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 silicon would it contain? (There are exactly 5 carats per gram)
Total mass = 15x5 = 75g of BaTi(SiO3)3
n = m / M
n = 75g / 413.45 g/mol
n = 0.181 moles BaTi(SiO3)3
0.181 moles BaTi(SiO3)3 * (3 moles Si / 1 mole BaTi(SiO3)3
= 0.544 moles of Si
Total mass = 15x5 = 75g of BaTi(SiO3)3 should be
15 carats x (1 g/5 carats) = 3 grams and go from there.
To determine the number of moles of silicon in a 15-carat stone of pure BaTi(SiO3)3, we'll use the following steps:
1. Determine the number of grams in a 15-carat stone:
Since there are exactly 5 carats per gram, a 15-carat stone would be equivalent to 15/5 = 3 grams.
2. Find the molar mass of BaTi(SiO3)3:
The molar mass can be calculated by adding up the atomic masses of all the elements in the chemical formula. For BaTi(SiO3)3, the molar masses are:
- Ba (Barium): 137.33 g/mol
- Ti (Titanium): 47.867 g/mol
- Si (Silicon): 28.0855 g/mol (atomic mass is provided with more decimal places)
- O (Oxygen): 16.00 g/mol (since there are 3 oxygen atoms, we multiply by 3)
So, the molar mass of BaTi(SiO3)3 is: (137.33 + 47.867 + 28.0855 + (16.00 x 3)) g/mol = 227.4285 g/mol.
3. Obtain the number of moles of silicon:
Since the molar mass of BaTi(SiO3)3 is 227.4285 g/mol, we can use this to find the number of moles of silicon in the 3-gram stone:
Number of moles = mass (in grams) / molar mass
Number of moles of silicon = (3 g / 227.4285 g/mol) = 0.01316 moles.
Therefore, a 15-carat stone of pure BaTi(SiO3)3 would contain approximately 0.01316 moles of silicon.