Freundlich Adsorption on Charcoal theory

Physisorption involves weak, non-specific long-range intermolecular forces (primarily London dispersion forces, dipole-dipole, and van der Waals attractions) between the adsorbate and the adsorbent surface, with low adsorption enthalpies (ΔH_ads typically −10 to −40 kJ/mol). It exhibits low activation energy, is readily reversible, and can form multimolecular layers at high relative pressures. In contrast, chemisorption involves true chemical bond formation (covalent, ionic, or coordination charge transfer) with high enthalpies (ΔH_ads −80 to −400 kJ/mol), requires activation energy, is usually irreversible, and is strictly restricted to a single monolayer on specific active sites.

The Freundlich isotherm, x/m = K_F · C_eq^(1/n), was developed empirically and later justified theoretically by Zeldowitsch as an exponential distribution of adsorption site energies on heterogeneous surfaces. The parameter K_F relates to overall adsorption capacity, while 1/n (the Freundlich exponent) reflects the adsorption intensity and surface heterogeneity. For favorable physical adsorption on heterogeneous adsorbents, 1/n lies between 0.1 and 1.0. A value of 1/n < 1 indicates that high-energy adsorption sites are filled first, with adsorption affinity decreasing exponentially as surface coverage increases. A value of 1/n = 1 corresponds to linear Henry's law behavior, while 1/n > 1 signifies unfavorable cooperative adsorption.

Langmuir's model assumes: (1) Adsorption occurs on a fixed number of localized, equivalent surface sites; (2) Each site can accommodate at most one adsorbate molecule (monolayer saturation); (3) All sites are energetically identical (homogeneous surface with constant adsorption enthalpy); and (4) There are no lateral interactions between adjacent adsorbed molecules. On activated charcoal, Langmuir's model fails because the carbon surface is structurally and energetically heterogeneous, possessing a vast pore size distribution (micropores < 2 nm, mesopores 2–50 nm) with varying localized surface potentials, functional groups (carboxyl, phenolic, lactone), and capillary condensation phenomena.

Quantitative filter paper contains cellulose fibers possessing hydrophilic hydroxyl groups and capillary pores. When the initial charcoal suspension is poured onto the filter, the dry cellulose fibers can preferentially adsorb either acetic acid molecules or water molecules from solution. Discarding the first 15 mL of filtrate allows the filter paper to become completely pre-equilibrated with the solution, ensuring that subsequent collected filtrate accurately reflects the true bulk equilibrium concentration C_eq without chromatographic retention artifacts.

Activated carbon possesses an intricate hierarchy of pores: macropores (diameter > 50 nm) act as transport conduits allowing rapid hydrodynamic diffusion into the interior of carbon grains; mesopores (2–50 nm) provide transition channels; and micropores (< 2 nm) constitute over 90% of the total internal surface area (typically 800–1200 m²/g). Acetic acid has an effective molecular diameter of ~0.43 nm, allowing it to penetrate freely into the micropores where overlapping potential fields from opposite pore walls create enhanced adsorption potentials, resulting in the high capacity observed at low concentrations.

When an acetic acid molecule adsorbs onto the solid charcoal surface, its translational and rotational degrees of freedom are severely restricted, resulting in a decrease in entropy (ΔS_ads < 0). For the adsorption process to occur spontaneously under constant temperature and pressure, the Gibbs free energy change must be negative (ΔG_ads = ΔH_ads − T·ΔS_ads < 0). This requires that the enthalpy change must be negative (ΔH_ads < 0), meaning physisorption is universally exothermic. According to Le Chatelier's principle, increasing temperature shifts the equilibrium in the endothermic reverse direction, decreasing the amount of acid adsorbed at any given equilibrium concentration.

Activated carbon surfaces contain various oxygenated functional groups formed during activation: acidic groups (carboxylic, lactonic, phenolic) and basic groups (pyrone, chromene). In aqueous solutions, neutral undissociated acetic acid (pKa = 4.76) adsorbs primarily via hydrophobic interactions and dispersion forces onto graphene basal planes, as well as hydrogen bonding with surface carbonyl and hydroxyl groups. At solution pH values below pKa, the acid exists predominantly as neutral CH3COOH, maximizing adsorption affinity compared to the hydrated, repulsive acetate anion (CH3COO⁻).