I am studying surface chemistry in high school I have this doubt and I am unable to find a answer your help is appreciated I searched for the answer on google I asked my chemistry teacher he said the question is beyond high school's curriculum and I even asked some of my friends but all in vain.
Well, it usually depends on the temperature: if temperature is too low, molecules cannot move so freely so they are localized on top of the solid without much movement.
However, in general cases the adsorbed gas behaves like a liquid in two dimensions. Near the surface, the gas molecules are 'trapped' in the force field of the solid, so they don't escape so easily. Then the freedom of movement occurs only in two dimensions (the molecules travel on the surface).
I made some time ago a movie calculating (using molecular dynamics) movement nitrogen molecules adsorbed on a graphene surface at 77 K. This can give you a clear image of what happens on the surface. As you can see, the molecules can travel on top of the graphene in two dimensions (we can call it a 2D phase). This movie is the case when still a monolayer of gas does not complete. There can be cases with less molecules, say, less pressure of nitrogen in the gas phase; or more molecules.
The physical states can be observed more clearly in phase diagrams of the adsorbed surfaces. Typical examples shows a plot of the adsorbed phase transitions in a P vs. 1/T plot. This topic is extensively covered in the nice monograph on Physical Adsorption by Bruch, Cole and Zaremba, for example.