Given the mineral emerald, in which the mass fraction of beryllium = 5.06, mass fraction of aluminum

Given the mineral emerald, in which the mass fraction of beryllium = 5.06, mass fraction of aluminum = 10.05%, mass fraction of silicon = 31.49%, mass fraction of oxygen = 53.4%. Determine the mineral formula.

Given:
ω (Be) = 5.06%
ω (Al) = 10.05%
ω (Si) = 31.49%
ω (O) = 53.4%

To find:
BexAlySizOi -?

1) Let m (BexAlySizOi) = 100 g;
2) m (Be) = ω (Be) * m (BexAlySizOi) / 100% = 5.06% * 100/100% = 5.06 g;
3) n (Be) = m / M = 5.06 / 9 = 0.562 mol;
4) m (Al) = ω (Al) * m (BexAlySizOi) / 100% = 10.05% * 100/100% = 10.05 g;
5) n (Al) = m / M = 10.05 / 27 = 0.372 mol;
6) m (Si) = ω (Si) * m (BexAlySizOi) / 100% = 31.49% * 100/100% = 31.49 g;
7) n (Si) = m / M = 31.49 / 28 = 1.125 mol;
8) m (O) = ω (O) * m (BexAlySizOi) / 100% = 53.4% * 100/100% = 53.4 g;
9) n (O) = m / M = 53.4 / 16 = 3.338 mol;
10) x: y: z: i = n (Be): n (Al): n (Si): n (O) = 0.562: 0.372: 1.125: 3.338 = 1.5: 1: 3: 9 = 3: 2: 6: 18;
11) Be3Al2Si6O18.

Answer: Unknown substance – Be3Al2Si6O18.