To determine the number of oxygen atoms in 1 kg of calcium carbonate (CaCO₃), we need to use the molar mass and stoichiometry of the compound.
The molar mass of calcium carbonate (CaCO₃) can be calculated by adding the atomic masses of its constituent elements:
- Calcium (Ca): 40.08 g/mol
- Carbon (C): 12.01 g/mol
- Oxygen (O): 16.00 g/mol (x3, as there are three oxygen atoms in CaCO₃)
Molar mass of CaCO₃ = (40.08 g/mol Ca) + (12.01 g/mol C) + (16.00 g/mol O) x 3 = 100.09 g/mol
Now, we can determine the number of moles of CaCO₃ in 1 kg (1000 g): Number of moles = mass / molar mass Number of moles = 1000 g / 100.09 g/mol = 9.993 moles (rounded to three decimal places)
In one mole of CaCO₃, there are three moles of oxygen atoms, so the number of moles of oxygen in 9.993 moles of CaCO₃ would be: Number of moles of oxygen = 3 moles O/mol CaCO₃ × 9.993 moles CaCO₃ = 29.979 moles (rounded to three decimal places)
Since 1 mole contains approximately 6.022 × 10²³ atoms (Avogadro's number), we can calculate the number of oxygen atoms in 29.979 moles of oxygen: Number of oxygen atoms = 29.979 moles × 6.022 × 10²³ atoms/mole = 1.805 × 10²⁵ oxygen atoms (rounded to three significant figures)
Therefore, there are approximately 1.805 × 10²⁵ oxygen atoms in 1 kg of calcium carbonate (CaCO₃).