Problem 33 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following is the correct Freundlich's formula? (a) \(\mathrm{w} / \mathrm{m}=\mathrm{kP}^{1 / \mathrm{n}}\) (b) \(\mathrm{w} / \mathrm{m}=\mathrm{kP}^{2 \mathrm{n}}\) (c) \(\mathrm{w} / \mathrm{m}=\mathrm{kP}^{\mathrm{n}}\) (d) \(\mathrm{m} / \mathrm{w}=\mathrm{kp}^{1 / \mathrm{n}}\)

Step-by-Step Solution

Answer

Option (a) \( \frac{w}{m} = kP^{1/n} \) is the correct Freundlich's formula.

Step 1: Understanding Freundlich's Isotherm

Freundlich's adsorption isotherm describes how adsorbate molecules distribute between the liquid phase and the solid phase at equilibrium. It is expressed as: \( \left(\frac{w}{m}\right) = kP^{1/n} \), where \( w \) is the mass of the adsorbate, \( m \) is the mass of the adsorbent, \( P \) is the pressure, \( k \) and \( n \) are constants.

Step 2: Analyzing the Options

Look at each given option: (a) \( \frac{w}{m} = kP^{1/n} \), (b) \( \frac{w}{m} = kP^{2n} \), (c) \( \frac{w}{m} = kP^{n} \), (d) \( \frac{m}{w} = kp^{1/n} \). Compare them with the general form of Freundlich's isotherm equation.

Step 3: Matching the Correct Formula

The correct formula matches the standard form \( \frac{w}{m} = kP^{1/n} \). Notice that option (a) is exactly the same as this general form, hence it corresponds to Freundlich's equation correctly.

Key Concepts

Adsorbate Distribution

Adsorbate distribution refers to how particles, called adsorbates, spread or partition between liquid and solid surfaces during the process of adsorption. In many applications, including purification processes and chemical reactions, knowing how adsorbates are distributed is crucial. The distribution is influenced by factors like:

• The type of adsorbate - whether it's a gas or a dissolved solid can affect interaction with the adsorbent surface.
• The properties of the adsorbent - its surface area and porosity play vital roles in how adsorbates bind.
• Temperature and pressure conditions - these environmental conditions determine how much and how quickly adsorbates will adhere.

Equilibrium Adsorption

Equilibrium adsorption occurs when the rate at which adsorbates adhere to the adsorbent surface equals the rate at which they leave. At this point, the amount of adsorbate on the adsorbent no longer changes, signifying a stable situation. This balance is vital as it demonstrates the maximum adsorption capacity of the system under the given conditions.

• Adsorption processes initially see rapid changes until equilibrium is reached.
• Understanding equilibrium helps scientists design more efficient industrial processes.
• The equilibrium state is important for technological applications such as water purification, where precise adsorption levels are needed.

Studying equilibrium adsorption enables researchers to predict how a system will respond to changing conditions.

Isotherm Equation

An isotherm equation models the relationship between the concentration of the adsorbate and the amount adsorbed at constant temperature. Freundlich's adsorption isotherm is a widely used isotherm in adsorption studies, represented as:\[ \left(\frac{w}{m}\right) = kP^{1/n} \]Where:
- \( w \) is the mass of the adsorbate,
- \( m \) is the mass of the adsorbent,
- \( P \) is the pressure or concentration constant,
- \( k \) and \( n \) are system-specific constants.
The Freundlich equation is non-linear, indicating varying adsorption intensity across different pressures or concentrations.Applications include predicting how different substances will adsorb under certain conditions, crucial in optimizing industrial adsorption processes like gas purification.

Adsorption Constants

In Freundlich's adsorption isotherm, the constants \( k \) and \( n \) are pivotal in understanding adsorption behavior.

• \( k \) is the Freundlich constant indicating the adsorption capacity. A higher \( k \) value implies greater capacity.
• \( n \) is the heterogeneity index depicting surface diversity. Values of \( n \) greater than 1 suggest favorable adsorption conditions.

By analyzing these constants, scientists can infer about the strength and extent of adsorption processes on specific adsorbents. Accurate determination of \( k \) and \( n \) aids in designing adsorbents for targeted applications and evaluating performance efficiency over time.Moreover, these constants provide essential insights in environmental studies, where the removal of pollutants from water or air is critical.