Langmuir's adsorption equation which describes the amount of gas adsorbed on a solid surface is written as
`(P)/(x//m)=(1)/(ab)+(P)/(b)`
where `x//m` is the extent of adsorption, `a` and `b` are constants and `P` is the gas pressure. On the basis of the above equation indicate which of the following statements is correct ?

Options

A. At low vslue of `P,x//mpropP`
B. At high value of `P,x/mrarra//b` (i.e adsorption is indenpendent of pressure)
C. Between the low and high values of `P` , the above equation becomes `x//m=kP^(1//n)` , which is the Freundlich equation (here `K` and `n` are constant).
D. All of these

Answer

D

Explanation

The Langmuir adsorption isotherm is usally represented by the relation
`(x)/(m)=(aP)/(1+bP)`
where `a` and `b` are two Langmuir paramenters. At very low pressures, `("bpltlt1")` , the equation `(1)` is reduced to `(x)/(m)=aP` or `(x)/(m)propP^(1)`
At very high pressure, `("bpgt gt1")` , thus equation `(1)` is reduced to
`(x)/(m)=ab` or `(x)/(m)propP^(0)`
Thus, between the low and high pressures, equation `(1)` is reduced to
`(x)/(m)=kP^(1//n)`
where `1//n` varies from `0` to `1`
In order to determine the parameters `a` and `b` , equation `(1)` may be written in its inverse from: `(m)/(x)=(1+bP)/(aP)=(b)/(a)+(1)/(aP)`
A plot of `m//x` against `1//P` gives a straight line with slope and intercept equal to `1//a` and `b//a` respectively.