Question

When CaCO_3 is heated CaO and CO_2 are produced. How many kg of CO_2 will be produced in the decomposition of 10 kg of CaCO_3?

Answer 1

When decomposing 10 kg of calcium carbonate, the reaction would yield 4.4 kg of carbon dioxide, following the law of conservation of mass.

Step-by-step explanation:

The decomposition of calcium carbonate (CaCO3) into calcium oxide (CaO) and carbon dioxide (CO2) is a chemical reaction that abides by the law of conservation of mass. This means the mass of the reactants is equal to the mass of the products. From the example given, where heating 10 grams of CaCO3 produces 4.4 g of CO2 and 5.6 g of CaO, we can form a ratio to find out how much CO2 is produced from 10 kg of CaCO3.

To calculate the amount of CO2 produced from 10 kg of CaCO3, we scale up the given example:

• 10 g of CaCO3 yields 4.4 g of CO2

Using a ratio and proportion, we have:

(10 g CaCO3 / 4.4 g CO2) = (10,000 g CaCO3 / x g CO2)

Solving for x gives us the amount of CO2 produced:

x = (10,000 g CaCO3 × 4.4 g CO2) / 10 g CaCO3 = 4,400 g of CO2

Convert grams to kilograms:

4,400 g = 4.4 kg

Therefore, decomposing 10 kg of CaCO3 would produce 4.4 kg of CO2.

Answer 2

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.