Question

In the reaction CaCO3 → CO2 + CaO, if 30 grams of calcium carbonate are heated, what is the total mass of the products formed?

Answer 1

To determine the total mass of the products formed from the decomposition of calcium carbonate (CaCO3), we start with the initial equation:

\[
\text{CaCO}_3 \rightarrow \text{CO}_2 + \text{CaO}
\]

This reaction indicates that when 1 mole of calcium carbonate decomposes, it produces 1 mole of carbon dioxide (CO2) and 1 mole of calcium oxide (CaO).

1. **Calculate the molar mass of calcium carbonate (CaCO3)**:
- Calcium (Ca): 40.08 g/mol
- Carbon (C): 12.01 g/mol
- Oxygen (O) (3 atoms): \(3 \times 16.00 = 48.00\) g/mol

Therefore, the molar mass of CaCO3 is:
\[
40.08 + 12.01 + 48.00 = 100.09 \text{ g/mol}
\]

2. **Determine the number of moles of CaCO3 in 30 grams**:
\[
\text{moles of CaCO}_3 = \frac{\text{mass}}{\text{molar mass}} = \frac{30 \text{ g}}{100.09 \text{ g/mol}} \approx 0.2997 \text{ moles}
\]

3. **Using the stoichiometry of the reaction**:
From the balanced equation, 1 mole of CaCO3 produces 1 mole of CO2 and 1 mole of CaO. Therefore, 0.2997 moles of CaCO3 will produce:
- 0.2997 moles of CO2
- 0.2997 moles of CaO

4. **Calculate the total mass of the products**:
- Molar mass of CO2:
- Carbon (C): 12.01 g/mol
- Oxygen (O) (2 atoms): \(2 \times 16.00 = 32.00\) g/mol

Hence, the molar mass of CO2 is:
\[
12.01 + 32.00 = 44.01 \text{ g/mol}
\]

- Molar mass of CaO:
- Calcium (Ca): 40.08 g/mol
- Oxygen (O): 16.00 g/mol

Thus, the molar mass of CaO is:
\[
40.08 + 16.00 = 56.08 \text{ g/mol}
\]

5. **Convert moles of CO2 and CaO back to grams**:
- Mass of CO2 produced:
\[
\text{mass of CO}_2 = 0.2997 \text{ moles} \times 44.01 \text{ g/mol} \approx 13.18 \text{ g}
\]
- Mass of CaO produced:
\[
\text{mass of CaO} = 0.2997 \text{ moles} \times 56.08 \text{ g/mol} \approx 16.79 \text{ g}
\]

6. **Calculate the total mass of the products**:
\[
\text{Total mass of products} = \text{mass of CO}_2 + \text{mass of CaO}
\]
\[
= 13.18 \text{ g} + 16.79 \text{ g} \approx 29.97 \text{ g}
\]

Thus, the total mass of the products formed from the reaction when 30 grams of calcium carbonate are heated is approximately **29.97 grams**.

It's also interesting to note that the mass before the reaction (30 grams of CaCO3) is equal to the mass of the products formed (29.97 grams) plus the mass of the gases released (CO2), affirming the law of conservation of mass.