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)

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 silicon would it contain? (There are exactly 5 carats per gram)

Answer 1

so, you have 75 grams

How many moles of bentoite is that?
Note that each mole of bentoite contains 3 moles of Si.

Answer 2

I'm having a hard time setting it up to figure out the answer

Answer 3

15 carat*1gram/5carats=3 grams.

moles bentoite=3grams/molmassbentiote

mol mass is= 1Ba+1Ti + 3SI+9O3
look up the atomic mass of each of those...
mol mass= 137 + look these up and add them.
Calculate the moles of bentoite.

now for moles Si, multiply by three

Answer 4

I got ba-137 ti-48 si-28 and o-16. Now to get mol mass I understand I need to add these up but am I suppose to be multiplying o by 9 and si by 3 based on the formula for mol mass or just o times 3 and si by 3 after?

Answer 5

To find the number of moles of silicon in a 15-carat stone of pure BaTi(SiO3)3, we can follow these steps:

Step 1: Convert carats to grams
Since there are exactly 5 carats per gram, we divide 15 carats by 5 to convert it to grams.
15 carats ÷ 5 carats/gram = 3 grams

Step 2: Calculate the molar mass of BaTi(SiO3)3
The molar mass of BaTi(SiO3)3 can be calculated by summing the atomic masses of each element in its chemical formula.

- Ba: (1 Ba) × (137.33 g/mol) = 137.33 g/mol
- Ti: (1 Ti) × (47.87 g/mol) = 47.87 g/mol
- Si: (3 Si) × (28.09 g/mol) = 84.27 g/mol
- O: (9 O) × (16.00 g/mol) = 144 g/mol (3 oxygen atoms per silicate group, SiO3)

Now we add up these values:
137.33 g/mol + 47.87 g/mol + 84.27 g/mol + 144 g/mol = 413.47 g/mol

Step 3: Convert grams to moles
To convert grams to moles, we divide the mass (in grams) by the molar mass of the compound.
3 grams ÷ 413.47 g/mol = 0.007251 moles (rounded to six decimal places)

Therefore, a 15-carat stone of pure BaTi(SiO3)3 would contain approximately 0.007251 moles of silicon.