Question

In 1985 benitoite became the California "state gemstone." Found only in a tiny mine near Coalinga, California, it is a silicate of barium and titanium with trace impurities that cause a range of hues from colorless to blue to pink. Its general formula is BaTi(SiO3)3. If a 15-carat stone were pure BaTi(SiO3)3, how many moles of oxygen would it contain? (There are exactly 5 carats per gram.)

Answer 1

Answer is:  there are 0,06525 moles of oxygen in 15 carat benitoite.
m(BaTi(SiO₃)₃) = 15 carat ÷ 5 carat/g = 3 g.
M(BaTi(SiO₃)₃) = Ar(Ba) + Ar(Ti) + 3Ar(Si) + 9Ar(O) · g/mol.
M(BaTi(SiO₃)₃) = 137,33 + 47,87 + 3 · 28,09 + 9 · 16 · g/mol.
M(BaTi(SiO₃)₃) = 413,5 g/mol.
n(BaTi(SiO₃)₃) = m(BaTi(SiO₃)₃) ÷ M(BaTi(SiO₃)₃).
n(BaTi(SiO₃)₃) = 3 g ÷ 413,5 g/mol.
n(BaTi(SiO₃)₃) = 0,00725 mol.
In one molecule of benitoite there are nine oxygen atoms.
n(O) = 9 · 0,00725 mol.
n(O) = 0,06525 mol.