The differential equation for diffusion of a solute in a quasi-homogeneous, sphericol, ion exchange particle, previously solved for time-dependent boundary conditions, is applied to an activated carbon adsorption system. This solution differs from the infinite volume solution which assumes constant boundary conditions. The result is applied to experimental data and yields effective adsorbent-phase diffusion coefficients. Equilibrium and rate studies were performed by using the aqueous phenol solution-activated carbon system. Problems in design and operation of liquid-phase adsorption processes have two aspects, the adsorption equilibria and the rate mechanism involved in attaining these equilibria. Of fundamental importance is the determination of mass transfer parameters, that is, liquid film coefficients and effective adsorbent phase diffusion coefficients. After the design parameters have been obtained, one has the problem of simulating the transient response of a fixed-bed or batch process. In this work, a rigorous solution to the diffusion equation will be presented and used to determine an effective adsorbent-phase diffusion coefficient. A simplified rate equation will then be shown to be valid for the system studied. This simplified rate equation may be used in a simulation model for fixed-bed adsorbers. PHASE EQUILIBRIAPhenol was chosen as the adsorbate for two reasons: it is the primary reference solute used in liquid-phase adsorption studies, and it is a water pollutant in many industries, for example, the steel and pulp and paper indus tries.The properties of aqueous phenol solutions and the activated carbon are discussed in detail because it is felt that this is an excellent reference solute and should be used to facilitate comparison of proposed rate equations in adsorption. In this manner, investigators exploring a new theoretical rate equation will have a standard system for comparison.The concentration of phenol used for this study were approximately 1,000 p g.-moles/liter of solution. It was determined that phenol exhibits a strong absorption of radiant energy at a wavelength of 270 mp; therefore spectrophotometric analysis in the ultraviolet range was feasible. The concentrations were made up with a maximum error of about 5 pmoles/liter. The curve fit relation for the concentration-absorbance relationship is:The adsorbent used in this study was type CAL activated carbon. The carbon was thoroughly screened, and fifty particles of the desired fraction were chosen at random and measured under the microscope. The minimum and maximum characteristic dimensions were recorded, and an average of these two dimensions was taken as the particle diameter. This value was found to be 1.57 & 0.05 mm. The carbon had a total surface area (N2 B.E.T. method) of about 1,000 sq. m./g. The molecular surface area of nitrogen is 16.2 sq. A., while the molecular area for phenol is 41.2 sq. A. Therefore, the effective surface area for phenol adsorption will be considerably less than 1,000 sq. m./g. because the phenol mole...

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