Answer the question on the basis of the passage given below:

Adsorption is a surface phenomenon and it differs from absorption which occurs throughout the body of the substance which absorbs. In physisorption, the attractive forces are mainly van der Waal forces while in chemisorption actual bonding occurs between the particles of adsorbent and adsorbed more easily on the surface of a solid as compared to the gases which are liquified with difficulty. Adsorption increases with increase in pressure and decreases as the temperature is increased.

Freundlich adsorption isotherm gives a straight line on plotting

\(log\, \ x/m\) vs\(log\, \ p\)

The correct answer is option 3. \(log\, \ x/m\) vs\(log\, \ p\).

The Freundlich adsorption isotherm is an empirical equation that describes the relationship between the amount of gas adsorbed (\(x/m\)) on the surface of an adsorbent and the pressure of the gas (\(p\)) at a constant temperature. The equation is given by:

\[ \frac{x}{m} = K \cdot p^{1/n} \]

where:
\( \frac{x}{m} \) is the amount of gas adsorbed per unit mass of adsorbent,
\( p \) is the pressure of the gas,
\( K \) is the Freundlich constant, and
\( \frac{1}{n} \) is the Freundlich exponent.

Taking the logarithm (base 10) of both sides of the equation results in:

\[ \log\left(\frac{x}{m}\right) = \frac{1}{n} \cdot \log(p) + \log(K) \]

Now, the equation is in the form of a straight line equation \(y = mx + b\), where:
\(y\) is \( \log\left(\frac{x}{m}\right) \),
\(m\) is \( \frac{1}{n} \),
\(x\) is \( \log(p) \), and
\(b\) is \( \log(K) \).

When you plot \( \log\left(\frac{x}{m}\right) \) against \( \log(p) \), the resulting graph will be a straight line. This is a characteristic feature of systems that obey the Freundlich adsorption isotherm. The slope of the line is \( \frac{1}{n} \), and the intercept on the y-axis is \( \log(K) \). The Freundlich exponent (\(n\)) provides information about surface heterogeneity, and the Freundlich constant (\(K\)) is related to the adsorption capacity.

In summary, by plotting \( \log\left(\frac{x}{m}\right) \) against \( \log(p) \), you can analyze and interpret the Freundlich adsorption isotherm, gaining insights into the adsorption behavior and characteristics of the system.