Abstract illustration of adsorption with energy transfer.

Adsorption Equilibrium: Are You Calculating Thermodynamic Parameters Correctly?

Soraya Malik in Science & Nature August 2025 • 4 min read.

"A deep dive into the common pitfalls and best practices for estimating thermodynamic parameters in adsorption processes."

In the world of adsorption, accurately estimating thermodynamic parameters is crucial for understanding and optimizing various applications, from water treatment to gas separation. However, the seemingly straightforward calculations can be fraught with errors, leading to misleading conclusions. A recent review sheds light on these common pitfalls, offering guidance on how to ensure the reliability of your results.

The study emphasizes a critical aspect often overlooked: the proper use of the equilibrium constant (K) in the Van't Hoff equation. While this equation is fundamental for calculating thermodynamic parameters, its misuse is surprisingly widespread. The review pinpoints how incorrectly calculated equilibrium constants can skew thermodynamic calculations, leading to inaccurate values for enthalpy (ΔH°) and entropy (ΔS°).

This article aims to break down the complexities of estimating thermodynamic parameters in adsorption, offering clear insights into the correct methodologies and highlighting the consequences of common errors. Whether you are a seasoned researcher or a budding scientist, understanding these nuances is essential for achieving reliable and meaningful results.

The Van't Hoff Equation: A Foundation for Thermodynamic Calculations

Abstract illustration of adsorption with energy transfer.

The Van't Hoff equation measures the change in the equilibrium constant with variations in temperature, expressed as ΔG° = −RTLn(Ke°). Here, ΔG° represents the change in Gibbs free energy, R is the universal gas constant, T is the absolute temperature in Kelvin, and Ke° signifies the thermodynamic equilibrium constant. In simpler terms, the equation tells us how the equilibrium of an adsorption process shifts as temperature changes.

The common practice involves plotting Ln(Ke°) versus 1/T. From this graph, the change in entropy (ΔS°) is derived from the intercept, and the change in enthalpy (ΔH°) is calculated from the slope. As the review highlights, the crucial element here is ensuring that the equilibrium constant (Ke°) is calculated correctly, a point where many studies falter.

Dimensionless Equilibrium Constant: The equilibrium constant (K) must be dimensionless for the Van't Hoff equation to yield accurate results.
Isotherm Data: High-quality adsorption isotherms at multiple temperatures are essential for determining the equilibrium constant at each temperature.
Best-Fit Models: Employ best-fit models at different temperatures to derive reliable equilibrium constants.

The review underscores that equilibrium constants derived from isotherms—often expressed in L/mg—must be converted to a dimensionless form before being used in the Van't Hoff equation. The suggested conversion involves using the equation: K = (1000 Kg molecular weight of adsorbate) / γ. Here, Kg is the equilibrium constant from the isotherm, and γ is the activity coefficient (dimensionless). This conversion is pivotal for aligning the calculations with the principles of physical chemistry and ensuring the accuracy of thermodynamic parameters.

The Path to Accurate Adsorption Thermodynamics

Estimating thermodynamic parameters in adsorption processes demands meticulous attention to detail and a thorough understanding of the underlying principles of physical chemistry. By adhering to the correct methodologies for calculating equilibrium constants, and by employing high-quality experimental data, researchers can achieve reliable and meaningful results. This, in turn, enhances our understanding of adsorption phenomena and facilitates the development of more effective applications across various fields.

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This article is based on research published under:

DOI-LINK: 10.1016/j.molliq.2018.10.048, Alternate LINK

Title: A Critical Review Of The Estimation Of The Thermodynamic Parameters On Adsorption Equilibria. Wrong Use Of Equilibrium Constant In The Van'T Hoof Equation For Calculation Of Thermodynamic Parameters Of Adsorption

Subject: Materials Chemistry

Journal: Journal of Molecular Liquids

Publisher: Elsevier BV

Authors: Eder C. Lima, Ahmad Hosseini-Bandegharaei, Juan Carlos Moreno-Piraján, Ioannis Anastopoulos

Published: 2019-01-01

Everything You Need To Know

How does the Van't Hoff equation help in understanding adsorption processes, and what key parameters are derived from it?

The Van't Hoff equation, expressed as ΔG° = −RTLn(Ke°), relates the change in Gibbs free energy (ΔG°) to the thermodynamic equilibrium constant (Ke°) at a given absolute temperature (T), using the universal gas constant (R). It's essential for understanding how temperature affects the equilibrium of an adsorption process. By plotting Ln(Ke°) versus 1/T, we can derive the change in entropy (ΔS°) from the intercept and the change in enthalpy (ΔH°) from the slope. Ensuring the equilibrium constant (Ke°) is dimensionless is crucial for accurate results.

Why is it crucial for the equilibrium constant (K) to be dimensionless when using the Van't Hoff equation, and how do you convert it to a dimensionless form?

When applying the Van't Hoff equation, the equilibrium constant (K) *must* be dimensionless. Equilibrium constants derived from isotherms are often expressed in dimensions such as L/mg. To correct this, a conversion is necessary using the formula: K = (1000 * Kg * molecular weight of adsorbate) / γ, where Kg is the equilibrium constant from the isotherm and γ is the activity coefficient (dimensionless). Failing to use a dimensionless K will lead to inaccurate values for enthalpy (ΔH°) and entropy (ΔS°).

What are the implications of accurately estimating thermodynamic parameters in adsorption processes for practical applications?

Accurately estimating thermodynamic parameters enhances our understanding of adsorption phenomena, which is vital for optimizing processes like water treatment and gas separation. By using correct methodologies for calculating the equilibrium constant and employing high-quality experimental data, researchers can obtain reliable and meaningful results. Inaccurate estimations, stemming from incorrect use of the equilibrium constant in the Van't Hoff equation, can lead to flawed conclusions about the feasibility and efficiency of adsorption processes.

What specific steps should researchers take to ensure the reliability and accuracy of thermodynamic parameter estimations in adsorption studies?

To ensure the reliability of thermodynamic parameter estimations, several steps are essential. First, use high-quality adsorption isotherms at multiple temperatures to accurately determine the equilibrium constant at each temperature. Second, employ best-fit models to derive reliable equilibrium constants from the isotherm data. Finally, meticulously convert the equilibrium constant to a dimensionless form before using it in the Van't Hoff equation. Neglecting these steps can result in skewed thermodynamic calculations and inaccurate values for enthalpy and entropy.

What role does the activity coefficient play in converting the equilibrium constant to a dimensionless form, and why is it important to consider?

The activity coefficient (γ) accounts for the non-ideal behavior of the adsorbate in the system. It reflects the deviation from ideal conditions and ensures that the calculated equilibrium constant accurately represents the system's thermodynamics. Often, this value is assumed to be 1 in dilute solutions, but for more concentrated systems, it's crucial to consider and calculate γ to avoid inaccuracies in the dimensionless equilibrium constant (K) and subsequent thermodynamic parameter estimations. The activity coefficient ensures accurate thermodynamic parameter calculations that align with the principles of physical chemistry.