Toxicant adsorption on activated charcoal: is the fraction adsorbed a unique function of the charcoal:adsorbate ratio?

In several recent studies the adsorption of toxicants on activated charcoal has been reported graphically in the form of plots presenting the fraction of toxicant unadsorbed at equilibrium (F) as a unique function of the ratio (R) of the amount of activated charcoal to that of total toxicant. Derivation of the mathematical relationship between these two variables from either the Freundlich or Langmuir isotherms reveals F is not uniquely defined by R, unless the amount of activated charcoal, the equilibrium concentration of the toxicant, or its initial concentration is kept constant. For two agents known to adhere to the Freundlich isotherm, paraldehyde and metaldehyde, a good agreement was obtained between the F and R values predicted by the derived equations and those observed experimentally. The usefulness of F versus R plots is discussed.