Just wondering if there was a website or something where I could get more information on the subjects. I understand the methods of procedure, just not the why would one method be used over the other. So, any help or links would be appreciated.
In my own experience, gravity filtration is used for filtering largers size particles through media that is fairly coarse (if you consider #2 Whatman coarse). You can look up the micron size in a chemical supply catalog like the VWR or Fisher catalog. Gravity filtration is also best used when the solvent has a low boiling point such as ether or hexane or when the solution is hot. Pulling a vacuum on hot solutions, especially flammable ones, can cause all kinds of problems. I have also seen vacuum filtration not filter small particles where a gravity filtration works fine. Apparently, vacuum can force some near pore size solids through the filter media where gravity filtration wouldn't. It is easier to quantitatively recover something from a gravity filtration in most cases. Gravity filtration is more useful for filtering gel type substances like nickel DMG.
Vacuum filtration is usually performed with a filter aid such as diatomite. The real advantage for the filter aid/vacuum filtration is in the filtration of very small particles such as decolorizing carbon. Air can be drawn through the filter cake to minimize losses and solvent can be easily applied to rinse a valuable solid. Gravity filtration is not as useful for rinsing crystals, for example, because the rinse solvent would be in contact with the product longer and result in greater losses. Vacuum filtration can be used to dry crystals quickly to speed their analysis. Gravity filtration would require a more lengthy drying step either in the hood or in an oven (or drying thimble).
Vacuum filtration is useful if you are in a hurry but if you don't want to tie yourself up monitoring a filtration, gravity filtration can give you time to do other tasks.