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Isoterme di Adsorbimento I
Le isoterme di adsorbimento sono modelli matematici che descrivono come le molecole in una fase gassa o liquida interagiscono con le superfici. Due de…
Le isoterme di adsorbimento di tipo I descrivono la chemisorbtione, mettendo in relazione la quantità di molecole adsorbite alla pressione a una temperatura costante.
Secondo l'isoterma di Langmuir per l'adsorbimento non dissociativo, l'adsorbato forma un monostrato reversibile su siti superficiali identici che non interagiscono tra loro.
Consideriamo il gas A che adsorbisce in modo reversibile sulla superficie M, con l'adsorbimento governato dalla costante di velocità ka e dalla desorbia da kd. Il tasso di adsorbimento dipende dalla pressione e dal numero di siti vuoti, mentre il tasso di disorbimento dipende dal numero di siti occupati.
All'equilibrio, equiparando questi tassi si ottiene l'equazione di Langmuir, che collega la copertura frazionaria alla pressione tramite il parametro α— il rapporto tra le costanti della velocità di adsorbimento e di disorbio.
L'isoterma di Langmuir modificata spiega l'adsorbimento dissociativo, in cui molecole diatomiche si dissociano in atomi e occupano siti separati sulla superficie adsorbente. All'equilibrio, eguagliando i tassi di adsorbimento e disorbimento e riorganizzando l'espressione si ottiene l'equazione di Langmuir modificata.
In entrambi i modelli, la copertura frazionaria aumenta linearmente a basse pressioni e si avvicina alla saturazione solo a pressioni molto elevate, dove la maggior parte dei siti superficiali è occupata.
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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.