Question

The Langmuir adsorption isotherm is deduced by assuming that:
A.The heat of adsorption varies with coverage
B.The adsorbed molecules interact with each other
C.The adsorption takes place in multi layers
D.The adsorption sites are equivalent in their ability to adsorb the particles

Answer 1

Hint:Langmuir adsorption isotherm is a theoretical simple adsorption isotherm. Adsorbent with free surface available is more likely to show a high rate of adsorption than the one whose surface is filled with the adsorbed gas.

Complete answer:
Adsorption is defined as the phenomenon of attracting and retaining the molecules of a substance on the surface of a liquid or a solid resulting in a higher concentration of molecules on the surface. The substance which is getting adsorbed is known as adsorbate and on which surface adsorption is taking place is known as adsorbent. Various factors affect adsorption, some are nature of adsorbate, nature of adsorbent, pressure, temperature, etc.
To determine the effect of pressure, temperature is taken to be constant. It is experimentally found that mass of adsorbate adsorbed on unit mass of adsorbent is directly proportional to pressure upto certain stage. Freundlich adsorption isotherm gives the mathematical representation of effect of pressure on adsorption process.
\[\dfrac{{\text{x}}}{{\text{m}}} = {\text{k}}{{\text{P}}^{\dfrac{1}{{\text{n}}}}}\]
where \[\dfrac{{\text{x}}}{{\text{m}}}\] represents amount of adsorbate adsorbed on m mass of adsorbent, k and n are constant at a particular temperature and for a particular adsorbent and adsorbate, n is always greater than one, indicating that the amount of gas adsorbed does not increase as rapidly as the pressure. But this equation fails to explain adsorption at high pressure conditions.
Langmuir adsorption isotherm is a theoretical simple adsorption isotherm. It is deduced using the assumption that the adsorption sites are equivalent in their ability to adsorb the particles. It states that adsorption only takes place till the whole of the surface is completely covered with a unimolecular layer of the adsorbed gas. The rate at which gas will condensed at the surface of solid depends upon the free available surface and as initially the entire surface is freely available, thereby rate of adsorption is fast at initially but progressively slows down.
On the other hand, rate at which desorption of adsorbed gas takes place depends upon the covered surface and hence increases as more surface is covered. Finally, an equilibrium will be established when the rate of adsorption becomes equal to rate of desorption of gas.

Thus, the correct option is D.

Note:
The rate of adsorption also depends upon the pressure of gas since according to the kinetic theory of gases; the number of molecules striking per unit area is proportional to the pressure.