Question

For a linear plot of \[\log (x/m)\] versus \[\log p\] in a Freundlich adsorption isotherm, which of the following statements is correct ? (\[k\]and \[n\] are constants)
A. \[\dfrac{1}{n}\] appears as the intercept.
B. Only \[\dfrac{1}{n}\] appears as the slope.
C. log\[\dfrac{1}{n}\] appears as the intercept.
D. Both \[k\] and \[\dfrac{1}{n}\] appear in the slope term

Answer 1

Hint: An adsorption isotherm is a curve relating the equilibrium concentration of a solute on the surface of an adsorbent. The adsorption isotherm is also an equation relating the amount of solute adsorbed onto the solid.

Complete step by step answer:
Freundlich Adsorption Isotherm gives the variation in the quantity of gas adsorbed by a unit mass of solid adsorbent with the change in pressure of the system for a given temperature. The expression for the Freundlich isotherm can be represented by the following equation;
\[\Rightarrow \dfrac{x}{m}=k{{P}^{\dfrac{1}{n}}}\]
Where \[x\] is the mass of the gas adsorbed, \[m\]is the mass of the adsorbent, \[P\] is the pressure and \[n\] is a constant which depends upon the nature of adsorbent and the gas at a given temperature. Taking the logarithm on both the sides of the equation, we get;
\[\Rightarrow \log \dfrac{x}{m}=\log k+\dfrac{1}{n}\log {{P}^{{}}}\]
On comparing this equation with the equation of straight line(\[y=mx+c\]). The plot of this equation is a straight line as represented by the following curve.
                                        

From the graph, it is very clear that only \[1/n\] appears as the slope.

So, the correct answer is Option B.

Note: The Freundlich adsorption isotherm is followed by another two isotherms, Langmuir adsorption isotherms and BET theory. The Langmuir adsorption isotherms predict linear adsorption at low adsorption densities and a maximum surface coverage at higher solute metal concentrations.