There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

https://chemical.eng.usm.my/bassim/PDF/adsorption%20isotherm.pdf

Insights into the modeling of adsorption isotherm systems

Metal–Organic Frameworks for Separations

Kenji Sumida, David L. Rogow, Jarad A. Mason, Thomas M. McDonald, Eric D. Bloch, Zoey R. Herm, Tae-Hyun Bae, Jeffrey R. Long

Carbon Dioxide Capture in Metal–Organic Frameworks

A simple technique is described for calculating the adsorption equilibria for components in a gaseous mixture, using only data for the pure-component adsorption equilibria at the same temperature and on the same adsorbent. The proposed technique is based on the concept of an ideal adsorbed solution and, using classical surface thermodynamics, an expression analogous to Raoult's law is obtained. The essential idea of the calculation lies in the recognition that in an ideal solution the partial pressure of an adsorbed component is given by the product of its mole fraction in the adsorbed phase and the pressure which it would exert as a pure adsorbed component at the same temperature and spreading pressure as those of the mixture. Predicted isotherms give excellent agreement with experimental data for methane-ethane and ethylene-carbon dioxide on activated carbon and for carbon monoxide-oxygen and propane-propylene on silica gel. The simplicity of the calculation, which requires no data for the mixture, makes it especially useful for engineering applications.

Thermodynamics of mixed‐gas adsorption

A group-contribution method is presented for the prediction of activity coefficients in nonelectrolyte liquid mixtures. The method combines the solution-of-functional-groups concept with a model for activity coefficients based on an extension of the quasi chemical theory of liquid mixtures (UNIQUAC). The resulting UNIFAC model (UNIQUAC Functional-group Activity Coefficients) contains two adjustable parameters per pair of functional groups.

By using group-interaction parameters obtained from data reduction, activity coefficients in a large number of binary and multicomponent mixtures may be predicted, often with good accuracy. This is demonstrated for mixtures containing water, hydrocarbons, alcohols, chlorides, nitriles, ketones, amines, and other organic fluids in the temperature range 275° to 400°K.

Group‐contribution estimation of activity coefficients in nonideal liquid mixtures

A molecular-thermodynamic correlation is established for calculating vapor-liquid equilibria in aqueous solutions containing one or more volatile electrolytes: ammonia, carbon dioxide, hydrogen sulfide, sulfur dioxide, and hydrogen cyanide. The correlation is similar to that presented in 1975, but the domain of application has been increased. The present correlation holds from about 0° to 170°C and for ionic strengths of about 6 molal; for the weak electrolytes considered here, this corresponds to total concentrations between 10 and 20 molal. To represent activities at these high concentrations, activity coefficients are expressed as a function of molality by Pitzer's equation. Required parameters are estimated from data reduction or from correlations.

Special attention is given to the ternary systems ammonia-carbon dioxide-water and ammonia-hydrogen sulfide-water. Calculated equilibria are in satisfactory agreement with the severely limited experimental data now available.

Vapor‐liquid equilibria in multicomponent aqueous solutions of volatile weak electrolytes

Estimation of Parameters for the NRTL Equation for Excess Gibbs Energies of Strongly Nonideal Liquid Mixtures

The thermodynamics of ideal dilute solutions is applied toward establishing a method for predicting multi-solute adsorption using only data for single-solute adsorption from dilute liquid solution. The method is similar to that proposed by Myers and Prausnitz for adsorption of gas mixtures.

Experimental adsorption data for activated carbon at 25°C are reported for dilute aqueous solutions containing acetone and propionitrile, and p-chlorophenol and p-cresol. Calculated and experimental results are in excellent agreement for the first system and in fair agreement for the second system. It appears that the ideal dilute-solution theory for predicting multisolute adsorption is most reliable for those systems where solute adsorption loading is moderate. When solute adsorption loading is large, the simplifying assumptions in the theory must be relaxed to allow for solute-solute interactions on the surface. The method presented here is simple to use and provides good approximations for engineering design.

John M. Prausnitz

Papers

Thermodynamics of mixed‐gas adsorption

Group‐contribution estimation of activity coefficients in nonideal liquid mixtures

Vapor‐liquid equilibria in multicomponent aqueous solutions of volatile weak electrolytes

Estimation of Parameters for the NRTL Equation for Excess Gibbs Energies of Strongly Nonideal Liquid Mixtures

Thermodynamics of multi-solute adsorption from dilute liquid solutions