To solve this problem, we need to use the concept of Avogadro's number and molecular weight.
The molecular weight of calcium carbonate (CaCO3) can be calculated as follows:
- Calcium (Ca) atomic weight = 40 g/mol
- Carbon (C) atomic weight = 12 g/mol
- Oxygen (O) atomic weight = 16 g/mol
- Molecular weight of CaCO3 = (1 x 40) + (1 x 12) + (3 x 16) = 100 g/mol
Now, we can calculate the number of molecules in 3.0 x 10^2 grams of CaCO3 as follows:
- Convert the mass of CaCO3 to moles using the formula:
moles = mass / molecular weight
moles = 3.0 x 10^2 g / 100 g/mol
moles = 3.0 x 10^0 mol
- Use Avogadro's number to calculate the number of molecules:
number of molecules = moles x Avogadro's number
number of molecules = 3.0 x 10^0 mol x 6.02 x 10^23 molecules/mol
number of molecules = 1.806 x 10^24
Therefore, the answer is C) 1.81 x 10^24.