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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?

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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?

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  • $\begingroup$ If n is equal to 1, then as the pressure tends to infinity, the amount of gas adsorbed would also tend to infinity, which is not possible if the adsorbent has a limited surface area. As for the failure of Freundlich isotherm at high pressures, you might want to check out Langmuir's isotherm, which tends to a constant value at infinity. $\endgroup$
    – Aniruddha Deb
    Jan 16, 2020 at 2:07
  • $\begingroup$ Does n=1 ,when pressure equals 0 and n equals infinity when pressure becomes infinity. $\endgroup$
    – Grace
    Jan 16, 2020 at 3:02
  • $\begingroup$ no. $n$ is a constant, which depends upon the gas chosen $\endgroup$
    – Aniruddha Deb
    Jan 16, 2020 at 4:46
  • $\begingroup$ I knew n is temperature dependent quantity varying with nature of adsorbent and adsorbate .But my question is why this isotherm fails at high pressure $\endgroup$
    – Grace
    Jan 16, 2020 at 5:49

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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 .

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1/n is a parameter which is constant for a fixed system at a particular temperature. n depends on nature of adsorbent and gas at a particular temperature.(1/n doesn't change with pressure). Let 1/n = 0.4. then it will be 0.4 at all pressures(high, medium or low). Now we can not change (1/n) from 0.4 to 0 at high pressure. So adsorption will continue to occur even at high pressures and there won't be any saturation. This is the limitation.

Actually, 1/n varies with Pressure for the equation to hold valid with experimental graph of adsorption. And 1/n = 0 at high pressure.

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We can take the value of n as 1. Moreover the value of n lies between 0 and 1. So according to Freundlich for high pressure conditions n is always taken as 1. And hence x/m=1

But experimentally it was found that saturation still increases even after increasing the pressure.

This is how Freundlich equation fails at higher pressure

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