Question

Adsorption of a gas on a surface follows Freundlich adsorption isotherm. Plot of,  $ {\rm{log}}\dfrac{{\rm{x}}}{{\rm{m}}} $  versus log p gives a straight line with slope equal to  $ 0.5 $ , then:

( $ \dfrac{{\rm{x}}}{{\rm{m}}} $  is the mass of the gas adsorbed per gram of adsorbent)

A. Adsorption is proportional to the pressure.

B. Adsorption is proportional to the square of pressure.

C. Adsorption is independent of pressure.

D. Adsorption is proportional to the square root of pressure.

Answer 1

Hint: We know that adsorption is the process in which molecules are seen on the outer surface of the substituents. Generally, the molecular species which dissolved in water is termed as adsorbate, and the surface on which it gets deposited is termed as adsorbent and the full process is generally derived as chemical adsorption.

Complete answer

As we all know, the adsorption of gas on the surface which follows Freundlich adsorption isotherm. The graph generally plot of  $ {\rm{log}}\dfrac{{\rm{x}}}{{\rm{m}}} $  versus log p and usually get the straight line with a slope distance is equivalent to  $ 0.5 $ , then the adsorption value is proportional to the square root of the given pressure.

$ \dfrac{{\rm{x}}}{{\rm{m}}} = {\rm{k}}{{\rm{P}}^{\frac{{\rm{1}}}{{\rm{n}}}}}......\left( 1 \right) $ 

Where, k is the constant, P is the pressure, n is the slope and x and m is the constant.

Taking log on both side of the equation (2) we get,

$ \log \dfrac{{\rm{x}}}{{\rm{m}}} = \log {\rm{k}} + \dfrac{{\rm{1}}}{{\rm{n}}}{\rm{logP}}......\left( 2 \right) $ 

The value of slope that is  $ \dfrac{{\rm{1}}}{{\rm{n}}} $  is already given and it is equivalent to  $ 0.5 $ .

Substitute the value of slope in equation (1) we get,

$ \dfrac{{\rm{x}}}{{\rm{m}}} = {\rm{k}}{{\rm{P}}^{0.5}} $ 

As we all know, the k is the constant and proportional to the pressure. So we get,

$ \dfrac{{\rm{x}}}{{\rm{m}}}{\rm{\propto }}{{\rm{P}}^{0.5}} $ 

Hence, according to the obtained formula, we said that the adsorption is generally proportional to the square root of pressure. 

Thus, the correct option for this question is D.

Note:

The adsorption value is directly proportional to the pressure for the isotherm adsorption curve. The absorption and adsorption are two different phenomena to explain the state of matter. The adsorption is affected by the external factors like temperature.