in inorganic chemistry when we define a surface, how many molecular layers/ or 'depth' are we talking about.

Now thats an interesting question actually. It really depends on what area of inorganic chemistry you are talking about. If you are talking about the catalytic properties of a metal (e.g. palladium metal in hydrogenation reactions), then we usually only refer to the top most layer of atoms. This is because only the atoms on the surface can do anything in the reaction that we are interested in. In almost all cases, this is what people refer to when they say the surface of the metal; the outter most layer of atoms.

 

If we are talking about the structure of a crystal, then there we can use several layer of atoms to fully describe the structure of the crystal. These are normally expressed in Miller index. While using Miller indices, you are actually only looking at planes through the unit cell of the substance which sometimes need several levels of atoms to express them. I use these as an example, because the structure of a metal (i.e. its Miller index) has an effect on the reactivity of a metal. For example with the palladium example I used above, the three different crystal structures (001), (010) and (100) all have different reactivities.

Precisely.