When Should You Use the Grand Partition Function in Statistical Mechanics?

[secret2]

I am taking a statictical mechanics course, and one thing bothers me. I am not sure when we should use the normal partition function (Z) and when the grand partition function (twisty Z). In particular, why can we not use grand partition function when we are considering the following system:

He atoms may be adsorbed from vapor phase onto a solid surface, forming a 2-dimensional gas. If the adsorption energy is e, then by treating the vapor as a reservoir, find the density of He atom on the surface.

Shouldn't we always use grand partition function whenever the number of particle N is not constant? Or is there no limitation on which one we Have to use, just which is more convenient?

 

[Galileo]

For the adsorption problem, you should use the grand canonical ensemble (which uses the grand partition function), since the number of particles on the surface is clearly not constant.