Problem 91 - A Complete Resource Book in Chemistry for JEE Main

Question

Freundlich adsorption isotherm gives a straight line on plotting (a) \(\mathrm{x} / \mathrm{m}\) vs \(\mathrm{P}\) (b) \(\log \mathrm{x} / \mathrm{m}\) vs \(\mathrm{P}\) (c) \(\log x / m\) vs \(\log P\) (d) \(\mathrm{x} / \mathrm{m}\) vs \(1 / \mathrm{P}\)

Step-by-Step Solution

Answer

(c) \( \log x / m \) vs \( \log P \).

Step 1: Understand Freundlich adsorption isotherm

The Freundlich adsorption isotherm describes the adsorption characteristics of a solute onto a heterogeneous surface. It is an empirical relationship that explains how molecules accumulate at an interface.

Step 2: Recall the Freundlich Equation

The equation representing the Freundlich adsorption isotherm is given by: \[ \frac{x}{m} = k P^{1/n} \] where \(x\) is the amount of adsorbate, \(m\) is the mass of adsorbent, \(k\) and \(1/n\) are constants, and \(P\) is the pressure of the adsorbate.

Step 3: Convert to a Logarithmic Form

By taking the logarithm of both sides of the Freundlich equation, we obtain: \[ \log \left( \frac{x}{m} \right) = \log k + \frac{1}{n} \log P \] This is a straight-line equation similar to \( y = mx + c \), where \( \log (x/m) \) is on the y-axis and \( \log P \) is on the x-axis.

Step 4: Identify the Correct Plot from Options

Based on the logarithmic form, the correct option is \( \log (x/m) \) vs \( \log P \), which corresponds to a straight line. This is because the plot of \( \log (x/m) \) against \( \log P \) aligns with the linear equation format y = mx + c.

Key Concepts

Adsorption

Adsorption is a surface phenomenon where molecules from a gas or liquid accumulate on the surface of a solid or a liquid. The substance that gets accumulated is known as the adsorbate, while the surface on which the accumulation occurs is referred to as the adsorbent.

This process is distinct because it occurs at the interface between phases, such as gas-solid or liquid-solid. Adsorption is crucial in various industrial and natural processes.

• Key Characteristics of Adsorption: It is generally a reversible process.
• Types of Adsorption: There are two types—physical adsorption, where the forces are weak van der Waals forces, and chemical adsorption, where new chemical bonds form.

These unique attributes make adsorption an essential topic in fields such as chemistry and environmental science.

Heterogeneous Surface

A heterogeneous surface possesses non-uniform properties throughout its structure. When adsorption occurs on a heterogeneous surface, it means different parts of the surface have different energies of adsorption.

This variability can significantly affect the adsorption capacity and mechanisms. On such surfaces, molecules might prefer particular spots with higher affinity, leading to a more complex adsorption process.

• Importance: Heterogeneous surfaces are common in real-world applications, such as catalysts and activated carbons.
• Impact on Adsorption: Different sites result in varied adsorption energies, complicating the relationship between pressure and adsorption.

The Freundlich isotherm is an excellent model to describe adsorption on heterogeneous surfaces due to its empirical nature.

Empirical Relationship

An empirical relationship is one that has been derived from observation and experiment, rather than purely theoretical models.

The Freundlich adsorption isotherm is an example of such an empirical relationship. Instead of being based on fundamental constants, this relationship emerges from experimental data.

• Application: It's particularly useful in cases where theoretical modeling is too complex or not feasible.
• Flexibility: Being empirical, it can fit a wide range of adsorption scenarios.

This adaptability makes it a robust tool for understanding adsorption without the need for in-depth theoretical computations.

Adsorbate

An adsorbate is the molecule or atom that gets concentrated on the surface of the adsorbent during adsorption.

The characteristics of the adsorbate—such as its size, shape, and chemical reactivity—can significantly influence how adsorption occurs.

• Role in Adsorption: The more chemically active an adsorbate is, the stronger the adsorption.
• Variables: Adsorbate pressure is a critical variable in adsorption isotherms, as seen in the Freundlich model.

Understanding the nature of the adsorbate aids in predicting the behavior and efficiency of adsorption processes.

Isotherm Equation

The isotherm equation is a mathematical expression that describes how a substance adheres to a surface at constant temperature.

In the context of adsorption, isotherms illustrate the relationship between the concentration of adsorbate and the extent of adsorption on the adsorbent.

• Linear Form: The Freundlich isotherm, in its linear form, shows a plot of \( \log(\frac{x}{m}) \) against \( \log P \), resulting in a straight line.
• Formula Details: The equation \ \left( \frac{x}{m} = k P^{1/n} \right) \, consists of constants \k\ and \frac{1}{n}\ which adapt based on the system being studied.

Isotherms are essential tools in chemical engineering and environmental studies for optimizing adsorption processes.