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.)
15 carats x (1 g/5 carats) = ? grams BaTi(SiO3)3.
mols BaTi(SiO3)3 = grams/molar mass + xx.
There are 3 Si mols/1 mol BaTi(SiO3)3; therefore, there must be 3* mols BaTi(SiO3)3 = mools Si atoms.
To find the number of moles of silicon in a 15-carat stone of pure BaTi(SiO3)3, we need to follow these steps:
1. Convert 15 carats to grams:
Since there are exactly 5 carats per gram, we divide 15 carats by 5 carats/g to get the mass in grams.
15 carats / 5 carats/g = 3 g
2. Calculate the molar mass of BaTi(SiO3)3:
The molar mass can be determined by adding up the atomic masses of each element in the formula.
Ba: 1 atom x atomic mass of Ba = 1 x 137.33 g/mol = 137.33 g/mol
Ti: 1 atom x atomic mass of Ti = 1 x 47.87 g/mol = 47.87 g/mol
Si: 3 atoms x atomic mass of Si = 3 x 28.09 g/mol = 84.27 g/mol
O: 9 atoms x atomic mass of O = 9 x 16.00 g/mol = 144.00 g/mol
Summing up the masses:
137.33 g/mol + 47.87 g/mol + 84.27 g/mol + 144.00 g/mol = 413.47 g/mol
3. Convert the mass of the stone to moles of BaTi(SiO3)3:
Use the molar mass of BaTi(SiO3)3 calculated in step 2 to convert the mass (in grams) of the stone to moles.
moles = mass (in grams) / molar mass
moles = 3 g / 413.47 g/mol
moles ≈ 0.00726 mol
4. Determine the moles of silicon:
In one formula unit of BaTi(SiO3)3, there are 3 moles of silicon.
Therefore, the 15-carat stone of pure BaTi(SiO3)3 would contain:
0.00726 mol of BaTi(SiO3)3 x 3 mol Si / 1 mol BaTi(SiO3)3 ≈ 0.0218 mol Si
So, the 15-carat stone of pure BaTi(SiO3)3 would contain approximately 0.0218 moles of silicon.