You would have to divide it's mass by the number of moles. Mass is easy to find, but the moles would be more difficult. No chance it's a gas that you're trying to find is there? You could put a gas at standar conditions and it will occupy 22.4 Liters per mole. You could also try to react it with a known substance in excess and see what comes from that.
This is a different type of problem. In gen chem labs you usually know the substance and you have to prove its atomic weight. So maybe it is impossible to do without spectrometry or some other advanced tools.
Sorry I couldn't help much. Maybe it'll get you on the ride track though.
You could also take a known quantity (in grams) and react it with another element (or two or three...) to form another compound which is easy to quantify. For example, react 1 g of pure hydrogen with excess bromine, run the reaction to completion, then see how much HBr you've made. Then just back calculate.
I'm a little confused about Mass Spec here. Isn't mass spec isn't used mainly to determine molecular formula and weight of compounds, based on the mass/charge ratio of the different fragments of the original starting compound? If this is an element, there would be no fragments, you'd only have a single mass/charge ratio, which I guess would itself then be the mass of the element. But I'm guessing that this is some sort of stoichiometry question, in which case trying to react with a known quantity of other substance and crunching the numbers would be the way to go, as some other people suggested. It's hard to say without knowing the actual question. Anyways, just me thinking out loud. . .
I appreciate everyones replies. Unfortunately this is all I was left to go on. You see, this is a question which I need to write a lab write up on in order to turn in a independent study. But, this is all I have been given to go off of, namely what I stated above.
Just thinking out loud here, but if you can figure out what period and family the element is in, you'll know the number of electrons. If you know the number of electrons, you'll know the number of protons the element has (assuming this is a neutral species). If you can figure out the number of neutrons (I don't know how to do this) you can add up the masses of all the sub-atomic particles for the atomic mass of the element. Hope this helps.
Chem major here too, this ones easy if youv'e dealt w/ it before. Each element has it's own spectra when heated (emmission) and provides a fingerprint for the element (or combo of) which will id the unknown. This technique is used alot in astronomy (make up of stellar bodies) as well as in criminalistics and gen chem. analysis. Ahhh, a breath of chemistry after a long line-up of summer history classes.
WOW! I didn't realize there other chem people out there! Now my take on the question. Since it's a pure element and not an organic compound I personally wouldn't go with MS. Flame atomic absorption spectrophotometry or Atomic emission spectrometry would work for most metal ions. Both are based on quantum mechanics, which notes that each element (mostly metals) absorb and emit at specific wavelengths. Once you know the element.....
BTW: reacting with a known substance and backtracking won't work because you have no way of knowing in what proportion the element would combine with the known substance. perhaps it would be 1:1 but maybe 2:1 or more....if it reacted at all.
high tech way: use AES/AAS atomic emission/absorption spectroscopy and find the lamp that gives you the maximum absorbance/emission when the bands coincide you hit the jackpot.
low tech way: you could do something we do in general chem labs. if it's a metal find it's specific heat using a simple foam cup calorimeter. i doubt they would give you an unstable element and ask you to find it's weight. if it's a metal heat it up to a specified temperature and put it in a cold water bath and measure the heat transfer. then use trouton's rule (Cp * MW = 25 kJ/mol) and solve for MW. this will give you a rough estimate (do multiple trials and get a standard deviation) of what the metal is.
if it's a nonmetal you can use mass spectrometry like others have suggested. the ionization method might need to be tweaked however. FAB or electrospray might not work so well but electron impact ionization is perfect for elements.