Problem 156 - A Complete Resource Book in Chemistry for JEE Main

Question

Freundlich adsorption isotherm is given by expression \(\frac{x}{m}=k p^{\frac{1}{n}}\) which of the following conclusions can be drawing from this expression (a) When \(\frac{1}{\mathrm{n}}=0\), the adsorption is independent of pressure. (b) When \(\frac{1}{n}=0\), the adsorption is independent of pressure. (c) When \(\mathrm{n}=0\), plot of \(\frac{\mathrm{x}}{\mathrm{m}} \mathrm{Vs} \mathrm{p}\) is a curve. (d) When \(\mathrm{n}=\mathrm{m} 0, \frac{\mathrm{x}}{\mathrm{m}}\) Vs p graph is a line paralle to \(\mathrm{x}\) axis.

Step-by-Step Solution

Answer

The correct statement is option (a): when \( \frac{1}{n} = 0 \), adsorption is independent of pressure.

Step 1: Understanding the Freundlich Isotherm

The Freundlich adsorption isotherm is expressed as \( \frac{x}{m}=kp^{\frac{1}{n}} \), where \( \frac{x}{m} \) is the amount of solute adsorbed per unit mass of adsorbent, \( k \) is a constant, \( p \) is the pressure, and \( n \) is a positive constant greater than 1 that indicates the intensity of adsorption.

Step 2: Analyzing the Effect of \( \frac{1}{n} = 0 \)

If \( \frac{1}{n} = 0 \), it implies \( n \to \infty \). In this situation, \( kp^{0} = k \cdot 1 = k \). Thus, \( \frac{x}{m} = k \). The amount of adsorption (\( \frac{x}{m} \)) becomes constant for any pressure \( p \), indicating that adsorption is independent of pressure.

Step 3: Chemically Descriptive Terms

For the given possibilities, note that option (a) with "\( \frac{1}{n} = 0 \)" accurately describes the condition as \( n \to \infty \), where adsorption is independent of pressure. Option (b) incorrectly repeats the same statement using different wording, which appears to be a typographical error. Options (c) and (d) could be analyzed if they proposed reasonable values of \( n \).

Key Concepts

Adsorption

Adsorption is a process where molecules or atoms from a gas or liquid adhere to a solid surface. This is not to be confused with absorption, where a substance is absorbed into a material. Adsorption is crucial in many natural and industrial processes because it allows the concentration of substances from solutions or the air.
Adsorption can occur due to physical forces or chemical bonds being formed on the surface of a material. The strength of adsorption can vary widely, affecting how easily the adsorbed molecules can be removed.

• Physical adsorption involves weak van der Waals forces, making it easily reversible.
• Chemical adsorption involves chemical bonds, often making it stronger and more specific to the material used.

Understanding adsorption is essential in fields like catalysis, filtration, and sensor technology because it affects how materials interact with their surroundings and other substances.

Pressure Dependency

Pressure dependency in adsorption refers to how the amount of material being adsorbed changes with variations in pressure. In the Freundlich isotherm, this relationship is captured by the power term { rac{1}{n} } which influences how adsorption varies with pressure.
Under certain conditions, such as when { rac{1}{n} = 0 }, adsorption becomes independent of pressure; the amount adsorbed remains constant regardless of the pressure.
In general, higher pressures lead to increased adsorption, assuming the adsorbent's surface is not saturated. This is because more molecules are available to interact with the surface. However, this relationship doesn't always follow a simple linear trend due to potential limitations in the adsorbent's capacity.

Adsorption Isotherms

An adsorption isotherm is a graphical representation depicting the amount of solute adsorbed onto an adsorbent as a function of its pressure at constant temperature. The Freundlich isotherm, as expressed by { rac{x}{m} = k p^{rac{1}{n}} }, is one of the earliest and most widely used theoretical models to describe adsorption phenomena.
Freundlich isotherms are empirical and describe adsorption on heterogeneous surfaces. They are particularly useful for gaining insights when dealing with non-uniform energy distribution over the adsorbent surface.

• A linear form of the Freundlich equation is obtained using logarithms, which can be useful for data interpretation and analysis.
• The constant {n} reflects how favorable the adsorption process is; a value greater than one often indicates a good adsorption potential.

Understanding adsorption isotherms is critical for designing systems where adsorption is key, such as air purification systems or wastewater treatment facilities.

Chemical Equilibrium

Chemical equilibrium in adsorption contexts refers to when the rate of adsorption is balanced by the rate of desorption.
At this point, no net change in the amount of solute on the adsorbent occurs, implying a dynamic equilibrium where molecules constantly switch between being adsorbed and desorbed.
The Freundlich isotherm helps describe this balance by showing how, at constant temperature, the amount of adsorbed material reaches a steady state relative to the pressure. Understanding these interactions allows scientists and engineers to predict how systems will behave under varying conditions and design processes to maintain efficiency and stability across many industrial applications. Equilibrium concepts also form the basis for optimizing conditions under which adsorption systems operate, improving operational efficiency, and reducing costs.

Surface Chemistry

Surface chemistry is the study of chemical reactions that occur at the interface of two phases, such as solid-liquid or solid-gas systems. This field examines how the surface properties of materials influence their interactions with other substances.
Adsorption is a key aspect of surface chemistry, as it involves molecules interacting with the surface of materials. Alterations in surface properties can drastically change how a substance behaves in adsorption.• Surface area: Greater surface areas typically enhance adsorption capacity. • Porosity: The presence of pores increases available surface sites for adsorption. Surface chemistry principles guide the development of more effective adsorbent materials used in numerous applications, from environmental cleanup to developing catalysts for chemical reactions.
In the Freundlich adsorption context, surface heterogeneity plays a critical role, offering diverse energy sites for adsorption. These complex interactions at surfaces form a basis for technological innovations and improvements across various scientific fields.