The balanced chemical equation for the decomposition of calcium carbonate (CaCO3) is:
CaCO3(s) → CaO(s) + CO2(g)
According to the stoichiometry of the equation, 1 mole of calcium carbonate produces 1 mole of carbon dioxide. To determine the amount of CO2 produced from 10 kg of CaCO3, we need to convert the mass of CaCO3 to moles and then use the mole ratio to find the moles of CO2 produced. Finally, we can convert the moles of CO2 to kilograms.
1. Calculate the molar mass of CaCO3:
Ca: 1 atom * 40.08 g/mol = 40.08 g/mol
C: 1 atom * 12.01 g/mol = 12.01 g/mol
O: 3 atoms * 16.00 g/mol = 48.00 g/mol
Molar mass of CaCO3 = 40.08 g/mol + 12.01 g/mol + 48.00 g/mol = 100.09 g/mol
2. Convert the mass of CaCO3 to moles:
10 kg * (1000 g/kg) = 10,000 g
Moles of CaCO3 = 10,000 g / 100.09 g/mol ≈ 99.97 mol (approximately 100 mol)
3. According to the balanced equation, 1 mole of CaCO3 produces 1 mole of CO2.
Therefore, 100 mol of CaCO3 will produce 100 mol of CO2.
4. Convert the moles of CO2 to kilograms:
Molar mass of CO2 = 12.01 g/mol + 2 * 16.00 g/mol = 44.01 g/mol
Mass of CO2 = 100 mol * 44.01 g/mol = 4401 g = 4.401 kg
Therefore, the decomposition of 10 kg of CaCO3 will produce approximately 4.401 kg of CO2.