* Corresponding author. Tel.: #852-2358-7132; fax: #852-2358-54. E-mail address: kejep@ust.hk (J.F. Porter) Chemical Engineering Science 54 (1999) 5863}5885 The prediction of sorption from a binary mixture of acidic dyes using single- and mixed-isotherm variants of the ideal adsorbed solute theory J. F. Porter*, G. McKay, K. H. Choy Department of Chemical Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, People's Republic of China Received 9 September 1998; received in revised form 2 March 1999; accepted 19 March 1999 Abstract Equilibrium isotherms have been determined for the adsorption of two single-component and one binary acid dye solutions on carbon. The ideal adsorbed solute theory (IAST) has been used to predict isotherm data for the binary system using the single-component dye sorption data alone. A detailed analysis has been carried out to investigate the e!ect of di!erent error criteria for determining single-component isotherm parameters and their in#uence on the results of IAS model simulations using the Langmuir and Freundlich isotherm equations. It was found that the `best-"ta single-component isotherm based on the minimum error criteria did not result in the `best-"ta IAS model predictions. Furthermore, the IAS model producing the closest "t to the binary experimental data did not use the same isotherm model as the single-component data for one dye. Reasons for this apparently anomalous behaviour have been discussed and the most likely cause appears to be dye}dye interactions in the binary system.  1999 Elsevier Science Ltd. All rights reserved. Keywords: IAST; Acid dyes; Mixed isotherm; Carbon 1. Introduction Adsorption processes provide a feasible technique for the removal of pollutants from industrial wastewaters. The design of industrial adsorbers requires rate data and information on equilibrium properties, namely adsorp- tion isotherms. Since most industrial e%uents contain several components, there is major interest in and em- phasis on obtaining multicomponent equilibrium ad- sorption data for use in design models. This requirement necessitates extensive and laborious practical experi- mentation unless an accurate and reliable method can be developed for predicting multicomponent adsorption equilibrium data without using multisolute data. Several methodologies have been developed. The earliest at- tempt, by Butler and Ockrent (1930), extended the Lan- gmuir isotherm to account for competitive adsorption and this was later modi"ed to include a separate term for adsorption without competition (Jain & Snoeyink, 1973). Singer and Yen (1980) and McKay and Al-Duri (1989) applied the competitive Langmuir isotherm to phenols on carbon and basic dyes on carbon, respectively. McKay and Porter (1997) used the competitive Lan- gmuir for the sorption of metal ions on peat; however the agreement between the experimental data and theoretical predictions was poor. A Freundlich-type multicompo- nent equation has been developed and applied to binary systems (Sheindrof, Rebhun & Sheintuch, 1981, 1982; Fritz & Schlu K nder, 1974, 1981; McKay & Al-Duri, 1988) but these models are often only valid over selected con- centration ranges and require extensive computation. Three parameter equations have been developed and several equations with empirical parameters (Toth, 1962; Redlich & Peterson, 1959; Jossens, Prausnitz, Fritz, Schlu K nder & Myers, 1978; Crittenden & Weber, 1978; Fukuchi, Kobuchi & Arai, 1982; Seidel, Radeke, Tzscheutschler & Gelbin, 1985). The application of thermodynamic "rst principles to gas adsorption resulted in a major development in 0009-2509/99/$ - see front matter  1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 9 ) 0 0 1 7 8 - 5