm models and benchmarked them against the Clausius−Clapeyron equation. These are the Toth potential function model and the modified Clapeyron equation. Three adsorbate/adsorbent working pairs are used as examples: n-butane/BAX 1500 activated carbon, isobutane/BAX 1500 activated carbon, and ammonia/Fuji Davison type RD silica gel, all of which are examples of gas physisorption on adsorbents with both micro-and mesopores. Isotherms and corresponding integral heats of adsorption were measured in the range 298−348 K. For n-butane and isobutane, the pressures were up to 235 kPa, and for ammonia, the pressures were up to 835 kPa. Our two predictive methods consistently offer significant improvements over the Clausius−Clapeyron equation. Between the two predictive methods, the Toth model is more robust across all three working pairs studied with predictions generally falling within 10−15% of the values of the measured heats.
■ INTRODUCTIONMost gas adsorption data in the literature are presented as experimentally obtained isotherm measurements without measured heats of adsorption. This is presumably because adsorption experiments that incorporate calorimetry are more expensive and more complicated to both set up and operate than experiments based upon volumetric or gravimetric measurements alone. 1,2 However knowledge of the heat of adsorption can lend insight into surface phenomena. 3 Additionally thermal management is an integral part of the design and operation of systems which make use of adsorption phenomena such as adsorption chillers, 4,5 adsorbed gas storage tanks, 6 and adsorption separation units, 7 all of which require knowledge of the heat of adsorption.Conventionally experimentalists circumvent the dearth of calorimetric data by invoking the Clausius−Clapeyron equation, either through measuring many closely spaced isotherms and applying the equation directly to the data (to wit, the isostere method) 8,9 or by fitting the isotherm data with an isotherm model and then applying the Clausius−Clapeyron equation to the model. 10,11 The isostere method can lead to ambiguous results 1,2,12 particularly if the number of isotherms obtained is low, if the isotherms are widely spaced, or where the uncertainty in the isotherm measurement is high. Moreover even at moderate pressure (p < 1 MPa) the ideal gas assumption inherent in Clausius−Clapeyron can lead to large errors in predicting the heat of adsorption. 13 Theoretical models (e.g., refs 14−17) have been developed for this problem by using numerous isotherm models consistent with statistical mechanics and specific to various different adsorbate/adsorbent modes of interaction. However it remains a challenge to know which model to apply to get a correct prediction of the surface interactions and heat of adsorption without significant prior knowledge of the behavior of the adsorbate/adsorbent system. Savara et al. 18 developed a rigorous method for selecting between a number of 2...