Question

Freundlich isotherms is not applicable at (a) high pressure (b) low pressure (c) \(273 \mathrm{~K}\) (d) room temperature

Short answer

The answer is (a) high pressure.

Step-by-step solution

Understanding Freundlich Adsorption Isotherm

The Freundlich isotherm is an empirical relation which, under certain conditions, describes adsorption phenomena. However, it has limitations: it is not valid for extremely high or low pressures.

Evaluate Options

Let's look at each option: Option (a) high pressure - the Friendschlich isotherm is not valid at very high pressures. Option (b) low pressure - the model is also applicable at low pressures. So, this option is not correct. Options (c) at \(273 \mathrm{~K}\) and (d) room temperature - are temperature conditions, and Freundlich isotherm does not directly mention these are factors that affect its applicability.

Decide Correct Answer

Looking at the evaluated options, it becomes clear that the statement 'the Freundlich isotherm is not valid at high pressures', is correct. So, the right answer is option (a).

Key concepts

Adsorption Phenomena

Adsorption is a surface phenomenon where molecules, atoms, or ions from a gas, liquid, or dissolved solid adhere to a surface. This process creates a film of the adsorbate on the surface of the adsorbent.

Adsorption is different from absorption, where a substance diffuses into a liquid or solid to form a solution. In adsorption, the concentration of the adsorbate is higher on the surface than in the bulk phase. This process is crucial in various applications, such as in air filters, water purification, and in catalysts used in chemical reactions.

The extent of adsorption can be influenced by multiple factors, including the surface area of the adsorbent, the concentration of adsorbate, temperature, and pressure of the system. The study of adsorption isoforms like the Freundlich isotherm provides valuable insights into how these factors interact.

Empirical Relation

The Freundlich adsorption isotherm is an empirical relationship that describes how the amount of a substance adsorbed on a surface relates to the pressure or concentration of the substance in contact with the adsorbent.

An empirical relation, like the Freundlich isotherm, is based on experimental observations rather than derived from first principle equations. The isotherm can be represented by the equation: \[x/m = kP^{1/n}\] where:

• \(x\) = amount of adsorbate,
• \(m\) = mass of adsorbent,
• \(k\) and \(n\) are empirical constants for each adsorbent-adsorbate system,
• \(P\) = pressure of adsorbate.

This model implies that the adsorption capacity increases as the pressure increases, but not proportionately. It serves as a heuristic model that helps understand adsorption behavior in a range of conditions but has limitations at extremely high or low pressures.

Pressure Effects on Adsorption

The pressure of a gas plays a significant role in the adsorption process. According to the Freundlich adsorption isotherm, the quantity of gas adsorbed on a solid surface is partially dependent on the pressure of the gas.

As the pressure increases, gas molecules have a higher probability of colliding with the adsorbent surface, which can lead to an increase in adsorption. However, the Freundlich isotherm suggests that the relationship between pressure and adsorption is not linear, but rather a curve that eventually hits a plateau where increasing pressure will no longer result in additional adsorption.

This plateau is more significant at high pressures because at that point, most of the available sites for adsorption are occupied. The isotherm does not apply at very high pressures as the assumption of heterogeneous surface energies becomes less valid and other models, like Langmuir isotherm, may offer a better fit. Overall, the effect of pressure on adsorption is complex and depends on the specific system and conditions.