Freundlich Isotherm Parameters

Determination of Parameters in Freundlich Isotherm

• Freundlich isotherm equation: q = KF C^1/n, where q is the amount of adsorbate per unit weight of adsorbent, KF is the Freundlich constant, C is the equilibrium concentration, and n is the Freundlich exponent.
• Log C vs. log q plot produces a straight line with slope = 1/n and intercept = log KF.

Freundlich Parameters at Neutral pH

• Various compounds with their corresponding KF and 1/n values:
  • Hexachlorobutadiene: KF = 360, 1/n = 0.63
  • Anethole: KF = 300, 1/n = 0.42
  • Phenyl mercuric acetate: KF = 270, 1/n = 0.44
  • p-Nonylphenol: KF = 250, 1/n = 0.37
  • ...and many more compounds listed.

Definition of Adsorption

• Adsorption is the process of removing a substance from one phase to another phase by accumulating at the interface between the two phases.
• Examples of adsorption: gas-solid interface (VOC on activated carbon), liquid-solid interface (organic pollutant on activated carbon).

Definitions

• Adsorbate or solute: the material being adsorbed.
• Adsorbent: the solid material being used as the adsorbing phase.

Driving Force for Adsorption

• The driving force for adsorption is the reduction in interfacial (surface) tension between the fluid and the solid adsorbent.
• Surface or interfacial tension (σ) is defined as the change in free energy (G) resulting from an increase in area between two phases (A).

Adsorption vs. Absorption

• Adsorption is the accumulation of a substance at the interface between two phases.
• Absorption is the removal of a substance from one phase by dissolution in another phase.

Common Adsorbents

• Activated carbon: a char-like material with high surface area.
• Silica gel: a hard, granular, porous material made from sodium silicate solutions.
• Activated alumina: aluminum oxide activated at high temperature for moisture adsorption.
• Aluminosilicates (molecular sieves): porous synthetic zeolites used for separation processes.

Activated Carbon as an Adsorbent

• Activated carbon is the most common adsorbent used in wastewater treatment.
• The adsorbing capacity of activated carbon is associated with very high surface area per unit volume.

Production of Activated Carbon

• Activated carbon is produced through a two-step process: pyrolysis and activation.
• Pyrolysis involves heating a raw material to produce a charred, highly carbonaceous solid residue.
• Activation involves oxidation of the charred residue to form a network of pores and passages with high surface area.

Unsteady State Mass Balance for Batch Adsorption

• The unsteady state mass balance equation for batch adsorption is: C = Co - (q - qo) / B * V.
• The equation can be integrated to give: t = -1 / K * Ap * ∫(C' - C*) / (Co - C') dC'.

Multistage Crosscurrent Adsorption

• The total amount of carbon used per volume of liquid treated is a function of initial, intermediate, and final concentrations, equilibrium constant KF, and level of pollutant already present in the carbon.
• The equation for the total amount of carbon used is: Btot = B1 + B2 / V * (Co - C1) / (KF * C1^1/n - qo).

Multistage Countercurrent Adsorption

• The process involves multiple stages where wastewater and activated carbon flow in a countercurrent manner.
• The streams leaving each stage are assumed to be in equilibrium with each other.
• The rates of wastewater and activated carbon moving from stage to stage are constant.
• In wastewater applications, typically no more than two stages are used.