Freundlich Isotherm

Freundlich Isotherm

Edited By Shivani Poonia | Updated on Jul 02, 2025 06:34 PM IST

Imagine you are a coffee lover and obviously the perfect brewer from home. Now, the coffee grounds you use are not solely for flavor purposes; they play a very critical role in filtering and trapping impurities so that your coffee tastes just right—an everyday application of adsorption where the liquid phase molecules stick to the surface of the solid coffee grounds. The Freundlich isotherm, one of the models describing adsorption, will explain the process on a heterogeneous surface like coffee grounds and thus inform one how different categories of molecules interact with the surface at different concentrations.

This Story also Contains
  1. Understanding Freundlich Isotherm
  2. Freundlich adsorption isotherm:
  3. Logarithmic graph of Freundlich isotherm
  4. Features of Freundlich Isotherm
  5. Comparison to Other Isotherms
  6. Examples of Use
  7. Relevance and Applications
  8. Food Science
  9. Some Solved Examples
  10. Summary
Freundlich Isotherm
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.

Surface Chemistry Image 1

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.
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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.

Frequently Asked Questions (FAQs)

1. How does the Freundlich isotherm differ from the Langmuir isotherm?
The Freundlich isotherm assumes a heterogeneous surface with non-uniform distribution of adsorption heat, while the Langmuir isotherm assumes a homogeneous surface with uniform adsorption energy. Freundlich isotherm allows for multilayer adsorption, whereas Langmuir isotherm is limited to monolayer adsorption.
2. Can the Freundlich isotherm predict multilayer adsorption?
Yes, the Freundlich isotherm can accommodate multilayer adsorption. Unlike the Langmuir isotherm, it doesn't assume a maximum adsorption capacity, allowing for the possibility of multiple layers of adsorbate molecules on the surface.
3. Can the Freundlich isotherm be used to predict adsorption behavior at very low concentrations?
Yes, the Freundlich isotherm is often more accurate than the Langmuir isotherm at low concentrations. It can describe adsorption behavior in dilute solutions where the adsorbate-adsorbate interactions are minimal.
4. What are the limitations of the Freundlich isotherm?
The Freundlich isotherm has limitations: it lacks a theoretical basis, doesn't have a saturation limit for adsorption, and is not applicable at very high concentrations. It also doesn't provide information about the maximum adsorption capacity.
5. How does competitive adsorption affect the applicability of the Freundlich isotherm?
Competitive adsorption can complicate the applicability of the Freundlich isotherm. While the model can still be used, the presence of multiple adsorbates competing for sites may alter the observed K and 1/n values compared to single-component systems.
6. What is the importance of the Freundlich isotherm in catalysis studies?
In catalysis studies, the Freundlich isotherm is important for understanding the adsorption of reactants onto catalyst surfaces. It can provide insights into the distribution of active sites and help predict catalyst performance under various conditions.
7. How does the pH of the solution affect the Freundlich isotherm parameters?
The pH of the solution can significantly affect the Freundlich isotherm parameters. Changes in pH can alter the surface charge of the adsorbent and the ionization state of the adsorbate, potentially changing both K and 1/n values.
8. Can the Freundlich isotherm predict adsorption behavior at high pressures or concentrations?
The Freundlich isotherm is less accurate at very high pressures or concentrations. It doesn't account for saturation effects, potentially overestimating adsorption at extreme conditions where surface saturation becomes significant.
9. Can the Freundlich isotherm be used to calculate the surface area of an adsorbent?
Unlike the BET isotherm, the Freundlich isotherm is not typically used to calculate surface area. It doesn't provide direct information about monolayer coverage, which is crucial for surface area determination.
10. How does the polarity of the adsorbate affect the Freundlich isotherm parameters?
The polarity of the adsorbate can significantly affect the Freundlich parameters. More polar adsorbates may show higher K values on polar surfaces due to stronger interactions. The 1/n value might change if polarity affects how the adsorbate interacts with different surface sites.
11. What does the value of 1/n in the Freundlich equation indicate?
The value of 1/n in the Freundlich equation indicates the adsorption intensity or surface heterogeneity. When 1/n is closer to 0, the surface is more heterogeneous, while values closer to 1 indicate a more homogeneous surface.
12. What is the physical significance of the Freundlich constant K?
The Freundlich constant K is related to the adsorption capacity of the adsorbent. A higher value of K indicates a greater adsorption capacity, meaning the adsorbent can hold more adsorbate at a given equilibrium concentration.
13. How does the Freundlich isotherm account for surface heterogeneity?
The Freundlich isotherm accounts for surface heterogeneity through the parameter 1/n. As 1/n decreases (becomes closer to 0), it indicates a more heterogeneous surface with a wider distribution of adsorption energies across different adsorption sites.
14. What does it mean when the Freundlich exponent (1/n) is greater than 1?
When the Freundlich exponent (1/n) is greater than 1, it indicates cooperative adsorption, where the presence of adsorbed molecules increases the likelihood of further adsorption. This is less common and suggests a complex adsorption mechanism.
15. How does the Freundlich isotherm relate to adsorption favorability?
The Freundlich isotherm relates to adsorption favorability through the value of 1/n. When 1/n is between 0 and 1, adsorption is considered favorable. The closer 1/n is to 0, the more favorable the adsorption process.
16. How can the Freundlich isotherm be used to optimize adsorption processes in industrial applications?
In industrial applications, the Freundlich isotherm helps optimize adsorption processes by predicting adsorbent performance under various conditions. It aids in selecting appropriate adsorbents, determining optimal operating conditions, and estimating adsorbent capacity and lifespan.
17. Can the Freundlich isotherm be applied to liquid-liquid extraction processes?
While primarily used for solid-liquid or gas-solid systems, the Freundlich isotherm concept can be adapted to describe some liquid-liquid extraction processes, especially when dealing with the partitioning of solutes between two immiscible liquid phases.
18. How does the presence of a solvent affect the Freundlich isotherm parameters in liquid-phase adsorption?
The solvent can significantly affect Freundlich parameters in liquid-phase adsorption. It may compete with the adsorbate for surface sites, alter adsorbate-surface interactions, and change the effective concentration of the adsorbate, potentially modifying both K and 1/n values.
19. What is the significance of the Freundlich isotherm in understanding the adsorption of mixtures?
For mixtures, the Freundlich isotherm can be applied to individual components, helping understand competitive adsorption. However, interactions between adsorbates may lead to deviations from single-component behavior, requiring more complex multi-component adsorption models.
20. Can the Freundlich isotherm be used to describe chemisorption processes?
While the Freundlich isotherm is more commonly associated with physisorption, it can sometimes describe chemisorption processes, especially when there's a range of binding energies due to surface heterogeneity. However, it may not capture all aspects of chemical bonding.
21. What is the Freundlich isotherm?
The Freundlich isotherm is an empirical model that describes the non-ideal and reversible adsorption of molecules onto a heterogeneous surface. It relates the amount of adsorbate on the adsorbent to the concentration of adsorbate in the solution at equilibrium.
22. What is the mathematical expression for the Freundlich isotherm?
The Freundlich isotherm is expressed as x/m = KCe^(1/n), where x/m is the amount adsorbed per unit mass of adsorbent, Ce is the equilibrium concentration of adsorbate, K is the Freundlich constant related to adsorption capacity, and 1/n is the adsorption intensity.
23. What is the relationship between the Freundlich isotherm and adsorption energy distribution?
The Freundlich isotherm relates to adsorption energy distribution through the 1/n parameter. A smaller 1/n value indicates a wider distribution of adsorption energies, reflecting a more heterogeneous surface with diverse adsorption sites.
24. How does the Freundlich isotherm account for adsorbate-adsorbate interactions?
The Freundlich isotherm indirectly accounts for adsorbate-adsorbate interactions through the parameter 1/n. As 1/n deviates from 1, it suggests stronger adsorbate-adsorbate interactions or surface heterogeneity effects.
25. How does the molecular size of the adsorbate influence the Freundlich isotherm parameters?
The molecular size of the adsorbate can influence both K and 1/n. Larger molecules may result in lower K values due to reduced accessibility to adsorption sites. The 1/n value might change if larger molecules interact differently with the surface heterogeneity.
26. How can you linearize the Freundlich isotherm equation?
The Freundlich isotherm can be linearized by taking the logarithm of both sides: log(x/m) = log K + (1/n)log Ce. This allows for easier graphical representation and determination of constants K and 1/n from the y-intercept and slope, respectively.
27. How do you determine if experimental data fits the Freundlich isotherm?
To determine if data fits the Freundlich isotherm, plot log(x/m) vs. log(Ce). If the resulting graph is a straight line, the adsorption follows the Freundlich model. The slope gives 1/n, and the y-intercept gives log K.
28. What are the implications of a changing 1/n value with adsorbate concentration in the Freundlich isotherm?
A changing 1/n value with adsorbate concentration suggests that the adsorption process becomes more or less favorable as concentration changes. This could indicate complex surface interactions, adsorbate-adsorbate effects, or changes in the accessible surface heterogeneity.
29. How does the Freundlich isotherm relate to the concept of surface coverage?
The Freundlich isotherm doesn't explicitly define surface coverage like the Langmuir isotherm. However, the amount adsorbed (x/m) can be related to surface coverage, with the non-linear nature of the isotherm reflecting how coverage changes with concentration.
30. In what types of adsorption systems is the Freundlich isotherm commonly applied?
The Freundlich isotherm is commonly applied in systems with heterogeneous surfaces, such as activated carbon adsorption of organic compounds from water, adsorption of dyes on various adsorbents, and in some gas-solid adsorption processes.
31. What is the significance of the Freundlich isotherm in environmental applications?
The Freundlich isotherm is significant in environmental applications as it often describes the adsorption of pollutants onto soil, activated carbon, and other natural or engineered adsorbents used in water and air purification processes.
32. Can the Freundlich isotherm be applied to gas adsorption processes?
Yes, the Freundlich isotherm can be applied to gas adsorption processes, particularly for heterogeneous surfaces. It's often used to describe the adsorption of gases on activated carbon and other porous materials.
33. How does temperature affect the Freundlich isotherm?
Temperature affects the Freundlich isotherm by influencing the values of K and 1/n. Generally, an increase in temperature leads to a decrease in adsorption capacity (K) and may change the adsorption intensity (1/n), reflecting the typically exothermic nature of adsorption processes.
34. How does surface area affect the parameters of the Freundlich isotherm?
Surface area generally affects the Freundlich constant K. A larger surface area typically results in a higher K value, indicating greater adsorption capacity. The 1/n value may also change if the increase in surface area alters the distribution of adsorption site energies.
35. What is the significance of the Freundlich isotherm in chromatography?
In chromatography, the Freundlich isotherm helps understand the distribution of analytes between the mobile and stationary phases, especially for non-linear adsorption behaviors. It aids in predicting retention times and peak shapes in complex separations.
36. What role does the Freundlich isotherm play in understanding soil contamination and remediation?
The Freundlich isotherm is crucial in soil contamination studies as it often describes the adsorption of pollutants onto soil particles. It helps predict contaminant mobility and retention in soil, guiding remediation strategies and risk assessments.
37. How can the Freundlich isotherm be modified to account for irreversible adsorption?
To account for irreversible adsorption, the Freundlich isotherm can be modified by including an additional term representing the irreversibly adsorbed fraction. This modification helps distinguish between reversible and irreversible adsorption processes.
38. How does the Freundlich isotherm relate to the concept of adsorption hysteresis?
The Freundlich isotherm itself doesn't directly account for adsorption hysteresis. However, differences in Freundlich parameters between adsorption and desorption processes can indicate the presence of hysteresis, suggesting complex surface interactions or pore structure effects.
39. How does surface roughness affect the applicability of the Freundlich isotherm?
Surface roughness generally increases surface heterogeneity, which is well-described by the Freundlich isotherm. Increased roughness often leads to a lower 1/n value, indicating a more heterogeneous adsorption process with a wider range of adsorption energies.
40. How does the Freundlich isotherm compare to the BET (Brunauer-Emmett-Teller) isotherm?
The Freundlich isotherm is simpler and more empirical compared to the BET isotherm. While Freundlich can describe multilayer adsorption, the BET isotherm specifically models multilayer adsorption with a theoretical basis, making it more suitable for gas adsorption analysis.
41. What is the relationship between the Freundlich isotherm and the Temkin isotherm?
Both the Freundlich and Temkin isotherms describe heterogeneous surfaces, but the Temkin isotherm assumes a linear decrease in adsorption energy with coverage. The Freundlich isotherm is more general and can be seen as encompassing the Temkin model in certain cases.
42. How does the Freundlich isotherm relate to the concept of adsorption kinetics?
While the Freundlich isotherm describes equilibrium adsorption, it doesn't directly address kinetics. However, the K and 1/n parameters can provide insights into the ease and rate of adsorption, which are related to kinetic processes.
43. Can the Freundlich isotherm be used to predict breakthrough curves in fixed-bed adsorption columns?
The Freundlich isotherm alone cannot predict breakthrough curves, as it describes equilibrium, not dynamics. However, it can be incorporated into more complex models that account for mass transfer and flow dynamics to help predict breakthrough behavior in fixed-bed columns.
44. How does the crystal structure of the adsorbent influence the Freundlich isotherm parameters?
The crystal structure of the adsorbent affects surface properties and thus influences Freundlich parameters. Different crystal faces may have varying adsorption energies, contributing to surface heterogeneity and potentially affecting both K and 1/n values.
45. What is the importance of the Freundlich isotherm in predicting the fate of pollutants in natural systems?
The Freundlich isotherm is crucial in predicting pollutant fate in natural systems as it often accurately describes the adsorption of contaminants onto soil, sediments, and natural organic matter. This helps in modeling pollutant transport, bioavailability, and persistence in the environment.
46. How can the Freundlich isotherm be integrated with thermodynamic models?
The Freundlich isotherm can be integrated with thermodynamic models by relating the K and 1/n parameters to thermodynamic quantities like enthalpy and entropy of adsorption. This integration helps in understanding the energetics and spontaneity of the adsorption process.
47. What is the role of the Freundlich isotherm in designing and optimizing water treatment processes?
In water treatment, the Freundlich isotherm helps in designing and optimizing adsorption processes for removing contaminants. It aids in selecting appropriate adsorbents, determining required adsorbent doses, and predicting treatment efficiency under various water quality conditions.

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