11.13
Adsorption Isotherms I
Adsorption isotherms are mathematical models that describe how molecules in a gas or liquid phase interact with surfaces. Two of the most common isoth…
Type I adsorption isotherms describe chemisorption, relating the amount of adsorbed molecules to pressure at a constant temperature.
According to the Langmuir isotherm for non-dissociative adsorption, the adsorbate forms a reversible monolayer on identical surface sites that do not interact with each other.
Consider gas A adsorbing reversibly on surface M, with adsorption governed by the rate constant ka and desorption by kd. The adsorption rate depends on pressure and the number of vacant sites, while the desorption rate depends on the number of occupied sites.
At equilibrium, equating these rates yields the Langmuir equation, linking fractional coverage to pressure through the parameter α— the ratio of the adsorption and desorption rate constants.
The modified Langmuir isotherm explains dissociative adsorption, where diatomic molecules dissociate into atoms and occupy separate sites on the adsorbent surface. At equilibrium, equating the adsorption and desorption rates and rearranging the expression gives the modified Langmuir equation.
In both models, fractional coverage increases linearly at low pressures and approaches saturation only at very high pressures, where most surface sites are occupied.
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Q1: What is the Langmuir isotherm and how does it describe adsorption?
The Langmuir isotherm describes chemisorption by relating the amount of adsorbed molecules to pressure at constant temperature. It assumes adsorbate molecules form a reversible monolayer on identical, non-interacting surface sites. At equilibrium, the adsorption rate equals the desorption rate, yielding an equation that links fractional coverage to pressure through a parameter representing the ratio of adsorption and desorption rate constants.
Q2: How does fractional coverage change with pressure in the Langmuir model?
At low pressures, fractional coverage increases linearly with partial pressure of gas molecules. As pressure increases, coverage rises more gradually and approaches saturation only at very high pressures where most surface sites are occupied. This behavior reflects the competition between adsorption collisions and desorption from occupied sites.
Q3: What are the four key assumptions underlying the Langmuir isotherm?
The Langmuir model assumes adsorption cannot exceed monolayer coverage, all surface sites are equivalent, molecules adsorb only at vacant sites, and there are no interactions between adsorbed molecules. These assumptions simplify the mathematical treatment of gas-surface interactions and make the model applicable to many chemisorption systems.
Q4: How does dissociative adsorption differ from non-dissociative adsorption?
In non-dissociative adsorption, each molecule occupies one surface site and fills the surface rapidly. In dissociative adsorption, diatomic molecules dissociate into atoms that occupy separate sites, requiring a pair of adjacent vacant sites. This stoichiometric difference means dissociative adsorption progresses more slowly and shows different pressure dependence in the modified Langmuir equation.
Q5: What role do adsorption and desorption rate constants play in the Langmuir equation?
The adsorption rate depends on pressure and vacant sites, governed by the adsorption rate constant. The desorption rate depends on occupied sites, governed by the desorption rate constant. At equilibrium, these rates are equal. The ratio of these constants, called alpha, directly determines how fractional coverage responds to changes in pressure.
Q6: When is the Freundlich isotherm more accurate than the Langmuir model?
The Freundlich isotherm is often more accurate than the Langmuir isotherm at intermediate pressures. Unlike Langmuir, it allows for multiple types of adsorption sites on the solid, each with different heats of adsorption. However, the Freundlich model is not valid at high pressures and is typically applied to adsorption of solutes from liquid solutions onto solids.
Q7: How does dynamic equilibrium establish the Langmuir isotherm relationship?
Dynamic equilibrium occurs when the rate of molecules colliding with and adsorbing onto the surface equals the rate of desorption from occupied sites. At this point, there is no net change in surface coverage. Equating the adsorption and desorption rate expressions and solving yields the Langmuir isotherm, which mathematically relates surface coverage to gas phase pressure.