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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:

$$V\cdot (p+q) = RT$$

Where $V$ is the volume, $p$ the pressure, $R$ the gas constant, $T$ the temperature, and $q$ a 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.

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    $\begingroup$ Neither van der Waals' gases neither pseudo van der Waals' gases exist. They are theoretical simplifications. It is similar as for ideal gases, just closer to real gases. $\endgroup$
    – Poutnik
    Dec 27, 2022 at 6:41
  • $\begingroup$ What I meant is if they are even defined. I know they both are just models. $\endgroup$
    – David Moldes
    Dec 27, 2022 at 9:16
  • $\begingroup$ Then it would be better to use other verb than exist. IMHO, it was just ad-hoc definition for the purpose of the lecture. Another variant would be with own volume, but without cohesion. $\endgroup$
    – Poutnik
    Dec 27, 2022 at 11:55

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