A method based on the maximum likelihood principle has been developed for the determination of model parameters from experimental data when all the measured variables are subject to error. In addition to the best estimates of the parameters, this method also yields information useful in selection of appropriate models and evaluation of the accuracy of the data. Application of the method is illustrated in the reduction of binary vapor-liquid equilibrium data.

AbstractSince vapor pressures of very high‐boiling hydrocarbons are of increasing interest in energy‐related processes, a new correlation has been established for estimating these vapor pressures over a wide range of temperature. The new SWAP correlation, based on Prigogine's theory for polysegmented molecules, is particularly useful for hydrocarbons (and petroleum cuts or coal tars) which deviate from normal‐paraffin structure: branching, saturated and unsaturated rings. Extensive comparison with experimental data shows that whereas for normal paraffins SWAP gives results comparable to those obtained by previously‐published correlations, SWAP gives significantly better results for large aromatic, naphthenic and branched hydrocarbons. To use SWAP, the only input data required are T10 (boiling point at 10 mm Hg) and approximate characterization of molecular structure.

Experimental measurements are reported for the equilibrium distribution of phenol, o-cresol, m-cresol, 2,6-xylenol, 3,5-xylenol, and 2,3-xylenol between water and several non-polar organic solvents. These new results, as well as those previously published, are correlated within the framework of the theory of associated solutions. Theoretical analysis shows that while the distribution coefficient is essentially independent of solute concentration when that concentration is very low, the distribution coefficient rises with solute concentration at intermediate concentrations, especially when aromatic solvents are used. For phenolic solutes and non-polar solvents, the correlation can be used to estimate distribution coefficients for those systems or those operating conditions (temperature, concentration) where experimental results are not available.

To obtain a semi-theoretical equation for the excess Gibbs energy of a liquid mixture, Guggenheim's quasi-chemical analysis is generalized through introduction of the local area fraction as the primary concentration variable. The resulting universal quasi-chemical (UNIQUAC) equation uses only two adjustable parameters per binary. Extension to multicomponent systems requires no ternary (or higher) parameters. The UNIQUAC equation gives good representation of both vapor-liquid and liquid-liquid equilibria for binary and multicomponent mixtures containing a variety of nonelectrolyte components such as hydrocarbons, ketones, esters, amines, alcohols, nitriles, etc., and water. When well-defined simplifying assumptions are introduced into the generalized quasi-chemical treatment, the UNIQUAC equation reduces to any one of several well-known equations for the excess Gibbs energy, including the Wilson, Margules, van Laar, and NRTL equations. The effects of molecular size and shape are introduced through structural parameters obtained from pure-component data and through use of Staverman's combinatorial entropy as a boundary condition for athermal mixtures. The UNIQUAC equation, therefore, is applicable also to polymer solutions.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTThermodynamics of Multicomponent Liquid Mixtures Containing Subcritical and Supercritical ComponentsD. S. Abrams, Fausto Seneci, P. L. Chueh, and J. M. PrausnitzCite this: Ind. Eng. Chem. Fundamen. 1975, 14, 1, 52–54Publication Date (Print):February 1, 1975Publication History Published online1 May 2002Published inissue 1 February 1975https://pubs.acs.org/doi/10.1021/i160053a009https://doi.org/10.1021/i160053a009research-articleACS PublicationsRequest reuse permissionsArticle Views379Altmetric-Citations9LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access options Get e-Alerts

Chemischer InformationsdienstVolume 6, Issue 14 Article ChemInform Abstract: DISTRIBUTION OF PHENOLIC SOLUTES BETWEEN WATER AND NON-POLAR ORGANIC SOLVENTS D. S. ABRAMS, D. S. ABRAMSSearch for more papers by this authorJ. M. PRAUSNITZ, J. M. PRAUSNITZSearch for more papers by this author D. S. ABRAMS, D. S. ABRAMSSearch for more papers by this authorJ. M. PRAUSNITZ, J. M. PRAUSNITZSearch for more papers by this author First published: April 8, 1975 https://doi.org/10.1002/chin.197514072Citations: 1Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article.Citing Literature Volume6, Issue14April 8, 1975 RelatedInformation

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTVapor Pressures of Liquids as a Function of Temperature. Two-Parameter Equation Based on Kinetic Theory of FluidsD. S. Abrams, H. A. Massaldi, and J. M. PrausnitzCite this: Ind. Eng. Chem. Fundamen. 1974, 13, 3, 259–262Publication Date (Print):August 1, 1974Publication History Published online1 May 2002Published inissue 1 August 1974https://pubs.acs.org/doi/10.1021/i160051a018https://doi.org/10.1021/i160051a018research-articleACS PublicationsRequest reuse permissionsArticle Views223Altmetric-Citations35LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access options Get e-Alerts

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTGeneralized Correlation for Fugacity Coefficients in Mixtures at Moderate Pressures. Application of Chemical Theory of Vapor ImperfectionsK. -H. Nothnagel, D. S. Abrams, and J. M. PrausnitzCite this: Ind. Eng. Chem. Process Des. Dev. 1973, 12, 1, 25–35Publication Date (Print):January 1, 1973Publication History Published online1 May 2002Published inissue 1 January 1973https://pubs.acs.org/doi/10.1021/i260045a006https://doi.org/10.1021/i260045a006research-articleACS PublicationsRequest reuse permissionsArticle Views949Altmetric-Citations89LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access options Get e-Alerts

In reducing experimental vapour–liquid equilibrium data it is common to calculate the Gibbs energy of mixing in excess of that for a solution whose entropy of mixing is given by one of two expressions; ideal entropy or Flory–Huggins entropy. The first of these is proper for a mixture of small molecules of similar size and the second one is proper for a mixture of monomer and chain polymer. This paper considers intermediate cases where there are significant differences in molecular shape as well as size. An expression is derived for the combinatorial entropy of mixing; this expression has Flory's result as the leading term but also contains corrections for molecular bulkiness. The combinatorial entropy of mixing depends on characteristic parameters reflecting both molecular size and shape. Methods are given for simple evaluation of these parameters and illustrations for representative mixtures are presented. In some case, the corrections for bulkiness can be very large.