Question

In college, when deriving the Langmuir isotherm for gas-solid adsorption, the professor proposed a modified version of the Van der Waals state equation, what he called the pseudo Van der Waals gas state equation. The derivation implied equaling the chemical potential for a certain compound in the gas and interphase, and when dealing with the volume for the interphase: V⋅(p+q)=RTV⋅(p+q)=RT WhereVVis the volume,ppthe pressure,RRthe gas constant,TTthe temperature, andqqa correction term to account for the adsorbate cohesion. He argued that the interphase was something similar to a very condensed gas, so that equation of state was valid. Indeed, he obtained correctly the Langmuir isotherm, that later was derived using the kinetic approach. However, I have been reading a lot of books and articles looking for that pseudo Van der Waals gas, and I haven't found anything similar. I guess the approximation is just to neglect the excluded volume, but I am not sure whether my professor was right or he took some license by himself.

Answer 1

The van der Waals equation accounts for non-ideal gas behavior by including molecular volume and intermolecular forces, adjustments not usually applied to adsorption phenomena. The pseudo van der Waals equation your professor used for deriving the Langmuir isotherm appears to be a situational adaptation rather than a widely recognized modification.

Step-by-step explanation:

The van der Waals equation of state is a modified version of the ideal gas law, introduced to account for non-ideal gas behavior through the inclusion of molecular volume and intermolecular forces. This equation is especially useful at lower temperatures and higher pressures where molecular interactions become significant.

In the context of gas-solid adsorption and the derivation of the Langmuir isotherm, your professor's modification, the pseudo van der Waals gas state equation, could be seen as an attempt to account for the dense phase of adsorbates on a surface.

This approach posits treating the adsorbed layer as a condensed gas phase, applying a similar logic as the van der Waals equation but possibly omitting the excluded volume correction due to the high density of the adsorbate layer.

While the idea of a condensed phase may seem viable, and your professor's derivation correctly leading to the Langmuir isotherm might suggest that, the traditional form of the van der Waals equation does not inherently cover such adsorption phenomena. The approximation you mentioned, which neglects the excluded volume, might indeed be a simplification specific to your professor's approach as mainstream literature may not directly refer to this modified equation.