The following data were recorded for the adsorption of a gas $A$ on a solid at STP:

$\backslash$table$[[\backslash$table$[[$Volume adsorbed$],[\frac{3^3}{g}$ solid$)]],\backslash$table$[[$Equilibrium$],[$pressure of $A($Pa$)]]],[2\mathrm{.}2,0\mathrm{.}11],[3\mathrm{.}6,0\mathrm{.}20],[5\mathrm{.}2,0\mathrm{.}31],[7\mathrm{.}3,0\mathrm{.}49],[10\mathrm{.}1,0\mathrm{.}79],[14\mathrm{.}9,1\mathrm{.}71]]$

a$.$ Show that the above data fits the undissociative Langmuir isotherm by plotting $\frac{1}{V}$ vs $\frac{1}{p_A}.$ Mention the adsorption isotherm equation used and determine the parameters and $($:$\}$ with their units.

b$.$ If the area occupied by one gas molecule is $18(A{)}^2,$ determine the specific surface area $(\frac{m^2}{g})$ and surface area $(m^2)$ for a solid with weight of $0\mathrm{.}0615g.$

c$.$ At what pressure will the coverage be $50\%?$