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?
1 carat = 0.2 g; therefore, 15 carats = 3 g.
Then mol = grams/molar mass = ? That gives you mols in the mineral. Since there are 3 mols of Si in 1 mole of the mineral, mols Si will be 3x mols in the mineral.
To calculate the number of moles of silicon (Si) in a 15-carat stone of pure BaTi(SiO3)3, we need to use the molar mass of silicon and the given weight of the stone.
1. Find the molar mass of silicon:
- The atomic mass of silicon (Si) is approximately 28.086 g/mol.
2. Convert the weight of the stone from carats to grams:
- 1 carat is equivalent to 0.2 grams.
- Therefore, a 15-carat stone would weigh 15 x 0.2 = 3 grams.
3. Calculate the number of moles of silicon:
- Divide the weight of the stone (in grams) by the molar mass of silicon.
- 3 g / 28.086 g/mol = 0.1068 mol.
Therefore, a 15-carat stone of pure BaTi(SiO3)3 would contain approximately 0.1068 moles of silicon.
To find the number of moles of silicon in a 15-carat benitoite stone, we need to use its formula, BaTi(SiO3)3, and calculate the molar mass of silicon (Si).
The molar mass of silicon (Si) is approximately 28.0855 grams per mole (g/mol).
First, let's calculate the molar mass of the benitoite formula:
- Molar mass of Ba (barium): 137.327 g/mol
- Molar mass of Ti (titanium): 47.867 g/mol
- Molar mass of SiO3 (silicate group):
- Molar mass of Si = 28.0855 g/mol
- Molar mass of O (oxygen) = 15.999 g/mol
- So, molar mass of SiO3 = (28.0855 g/mol) + (3 x 15.999 g/mol)
After calculating the molar mass of each component, we can now calculate the molar mass of BaTi(SiO3)3 by adding them together.
- Molar mass of BaTi(SiO3)3 = (molar mass of Ba) + (molar mass of Ti) + (3 x molar mass of SiO3)
Once we have the molar mass of BaTi(SiO3)3, we can calculate the number of moles of silicon (Si) in a 15-carat benitoite stone.
1. Convert the mass of the benitoite stone from carats to grams:
- 1 carat = 0.2 grams (approximately)
- So, 15 carats = 15 x 0.2 grams
2. Calculate the moles of silicon (Si):
- Moles of Si = (Mass of stone in grams) / (molar mass of BaTi(SiO3)3) x (number of Si atoms in BaTi(SiO3)3)
Now, plug in the values into the equation and calculate the moles of silicon.