Freundlich Isotherm

Understanding Freundlich Isotherm

Definition and Explanation

The Freundlich isotherm is an empirical equation that describes the adsorption of solutes from a liquid onto a solid surface. It was found quite useful for heterogeneous surfaces. Mathematically, it is well expressed as:

$
x/m = kP^{1/n}
$

where:
$x/m$ is the amount of adsorbate per unit mass of adsorbent.
$P$ is the pressure of the adsorbate.
$k$ and $n$ are empirical constants specific to the

Freundlich adsorption isotherm:

Freundlich, in 1909, gave an empirical relationship between the quantity of gas adsorbed by unit mass of solid adsorbent and pressure at a particular temperature. The relationship can be expressed by the following equation:

x/m = kP^{1/n} (n>1)

where x is the mass of the gas adsorbed on mass m of the adsorbent at pressure P, k, and n are constants that depend on the nature of the adsorbent and the gas at a particular temperature.

The relationship is generally represented in the form of a curve where the mass of the gas adsorbed per gram of the adsorbent is plotted against pressure (Fig). These curves indicate that at a fixed pressure, there is a decrease in physical adsorption with an increase in temperature. These curves always seem to approach saturation at high pressure.

Logarithmic graph of Freundlich isotherm

Taking the logarithm of Eq. we get

$\log \frac{\mathrm{x}}{\mathrm{m}}=\log \mathrm{k}+\frac{1}{\mathrm{n}} \log \mathrm{p}$

The validity of the Freundlich isotherm can be verified by plotting log(x/m) on the y-axis (ordinate) and log(p) on the x-axis (abscissa). If it comes to be a straight line, the Freundlich isotherm is valid, otherwise not (Fig.). The slope of the straight line gives the value of 1/n. The intercept on the y-axis gives the value of log k.

Key Concepts

• Heterogeneous Surfaces: The Freundlich Isotherm considers that an adsorbent surface consists of a variety of sites that possess different energies.
• Non-linear Adsorption: The adsorbed amount is related nonlinearly to the concentration of the adsorbate. This non-linearity is a characteristic of real-world surfaces and their complex nature.

Features of Freundlich Isotherm

Assumptions and Characteristics

• Empirical Nature: Freundlich isomerism is empirical in nature and not based on any theoretical model.
• Heterogeneity: It considers a diversified adsorption site heterogeneity with a variable affinity towards the adsorbate.
• Limitations: Though versatile, it fails to predict adsorption at high pressures where monolayer adsorption may dominate.

Comparison to Other Isotherms

• Langmuir Isotherm: Presumes a homogeneous surface with a finite number of identical sites leading to monolayer adsorption.
• BET Isotherm: Development of the Langmuir model for multi-layer adsorption that is very often applied for porous materials.

Examples of Use

• Water Treatment: One major area of application for Freundlich Isotherm is the design of the activated carbon-based water purification process intended for removing some contaminants.
• Pharmaceuticals: It finds application in the study of drug adsorption onto a variety of carriers that explain, in detail, their impact on drug delivery and efficiency.

Relevance and Applications

Environmental Engineering

The Freundlich Isotherm has a very important place in environmental engineering while designing systems to treat both polluted water and air. For example, it guides the type of adsorbent to be used, such as activated carbon, for the removal of organic contaminants from water. Because of the developed understanding of how pollutants behave in various adsorbents, engineers can fine-tune treatment processes for maximum efficiency while adhering to environmental legislation.

Pharmaceuticals

The Freundlich isotherm has been widely applied in pharmaceutical applications aimed at elucidating drug interactions with excipients and delivery systems. This information is highly critical in the formulation of products that will provide the best conditions for the release and subsequent uptake of active ingredients. In this regard, the study of adsorption/runoff of antibiotics by/in various carriers, for instance, would be Six months after enrollment, Morietal. assessed whether adjustments to the medication regimen had been made and if decisions about the medication regimens were based on pharmacokinetic consultation.

Food Science

In food science, the Freundlich isotherm enables design processes related to food preservation and flavor improvement. For example, the optimization of the adsorption mechanisms that transfer Flavors and preservatives onto food packing materials to maintain freshness and flavor over a longer period.

Academic Research

The Freundlich isotherm can be considered one of the simplest models that can be found in any academic research where the characterization of new materials makes use of studying their adsorption properties. This model will help in studying interactions between adsorbates and adsorbents at an atomic scale; hence, advanced material development for tenable adsorption properties ensues.

Recommended topic video on (Freundlich Isotherm)

Some Solved Examples

Example 1

Question:
According to Freundlich adsorption isotherm, which of the following relationships is correct?

1) $(\frac{x}{m} \propto P^0) $
2) $(\frac{x}{m} \propto P^1)$
3) $(\frac{x}{m} \propto P^{1/n})$
4) All the above are correct for different ranges of pressure

Solution:
The correct answer is option (4). According to the Freundlich adsorption isotherm, $(\frac{x}{m} = K P^{1/n})$, where (n) is a constant greater than 1. This equation shows that $(\frac{x}{m})$ varies with pressure in different ways depending on the value of (n).

Example 2

Question:
If the adsorption of a gas follows the Freundlich adsorption isotherm, what is $(\frac{x}{m})$ proportional to?

1) $(P^2)$
2) $(P^{1/4})$
3) $(P^{1/2})$
4) (P)

Solution:
The correct answer is option (3), $(P^{1/2})$. According to the Freundlich adsorption isotherm, $(\frac{x}{m} = K P^{1/n})$, where (n) typically equals 2 for many cases. Thus, $(\frac{x}{m})$ is proportional to $(P^{1/2})$ when (n = 2).

Example 3

Question:
If the plot of $(log \frac{x}{m})$ versus (log P) for a gas adsorption process follows the Freundlich adsorption isotherm, what is $(\frac{x}{m})$ proportional to?

1) $(P^{2/3})$
2) $(P^{3})$
3) $(P^{2})$
4) $(P^{3/2})$

Solution:
The correct answer is option (1), $(P^{2/3})$. In a logarithmic plot where $(log \frac{x}{m})$ versus (log P) yields a slope corresponding to $(\frac{1}{n})$ in the Freundlich equation $((\frac{x}{m} = K P^{1/n}))$, and if the slope is $(\frac{2}{3})$, then $(\frac{x}{m})$ is proportional to $(P^{2/3})$.

These examples demonstrate the application of the Freundlich adsorption isotherm and how $(\frac{x}{m})$ varies with pressure under different conditions.

Summary

The Freundlich isotherm is just such a versatile, very widely applied model for the description of adsorption on heterogeneous surfaces. It, therefore, considers a more practical presentation of real-life adsorption processes by putting into consideration the diversity of the adsorption sites and their different affinities toward adsorbate. Premise: Basically, some concepts, key characteristics, and different applications of Freundlich isotherm have been explored. From environmental engineering to the pharma and food industries, Freundlich isotherm becomes very essential in optimizing adsorption processes toward developing new solutions to problems of these realities. Hence, understanding this model is also of importance to the scientists and engineers who are involved in deciding the optimization of efficiency and effectiveness of adsorption-based technologies.