It is well understood that under certain circumstances there exists an asymptotic solution for the adsorbate concentration profile in a fixed-bed adsorption system. The present study gives an analytical form of the asymptotic solution for an adsorption system subject to the isotherm of Freundlich type. It is also noticed that the adsorption zone thickness is directly proportional to the effective axial dispersion coefficient. This enables us to propose a scheme, the so-called asymptotic solution technique, to determine the effective axial dispersion coefficient. Breakthrough curves are measured for the acetic acid-water-charcoal system and comparison of those obtained from beds of different height demonstrates the applicability of the asymptotic solution. The experimental profile of the adsorbate concentration is then used to determine the adsorption zone thickness, from which the effective axial dispersion coefficient is computed. The dispersion coefficients determined in this manner turn out to be in good agreement with literature values. Consequently, the asymptotic solution technique may be used as a convenient method for measuring the effective axial dispersion coefficient.