Adsorption Isotherm

Adsorption occurs if a gas or liquid particle clings to a surface of adsorbent, causing the adsorbate to form an atomic layer. Absorption, in which the solute diffuses in the solid instead of on the surface, is not the same as diffusion.

Definition

At constant temperature and pressure, an isotherm is a curve that expresses the fluctuation in the amount of gas adsorbed by the adsorbent.

Freundlich Adsorption Isotherm

In 1909, German scientist Freundlich proposed an empirical relationship between the amount of gas adsorbed by a unit mass of solid adsorbent and pressure at a given temperature. It is expressed using the following equation.

x/m = k.P1/n  (n > 1) 

where ‘x’ denotes the mass of the gas adsorbed on the adsorbent’s mass ‘m’ under pressure ‘P’. The constants ‘k’ and ‘n’ are determined by the type of the adsorbent and the gas at a given temperature.

To demonstrate the relationship, the mass of the gas adsorbed per gramme of the adsorbent is plotted against pressure in the shape of a curve. Physical adsorption reduces with increasing temperature at a constant pressure. At high pressure, the curves achieve saturation. If you take the log of the equation above —

log x/m = log k + 1/n log P 

We can plot log x/m on the y-axis and log P on the x-axis to see if the Freundlich isotherm is valid. The Freundlich isotherm is legitimate if the plot shows a straight line; otherwise, it is not. The value of 1/n is given by the slope of the straight line, whereas the value of log k is given by the intercept on the y-axis.

isotherm of adsorption

Freundlich Isotherm’s Limitations

The Freundlich isotherm only approximates the adsorption behavior. Because the value of 1/n might be anywhere between 0 and 1, the equation is only valid for a narrow range of pressures.

1.When 1/n = 0, x/m is constant, adsorption is pressure independent.

2.Adsorption is exactly proportional to pressure when 1/n = 1, x/m = k P,

Both of the aforementioned conditions are supported by experimental results. The experimental isotherms always appear to approach saturation at high pressure. The Freundlich isotherm fails to explain this finding at high pressure since it does not account for it.

Two more isotherms followed the Freundlich isotherm: the Langmuir adsorption isotherm and the BET adsorption isotherm. The Langmuir isotherm assumed monolayer adsorption in nature, whereas the BET isotherm assumed multilayer adsorption.

Langmuir  Adsorption isotherms 

The Freundlich adsorption isotherm fails at high gas pressure, which is one of its shortcomings. On the basis of theoretical considerations based on kinetic theory of gases, Irving Langmuir derived a basic adsorption isotherm in 1916. The Langmuir adsorption isotherm is the name given to this phenomenon.

(a) Adsorption occurs on the solid’s surface only until the entire surface is entirely covered by a monomolecular layer of the adsorbed gas.

(b) Adsorption is made up of two opposing processes: gas molecule condensation on a solid surface and gas molecule evaporation (desorption) from the surface back into the gaseous phase.

(c) The rate of condensation is determined by the amount of uncovered (bare) adsorbent surface available for condensation. Naturally, while the entire surface is exposed, the rate of condensation is quite high, and as the surface is gradually covered, the rate of condensation gradually reduces. The rate of evaporation, on the other hand, is dependent on the covered surface and hence increases as more of the surface is covered. At some point, when the rate of condensation equals the rate of evaporation, an equilibrium will be reached (adsorption equilibrium).

(d) The rate of condensation is also affected by the gas’s pressure, because the number of molecules impacting per unit area is proportional to the pressure in the kinetic theory of gases.

[x/m]=[ap/(1+bp)] is a mathematical formula.

, where a and b are constants whose values are determined by the type of gas (adsorbate), the type of solid adsorbent, and the temperature. The experimental data can be used to calculate their values.

Langmuir’s idea has some limitations.

(a) The hypothesis of unimolecular adsorption proposed by Langmuir is only true at low pressures and high temperatures.

(b) Additional layers arise as the pressure is increased or the temperature is dropped. As a result, the contemporary notion of multilayer adsorption was born.

Conclusion

We conclude that When a solid (skin, hair, powder) is applied with a surfactant solution at a fixed temperature and reaches the equilibrium concentration, the adsorption isotherm is a graph that illustrates the surfactant concentration against the amount of surfactants adsorbed onto unit mass solid.