ent research:1. Theoretical rate equations have been derived for liquid phase mass transfer accompanied by first-order complex chemical reactions. The kinetics considered is a combination of consecutive, reversible, and parallel chemical reactions.2. The film-penetration model has been shown to be a general model among the theories considered. I t takes the film theory and the surface renewal theory as the lower and upper limits, respectively, in the theoretical predictions.3. The ratio of chemical to physical mass transfer coefficients is smaller than that for mass transfer with a firstorder irreversible reaction. The theories deviate significantly for cases where the reversible reaction is strong, and the diffusivities of the intermediate product and the reactant are quite different.

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A new modification of the Redlich-Kwong equation of stote is presented. The modification follows the procedure suggested by Redlich, Ackerman, et al., in which a deviation function (a function of temperature, pressure, and acentric factor) is added to the compressibility factor from the original equation to improve the agreement with data. The purpose of the present modification wos to improve predictions of the Redlich-Kwong equation in the saturated vopor rrgion up to the critical point while retaining a relatively simple form to make analytical relations for derived properties possible. The equation for pressure correction to vapor entholpy, derived from the compressibility factor by stundord thermodynamic procedures, is also presented. Comparisons of predicted vapor compressibility factors and vopor enthalpy pressure corrections with literature doto are given, demonstroting the advantages of the proposed modification when the saturated vapor region is of principal interest. The modification follows closely the work of Bamer et al. (3) in an effort to retain relative simplicity. However, it uses the deviation function approach, developed Vol. 16, No, 6 AlChE Journal Page 991 14 393 ( 6.2) 142 ( 2 . 2 ) 161 ( 2 . 5 ) 165 (2.6) (near saturation) t Data from Nelson and Holcomb ( 1 6 ) as reported by Bamer et al. ( 3 ) . Data from Yarborougb and Edmister ( 32 ) as reported by Bamer et al. ( 3 )

The coefficients of the Benedict-Webb-Rubin equation of state have been developed for argon. By employing these coefficients, the volumetric behavior of argon has been predicted with an average deviation of 0.241 % for five hundred ninety-seven smoothed and experimental data points in the superheated region.At temperatures below the critical, two sets of Go's, one for the liquid and one for the vapor, were needed to relate the vapor pressure to the densities of saturated argon. However, consistent fugacities for the saturated vapor and liquid argon could not be predicted with these Co values. Therefore, another set of C, ' s was developed by equating the pure component vapor and liquid fugacities along the vapor pressure curve. These values were used to test the applicability of the equation of state to predict derived thermodynamic properties.The original BWR expression for calculating isothermal pressure effects on enthalpy was modified to include explicitly the temperature dependence of the coefficient C,. Vapor-liquid equilibrium relations for the argon-nitrogen system predicted by the standard BWR procedure were compared with experimental data.The empirical equation of state of Benedict, Webb, and Rubin ( 3 ) was originally developed to correlate and predict the fugacities of light hydrocarbon mixtures. Since its publication, it has been used extensively to represent the volumetric and phase relations of light hydrocarbons and some nonhydrocarbons. Several papers (3 to 5, 8,13) have been published describing success in predicting high pressure phase behavior of multicomponent systems. AS the BWR technique gained widespread use, more and more shortcomings were reported (8, 1 3 ) . Most of the difficulties have been observed in predicting P-V-T relationship within the critical region, and predicting vaporliquid equilibrium ratios at low temperatures. As a result, it is widely believed that the BWR equation is inadequate for systems at low temperatures. Attempts have been made to modify the equation and the combining rules for mixtures in order to use it for low temperature predictions. The limitations of the BWR method and suggested modifications have been summarized by Canjar ( 8 ) , Ellington ( 1 3 ) , and Lin (20). The application of the BWR approach to the cryogenic systems nitrogen-methane (26) and nitrogen-carbon monoxide ( 2 4 ) at temperatures below 200"R. established that temperature is not a limiting condition for use of the technique. The results of the present work extend the application of the BWR method to another cryogenic material, namely, argon.As was recently stated by Thodos ( 2 5 ) , argon is a good substance to test the validity of an equation of state. Its molecule is monatomic and therefore its properties should resemble those expected from a simple fluid as defined by Pitzer ( 2 3 ) . Furthermore, its relatively high atomic weight provides a good test for any equation employing a high power series in density. Beattie and Bridgeman (2) showed that such an equation can apply to argon.Th...