New equations for the physical adsorption of gases on solids have been developed based on the vacancy solution model of adsorption in conjunction with the Flory-Huggins activity coefficient equations. The isotherm equation contains three regression parameters: a Henry's law constant, the limiting amount of adsorption, and a gas-solid interaction term. Pure-gas data over a range of temperature can be correlated using only five parameters. Gas-mixture equilibria can be predicted using only the parameters obtained from the pure-gas data. Pure-component, binary, and ternary adsorption equilibrium data on activated carbons, silica, and zeolites over a wide range of conditions have been used to evaluate the model. The results show that, except for a few systems, this model predicts gas-mixture equilibria better than any other model. SCOPEIn order to exploit the physical adsorption of gases in separation processes, quantitative characterization of the multicomponent adsorption equilibria are needed as functions of temperature and pressure. Experimental multicomponent adsorption data are difficult and tinie-consuming to obtain; therefore, a reliable method of predicting multicomponent equilibria at various temperatures and pressures from purecomponent adsorption data, and if necessary binary mixture data, would be preferred. Suwanayuen and Danner (1980a, b) proposed a vacancy solution model using the Wilson model for the activity coefficients. Although this approach has been successful for the prediction of isothermal multicomponent equilibria from single-gas isotherms alone, it fails to explicitly include the effect of temperature. Also, the equations in the Suwanayuen and Danner (S&D) model are complex, and it is often difficult to obtain physically significant parameters from the regression of limited isothermal data sets.The objective of this work was to develop a new gas adsorption model based on vacancy solution theory which corrects the deficiencies inherent in the S&D model and surpasses it in accuracy. Any new model should account for nonideal behavior in the adsorbed phase including the adsorbate-adsorbate interactions and should predict the temperature dependency of the equilibria as well as the pressure and compositional dependencies. The model should be flexible enough to allow the use of binary data to characterize the adsorbate-adsorbate interactions if such data are available and if such binary parameters are needed. Preferably the model should include a method of estimating these adsorbate-adsorbate parameters, thus eliminating the need for the binary data which are seldom available and difficult to obtain experimentally. The model presented in this paper meets these criteria. CONCLUSIONS AND SIGNIFICANCEA new model for pure-and multicomponent gas adsorption is developed based on the vacancy solution theory as presented by Suwanayuen and Danner (1980a, b). Activity coefficients based on a Flory-Huggins type expression have been introduced to account for the nonideality in the adsorbed phase. By regress...

This work is an experimental assessment of the Langmuir-Hinshelwood model of heterogeneous catalysis. The vopor-phase dehydration of ethanol to diethyl ether, as catalyzed by cation exchange resin in the acid form, was the reaction chosen for study.Initial reaction rate data, determined from the integral kinetic data obtained experimentally, allowed selection of the most suitable rate equation from among several plausible equations derived in accordance with the above model. The Langmuir equilibrium adsorption constants in the rate equation were compared with the corresponding constants determined directly from pure component studies in a static adsorption system. The adsorption constants determined for the three reacting components by these independent methods showed definite order-of-magnitude agreement. The adsorption studies also provided significant information about the nature of the catalytic site.The extent of agreement in the constants determined by these two independent approaches is considered to be evidence of the theoreticol validity of this model. Additional interpretation of the adsorption and kinetic data via this model suggests that the ethanol dehydration reaction proceeds through the reaction of adjacently adsorbed ethanol molecules.The Langmuir-Hinshelwood model of heterogeneous catalysis has been widely used by chemical engineers in the correlation of experimental reaction rate data. The model stems directly from the Langmuir theory of activated adsorption (14) and the application by Hinshelwood (8) of that theory to a large number of reactions. Hougen and Watson (10) extended and popularized this theory for chemical engineering use. Rate equations, derived for many situations, were systematized and put into a generalized form by Yang and Hougen ( 2 3 ) . Although the model has been used quite successfully in the correlation of kinetic data, its theoretical significance has been questioned. This argument has been put into focus in back-to-back articles by Weller ( 2 2 ) and Boudart (1).Weller suggests that the LangmuirHinshelwood approach does not have the theoretical validity commonly attributed to it and that, lacking theoretical validity, it is unnecessarily complex for use as an empirical equation when compared for simplicity to the common power function type of equation. Boudart has supported the rational use of the Langmuir-Hinshelwood approach with his discussion of the limitations and strengths of that theory. Because this model of heterogeneous catalysis has not been adequately tested the direct experimental evaluation presented in this paper has been carried out.The general approach utilized in this work was to correlate reaction rate data with an equation of the Langmuir-Hinshelwood model, obtaining values of the Langmuir equilibrium Robert L. Kabel is with the United States Air

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The vacancy solution model of adsorption which uses an activity coefficient equation of the Wilson form has been improved (1) by incorporating temperature dependency into the model, and (2) The vacancy solution model (VSM) of adsorption has been nurtured with one primary objective in mind: to facilitate the prediction of multicomponent adsorption equilibria from pure-component data. Because of the difficulty of obtaining gas-mixture adsorption data experimentally, a predictive scheme is needed. To be useful, the procedure must include a method of interpolating and extrapolating to different temperatures and pressures. If, on the other hand, binary adsorption data are available, it is important to use this information as effectively as possible when predicting multicomponent systems. Suwanayuen and Danner (1980a,b) presented a form of the VSM based on the Wilson activity coefficient equation, incorporating no temperature dependency and having two independent adsorbate-adsorbate interaction parameters. Cochran et al. (1985) introduced the Flory-Huggins activity coefficient into the VSM, incorporated temperature dependency, and reduced the number of binary interaction parameters. They were able to predict gas-mixture adsorption equilibria quite well for many systems using only pure-gas data. However, a number of systems involving zeolites led to less than satisfactory results. Furthermore, no significant improvements were attained by regressing a binary interaction parameter from the binary adsorption data.In an attempt to improve the predictions for zeolite systems, temperature dependence has been introduced into the Wilson form of the VSM and the number of binary regression parameters has been reduced. This modified Wilson form and the Flory-Huggins form of the VSM are examined in terms of their abilities to correlate or predict binary and ternary equilibria with and without parameters extracted from the binary data. CONCLUSIONS AND SIGNIFICANCETemperature dependency has been introduced into the Wilson form of the vacancy solution model. This allows purecomponent isotherms to be predicted at temperatures where no data are available, and gas-mixture adsorption equilibria to be predicted within this expanded temperature range. A relationship between the two adsorbate-adsorbate binary interaction parameters has been developed. Thus the number of regression parameters that must be determined is decreased with no reduction in the accuracy of the method.When pure-component isotherms are available at a number of temperatures, the temperature-dependent model should be used in preference to the isothermal model. In this way the regressed parameters attain more reasonable values. If only pure-component data are available, the Flory-Huggins form of the vacancy solution model should be used to predict gasmixture adsorption equilibria. If binary data are also available, predictions of the binary equilibria using only the puregas data with the Flory-Huggins form should be compared to the data. If these predictions are accurat...