# What is the simplest formula for the mineral beryl which contains 5.03% Be, 10.4% Al, 35.5% Si and 53.58% O?

Beryl is a mineral which contains 5.03% $$\ce{Be}$$, 10.4% $$\ce{Al}$$, 35.5% $$\ce{Si}$$ and 53.58% $$\ce{O}$$. What is the simplest formula for beryl?

So I tried to follow a 3 step rule to solving this equation:

1. Divide each % by it's own atomic mass
2. Divide each of those by whichever is smallest
3. Find the lowest whole #

Amount of $$\ce{Be}$$ = 5.03% / 9 = .558 moles
Amount of $$\ce{Al}$$ = 10.04 / 26.98 = .372 moles (smallest number)
Amount of $$\ce{Si}$$ = 31.35% / 32 = .979 moles
Amount of $$\ce{O}$$ = 54.58% / 16 = 3.3 moles

Proportionate amount of $$\ce{Be}$$ = .558 / .372 = 1.5
Proportionate amount of $$\ce{Al}$$ = .372 / .372 = 1
Proportionate amount of $$\ce{Si}$$ = .979 / .372 = 2.63
Proportionate amount of $$\ce{O}$$ = 53.58 / 16 = 3.3

From here I don't know what I have done wrong, but these numbers are all whack silly and I can't see to get a number that leads me to the answer.

The correct answer is $$\ce{Be4Al(SiO3)8}$$

• You have the wrong atomic mass for Si. I'd use 4 significant figures for all of the atomic masses also. – MaxW Sep 28 '16 at 4:07
• Good catch! I didn't even spot that. 32 is sulfur, not silicon. – orthocresol Sep 28 '16 at 5:41
• If you "cheat" (or want to use this as a check), you can render oxidation states which, in this setting, will be Be=+2, Al=+3, Si=+4, O=-2. No other oxidation states of these elements are likely to be found in naturally occurring minerals. Whatever formula you get should have these oxidation states, each multiplied by the number of atoms for that element, add up to zero. The answer in the back does not, the correct formula given in a correct answer below does. – Oscar Lanzi Jun 18 '20 at 18:51

Firstly the "correct" answer seems to be wrong, which is not an uncommon occurrence, so please do not always take answers at the back of books to be correct. Wikipedia lists the formula of beryl as $\ce{Be3Al2(SiO3)6}$ which is much more in accordance with what you have done.