Adsorption arises due to the fact that the surface particles of the adsorbent are not in the same environment as the particles inside the bulk. The extent of adsorption increases with the increase of surface are per unit mass of the adsorbent at a given temperature and pressure. Another important factor featuring adsorption is the heat of adsorption. During adsorption, there is always a decrease in residual forces of the surface, therefore, it is invariably an exothermic process or \(\Delta H\) and \(\Delta S\) are always negative. There are mainly two types of adsorption of gases on solids. In physisorption, the attractive forces are mainly van der Waals forces while in cemisorption, actual bonding occurs between the particles of adsorbate and adsorbent. Generally, easily liquifying gases are adsorbed more easily on the surface of a solid as compared to the gases which are liquified with difficulty. Freundlich gave an emperical relationship between the quantity of gas adsorbed by unit mass of solid adsorbent and pressure, at a particular temperature.

Which two parameters from the following are plotted to give a straight line on Freundlich adsorption isotherm?

\(log \frac{x}{m}\text{ vs }log P\)

The correct answer is option 4. \(log \frac{x}{m}\text{ vs }log P\).

The variation of extent of adsorption \((\frac{x}{m})\) with pressure \((P)\) at a particular temperature was given mathematically by Freundlich in 1909. From the adsorption isotherm, the following observations can be easily made:

(i) At low pressure, the graph is almost straight line which indicates that \(\frac{x}{m}\) is directly proportional to pressure. This may be expressed as:

\(\frac{x}{m}\propto P\)

or, \(\frac{x}{m} = kP\) -------(i)

where \(k\) is a constant

(ii) At high pressure, the graph becomes almost constant which means that \(\frac{x}{m}\) becomes independent of pressure. This may be expressed as:

\(\frac{x}{m} =\, \ constant\)

or, \(\frac{x}{m} \propto P^0\)    \(∵ P^0 = 1\)

or, \(\frac{x}{m} = kP^0\) -------(ii)

(iii) Thus, in the intermediate range of pressure, \(\frac{x}{m}\) will depend upon the power of pressure which lies between 0 to 1 i.e., fractional power of pressure (probable range 0.1 to 0.5). This may be expressed as

\(\frac{x}{m} \propto P^{1/n}\)

or, \(\frac{x}{m} = kP^{1/n}\) -------(iii)

where \(n\) can take any whole number value which depends upon the nature of adsorbate and adsorbent. The above relationship is also called Freundlich's adsorption isotherm and is shown in figure above.

Calculation of \(k\) and \(n\) of adsorption isotherm:

The constants k and n can be determined as explained below:

Taking logarithms on both sides of eq. (iii), we get

\(log\frac{x}{m} = log k + \frac{1}{n}log P\)

Thus, if we plot a graph between log \((\frac{x}{m})\) on y-axis(ordinate) and log P, on x-axis (abscissa), straight line will be obtained. This also shows the validity of Freundlich isotherm. The slope of the line (Fig. below) is equal to \(1/n\) and the intercept is equal to log k.