Why Freundlich adsorption isotherms fails at high pressure conditions? Experimentally it was determined that extent of gas adsorption varies directly with pressure, and then it directly varies with pressure raised to the power 1/n until saturation pressure Ps is reached. Beyond that point, the rate of adsorption saturates even after applying higher pressure. Thus, the Freundlich adsorption isotherm fails at higher pressure.


This is an extract taken from Wikipedia explaining limitation of Freundlich isotherm.But analyzing the freundlich adsorption equation we can reach the same conclusions 

The Freundlich adsorption isotherm is mathematically expressed as:
         $$X/M=KP^{1/n}$$

Giving whole number values to 'n' we can explain adsorption at various pressure conditions.If so why then it is said that Freundlich adsorption isotherm fails at high pressure?

Edit


  It cannot be used for a straight linear isotherm part occurring either at low pressures as the 
  value n =1 should be then assumed, or at high pressures as the curve increases 
  unreservedly, whereas a surface has a limited value and it must be in the condition of 
  saturation.


Why is it given here that it's not possible to assume a value of 1 for n?
There is a saturation level for the adsorption of any adsorbate on the adsorbent due to limited surface area of the adsorbent. So once that saturation level is reached , more pressure won't increase the number of particles adsorbed .