Why do both Freundlich and Langmuir adsorption isotherms hold good at high pressure and fail at low pressure?

Hint :The adsorption of a gas on a solid surface depends on the pressure of the gas. The variation in the amount of gas adsorbed by the adsorbent with pressure at a constant temperature can be expressed by means of a curve which is termed as adsorption isotherm.

Complete Step By Step Answer:
Freundlich in the year 1909, gave an empirical relationship between the quantity of gas that is adsorbed by unit mass of solid adsorbent and the pressure at a particular temperature. This is known as Freundlich adsorption isotherm. The relationship can be expressed by this equation, $ \dfrac{x}{m} = k.{p^{\dfrac{1}{n}}} $ where, $ \left( {n > 1} \right) $ and x is the mass of the gas adsorbed on mass m of the adsorbent at pressure p, k and n are constants which depend on the nature of the adsorbent and the gas at a particular temperature. Langmuir proposed an adsorption isotherm which is based on the kinetic theory of gases and this is known as Langmuir Adsorption Isotherm which could satisfy both at low and high pressures of the adsorbate gas. It was experimentally determined that the extent of gas adsorption varies directly with the pressure. It directly varies with the pressure raised to the power $ \dfrac{1}{n} $ until saturation pressure $ {P_s} $ is reached and beyond that point, the rate of adsorption saturates even after applying higher pressure. Thus, the Freundlich adsorption isotherm fails at higher pressure.

Note :
According to the Langmuir Adsorption isotherm, the rate of adsorption will depend upon the pressure of the adsorbate gas, which means higher the pressure, higher will be the number of adsorbate gas molecules that will strike the adsorption site on adsorbent surface as per kinetic theory of gases.