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I have taken the following from Wikipedia :

Limitation of Freundlich adsorption isotherm :

Experimentally it was determined that extent of gas adsorption varies directly with pressure, and then it directly varies with pressure raised to the power $\frac{1}{n}$ until saturation pressure $P_{s}$ is reached. Beyond that point, the rate of adsorption saturates even after applying higher pressure. Thus, the Freundlich adsorption isotherm fails at higher pressure.

I have a question. Here is the Freundlich adsorption equation :

$\frac{x}{m} = Kp^{\frac{1}{n}}$

Now at very high pressures, we may put $\frac{1}{n} = 0$. Then we have,

$\frac{x}{m} = Kp^{0}$

$\frac{x}{m} = K(1)$

$\frac{x}{m} = K$

which means that $\frac{x}{m}$ is a constant which means that the graph between $\frac{x}{m}$ and $p$ will be a straight line. This exactly matches with the experimental graph. As you can see in the image below, at very high pressures the graph is indeed a straight line and Freundlich adsorption equation beautifully explains it. Perfect! So, what is the problem here? Why in Wikipedia and even in my chemistry textbook it is written that Freundlich adsorption isotherm is not valid at high pressures? I just proved above that Freundlich adsorption equation beautifully explains that experimental graph at high pressures. Then why is it said that Freundlich adsorption isotherm is not valid at high pressures?

Graph

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    $\begingroup$ $n$ is meant to be independent on pressure, otherwise the equation has no meaning at all. $\endgroup$ Jun 24, 2021 at 17:21
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    $\begingroup$ In part because monolayer coverage is a baked-in assumption. At high pressure, you start to get island formation (at least) and this isotherm is not valid. $\endgroup$ Jun 24, 2021 at 17:34
  • $\begingroup$ No, @Nilay Ghosh, the answers in that question do not satisfy me. $\endgroup$ Jun 25, 2021 at 2:44
  • $\begingroup$ But @Todd Minehardt, I just proved that the graph indicated by Freundlich adsorption equation at high pressures is a straight line which exactly matches with the experimental graph. So Freundlich adsorption equation is indeed valid at high pressures, right? I don't see what is the problem here. $\endgroup$ Jun 25, 2021 at 13:11

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