The given graphs / data $\text{I, II, III}$ and $\text{IV}$ represent general trends observed for different physisorption and chemisorption processes under mild conditions of temperature and pressure. Which of the following choice (s) about $\text{I, II, III}$ and $\text{IV}$ is (are) correct?

The curve that best describes the adsorption of a gas $\left(\mathrm{x}\right)\mathrm{g}$ on $1.0 \mathrm{g}$ of a solid substrate as a function of pressure $\left(\mathrm{p}\right)$ at a fixed temperature

 is

Freundlich adsorption isotherms for the physical adsorption of a gas at temperature ${\mathrm{T}}_1, {\mathrm{T}}_2$ and ${\mathrm{T}}_3$ are shown in the graph given below. The correct relationship between ${\mathrm{T}}_1, {\mathrm{T}}_2$ and ${\mathrm{T}}_3$ is

The mass of gas adsorbed, $\mathrm{x}$, per unit mass of adsorbate, $\mathrm{m}$, was measured at various pressures, $\mathrm{p}.$A graph between $\log \frac{\mathrm{x}}{\mathrm{m}}$ and $\log \mathrm{p}$ gives a straight line with slope equal to $2$ and the intercept equal to $0.4771$. The value of $\frac{\mathrm{x}}{\mathrm{m}}$ at a pressure of $4 \mathrm{atm}$ is :

(Given $\log 3=0.4771$)

Consider the following statements about Langmuir isotherm.
I. The free gas and adsorbed gas are in dynamic equilibrium.
II. All adsorption sites are equivalent.
III. The initially adsorbed layer can act as a substrate for further adsorption.
IV. The ability of a molecule to get adsorbed at a given site is independent of the occupation of neighboring sites.

The correct statements are

In Freundlich adsorption isotherm, slope of $\mathrm{AB}$ line is:

If $\frac{\mathrm{x}}{\mathrm{m}}={\mathrm{kP}}^{1/\mathrm{n}}$ equation represents the Freundlich adsorption isotherm where $x$ is the mass of the gas adsorbed on mass $\text{'}\mathrm{m}\text{'}$ of the adsorbent at pressure $\mathrm{P}$. $\mathrm{k}$ and $\mathrm{n}$ are constants which depend on the nature of adsorbent and the gas. Which of the following conditions represents the figure?

${\mathrm{CO}}_2$ gas adsorbs on charcoal following Freundlich adsorption isotherm. For a given amount of charcoal, the mass of ${\mathrm{CO}}_2$ adsorbed becomes $64$ times when the pressure of ${\mathrm{CO}}_2$ is doubled.

The value of $\mathrm{n}$ in the Freundlich isotherm equation is $\_\_\_\_$ $\times {10}^2.$ (Round off to the Nearest Integer)