Analyses of Adsorption Kinetics Using a Stirred-Flow Chamber: I. Theory and Critical Tests

The study of ion-exchange kinetics on soils and soil constituents has attracted much interest throughout the last decade. The introduction of a stirred-flow method to study these reactions, as well as other adsorption-desorption phenomena, has stimulated this interest. However, the manner in which rate data are interpreted using this technique and other flow methods has been questioned. Accordingly, a numerical solution for various instantaneous equilibrium and kinetic models is presented. It was found that rate data that could be described using an instantaneous equilibrium model could also be interpreted using a kinetic model. Therefore, the validity of kinetic rate coefficients obtained by flow methods is questionable. An analytical approach was developed to outline experimental methods that could be used to distinguish between instantaneous equilibrium and time-dependent reactions and to differentiate between solution-concentration-dependent kinetic models vs. those that are independent of solution concentration. By using this approach, and employing various flow rates and influent concentrations, as well as using a stopped-flow technique, it is easy to decide whether rates of reactions can be measured using the stirred-flow method for specific experimental conditions. H the study of ion-exchange kinetics on soils has received less attention than chemical-equilibrium studies. During the last decade, however, much interest has been generated concerning ionexchange kinetics. However, the problems of correctly interpreting the experimental results and making comparisons between different kinetic methods have not been solved (Sparks, 1989). For example, in comparing the magnitude of rate coefficients for K-Ca exchange on two clay minerals and a soil, Ogwada and Sparks (1986) found that the rate coefficients were greatly affected by the type of kinetic method. To enable measurements of rapid reactions and to minimize transport phenomena, a new method, reA. Bar-Tal and S. Feigenbaum, Inst. of Soils and Water, Agric. Res. Organization, The Volcani Center, Bet Dagan 50250, Israel; D.L. Sparks, Dep. of Plant and Soil Sciences, and J.D. Pesek, College of Agricultural Sciences, Univ. of Delaware, Newark, DE 19717-1303. Contribution no. 2514-E, 1989 series, from the Agric. Res. Organization, The Volcani Center, Bet Dagan, Israel. Published with the approval of the director of the Delaware Agric. Exp. Stn. as Miscellaneous Paper no. 1322. Contribution no. 254 of the Dep. of Plant and Soil Sciences, Univ. of Delaware. Received 16 Feb. 1989. *Corresponding author. Published in Soil Sci. Soc. Am. J. 54:1273-1278 (1990). ferred to as a stirred-flow technique, was developed by Carski and Sparks (1985). This method combines some of the favorable aspects of both batch and miscible-displacement techniques. However, the data analyses employed by Carski and Sparks (1985) were based solely on the calculated adsorbed quantities, which are not measured directly. Consequently, this could lead to experimental and mathematical errors, and data analyses should be based on effluent solution concentration (Schnabel and Fitting, 1989). Fundamentally, all chemical reactions are time dependent but, if the reaction is too rapid to be determined by the employed method or under the specific conditions used in the measurements, the process can be denned as an instantaneous one. The flow methods used in soil chemistry for determination of kinetic rate coefficients are based on measurements of solutionconcentration change vs. time (Sparks, 1986, 1989). Consequently, the adsorbed amount as a function of time is also a function of solution concentration. These techniques have been used for studying adsorption isotherms, assuming instantaneous equilibrium (Egozy, 1980; Isaacson and Hayes, 1984; Miller et al., 1989). In a previous study (Seyfried et al., 1989), we posed the possibility that the cation-exchange reaction on soils is very rapid and, if the stirred-flow method is used under experimental conditions such as those described by Carski and Sparks (1985), a kinetic process is not measured. Rather, what occurs is a process of solution dilution in the chamber combined with an instantaneous equilibrium exchange reaction. Therefore, there is a need to establish systematic tests to distinguish between instantaneous and timedependent reactions for a range of experimental conditions, and between different types of kinetic models. The objectives of this paper are to develop experimental techniques to distinguish between: (i) instantaneous and time-dependent reactions; and (ii) kinetic reactions that are dependent on solution concentration vs. those that are independent using the stirred-flow chamber. MATERIALS AND METHODS Theoretical Considerations