Answer the questions based on the passage given below:

Adsorption is a surface phenomenon and it differs from absorption which occurs throughout the body of the substance that absorbs. In physisorption the attractive forces are mainly van der Waals forces while in chemisorption ionic / covalent bonds are formed between particles of adsorbent and adsorbate. The catalytic activity of finely divided iron in Haber's process of ammonia manufacture can be explained by adsorption theory. Adsorption being an exothermic process, the heat of adsorption is utilized in enhancing the rate of the reaction. Adsorption has many applications being used in gas masks, control of humidity, chromatograph separation, curing diseases etc.

Which of the following graph represents an adsorption isotherm?

The correct answer is option 3.

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.