Adsorption Concept and Laws

The Concept of Adsorption

• Adsorption is the phenomenon of accumulation of molecules of a gas or liquid on a solid surface.
• The amount of substance adsorbed is affected by the nature of the adsorbent and adsorbate, as well as the temperature of the system.

Laws Governing Adsorption

• Freundlich isotherm is a mathematical equation that relates the amount of gas adsorbed to the concentration of the gas in the solution.
• The equation is: $x/m = kP^{1/n}$, where x is the mass of gas adsorbed, m is the mass of adsorbent, P is the equilibrium pressure, and k and n are constants.

Freundlich Isotherm

• The Freundlich isotherm is especially useful in describing adsorption with porous adsorbents.
• There are two types of adsorption isotherms:
  • Type 1: represents adsorption where the surface is saturated at higher pressures.
  • Type 2: represents adsorption where the surface is not saturated even at higher pressures.

Taking Logarithms

• Taking logarithms on both sides of the Freundlich equation yields: $log x = log k + (1/n)log P$
• This equation is a linear equation with slope $1/n$ and intercept $log k$, which can be used to determine k and n.

Langmuir Model for Adsorption

• The Langmuir model is based on the following assumptions:
  • The surface contains a fixed number of adsorption sites.
  • All sites are equivalent.
  • The adsorption is localized.
  • There is no interaction between adsorbed molecules.
• The Langmuir equation is derived from the condensation and evaporation of gas molecules.
• The resulting equation is: $θ = \frac{k_c P}{k_e + k_cP} = \frac{KP}{1 + KP}$, where K = $k_c/k_e$.

Three Limiting Cases

• At low pressure, θ = KP, so θ is proportional to P.
• At very high pressure, θ = 1, so the surface is completely covered.
• At intermediate pressure, the equation yields a curved line.

The Freundlich Adsorption Isotherm

• The Freundlich equation is: $x/m = kP^{1/n}$, where x is the mass of adsorbate, m is the mass of adsorbent, P is the equilibrium pressure, and k and n are constants.
• The equation assumes that the adsorption process is not restricted to one molecule thick.
• The graph of the Freundlich isotherm is sigmoidal, showing the relationship between the amount of adsorbate adsorbed and the pressure at a constant temperature.

Assumptions of the Freundlich Equation

• The equation is empirical and based on experimental data.
• The adsorbent surface is heterogeneous and adsorption energy is not uniform.
• The adsorbate is physically adsorbed onto the adsorbent surface.

Limitations of the Freundlich Equation

• It does not account for the saturation of the adsorbent surface.
• It is not valid for high pressures or for adsorption of very large molecules.

Applications of the Freundlich Equation

• To study the adsorption of gases on solids.
• To study the adsorption of liquids on solids.
• To study the adsorption of dyes from solution.
• To design adsorption processes for the removal of pollutants from air and water.

Adsorption Isotherms

• The BET equation is: $\frac{P}{V(P_o-P)} = \frac{1}{V_mC} + \frac{C-1}{V_mC} \frac{P}{P_o}$
• The BET equation can be used to fit experimental data for values of P/P from 0.05 to 0.35.

Classification of Adsorption Isotherms

• Brunauer made a useful classification of adsorption isotherms, including:
  • Type I: linear increase in adsorption with pressure, followed by a plateau at high pressures.
  • Type II: sigmoid curve with an initial slow increase in adsorption, followed by a steep increase and finally a plateau.
  • Type III: concave curve with an initial steep increase, followed by a gradual increase towards a plateau.
  • Type IV: sigmoid curve similar to type II, but with a hysteresis loop.
  • Type V: sigmoid curve similar to type III, but with a hysteresis loop.
  • Type VI: stepped curve with multiple plateaus, indicating adsorption at different sites.