Question

In Langmuir's model of adsorption of a gas on a solid surface (a) the rate of dissociation of adsorbed molecules from the surface does not depend on the surface covered (b) the adsorption at a single site on the surface may involve multiple molecules at the same time (c) the mass of gas striking a given area of surface is proportional to the pressure of the gas (d) the mass of gas striking a given area of surface is independent of the pressure of the gas

Short answer

Correct options: (a) and (c).

Step-by-step solution

Understanding Langmuir's Model

Langmuir's model describes the adsorption process where gas molecules adhere to a solid surface forming a monolayer. This model assumes that adsorption occurs at distinct sites on the surface and that there is no interaction between adsorbed molecules.

Assessing the Given Options

Let's analyze each option based on Langmuir's assumptions: (a) This suggests that the rate of dissociation of adsorbed molecules is independent of how much of the surface is covered, aligning with Langmuir's view that adsorption sites are independent. (b) This option implies multiple molecules can adsorb at one site at a time, which contradicts the Langmuir model that assumes one molecule per site. (c) Langmuir's model aligns with this statement because the number of gas molecules hitting and adsorbing on a surface relates to the concentration of the gas, which is proportional to its pressure. (d) This indicates that adsorption doesn't depend on gas pressure, which contradicts the Langmuir model.

Determine the Correct Statements

Based on the evaluation: - Option (a) fits the Langmuir model since it suggests independence of surface coverage. - Option (b) is incorrect because Langmuir's model allows only one molecule per site. - Option (c) correctly states the relationship between pressure and adsorption rate. - Option (d) contradicts the model as Langmuir's concept of adsorption depends on gas pressure.

Key concepts

Monolayer Adsorption

In the realm of physical chemistry, monolayer adsorption refers to a scenario wherein molecules from a gas adhere to a solid surface to form a single layer, or monolayer. This is a foundational concept in Langmuir's adsorption isotherm model. Langmuir assumed that each adsorption site on a solid surface can bind to only one gas molecule. Here's how it works: - **Single Molecule per Site**: Once a molecule attaches to an adsorption site, no other molecule can stick to that particular site until the first one leaves. - **Homogeneous Surface**: It is assumed that all adsorption sites are energetically equivalent and identical, ensuring consistent binding energies across the surface. Because only one layer forms, the model simplifies calculations and predictions for adsorption dynamics. This also implies that once a monolayer is complete, no further adsorption can occur until desorption makes space for more molecules to adhere.

Adsorption Sites

Adsorption sites are critical to the Langmuir adsorption model, acting as unique spots on a solid surface where gas molecules can attach. This concept is visualized as a checkerboard: - **Distinct Positions**: Each adsorption site is like a square on a checkerboard, designed to host just one molecule at a time. - **No Molecular Interaction**: Molecules do not interact with each other once adsorbed; they only interact with the surface directly. This implies that the presence or absence of adjacent molecules doesn’t impact the binding of a new molecule. Langmuir's isotherm model highlights that adsorption cannot occur on sites that are already occupied. Furthermore, the model assumes that every site has the same energy level and accessibility, leading to uniform behavior across the entire surface.

Gas Pressure and Adsorption

Gas pressure plays a vital role in Langmuir's adsorption model. Essentially, the pressure of a gas determines how many of its molecules strike the surface, influencing the rate and extent of adsorption. Here's why pressure is crucial: - **Pressure-Proportional Rate**: The rate of adsorption is directly proportional to the gas pressure. Higher pressure means more molecules are available to hit and adhere to the surface. - **Dynamic Equilibrium**: As pressure increases, adsorption initially increases until the equilibrium is reached, where the rate of adsorption equals the rate of desorption. By understanding the influence of gas pressure, Langmuir's model helps predict adsorption behavior under varying environmental conditions. This concept underscores why some options in exercises align or misalign with the Langmuir model depending on how they interpret pressure's impact on adsorption.