A compound composed of sulfur and fluorine is found to contain 25.24% by mass of sulfur. If the molar mass of the compound is 254.11 g/mol, what is its molecular formula?
You’ve already got two perfectly good answers, both arrived at by the expected systematic mathematical approach. But really, do we need to go through all that?
molar mass of S = 32.06
molar mass of F = 18.99
And we’re told that the molar mass of the unknown is 254.11.
If there is one atom of S in the molecule,
254.11−32.0618.99=11.69 atoms of F
This isn’t good because we can’t have fractions of an atom in a molecule. Moving on, if there are two atoms of S in the molecule,
254.11−2×32.0618.99=10.00 atoms of F
and we are on to something.
You can check a few more cases with 3 or 4 atoms of S per molecule, but you’re going to find none of them give a whole number of F atoms.
QED, the unknown is S2F10 . If you want to back-calculate the percent S by mass to check the answer…
64.12 g S254.11 g = 25.23% S