Problem
The statement “matter cannot be created or destroyed” is tested using a closed (sealed) decomposition reaction. A sealed flask contains 15.0 g of calcium carbonate, CaCO3. When heated it decomposes:
After completion, 8.40 g of CaO is measured. Determine the mass of CO2 produced.
Concept: conservation of mass
In a closed system, total mass remains constant during a chemical reaction. Atoms are rearranged into new substances, but the total amount of matter is unchanged. This is the operational meaning of “matter cannot be created or destroyed.”
Step-by-step solution
Step 1: Identify what mass is conserved
The flask is sealed, so no gas escapes and no material enters. Therefore, the initial mass of CaCO3 must equal the combined masses of CaO and CO2 after reaction.
Step 2: Write the mass-balance equation
Step 3: Substitute values and solve for \(m(\text{CO}_2)\)
Result
The mass of carbon dioxide produced is \(6.60\ \text{g}\). The total product mass is \(8.40\ \text{g}+6.60\ \text{g}=15.0\ \text{g}\), matching the initial reactant mass, which directly illustrates that matter cannot be created or destroyed in a closed system.
Mass summary table
| Stage | Substance(s) | Mass (g) | Total mass (g) |
|---|---|---|---|
| Before heating | CaCO3 | 15.0 | 15.0 |
| After heating (sealed flask) | CaO + CO2 | 8.40 + 6.60 | 15.0 |
Visualization: mass balance in a sealed reaction
The diagram shows the same total mass on both sides (reactants vs products) for a closed system. The right pan separates the solid CaO and the gaseous CO2, but the sum remains unchanged.
Final answer
\(m(\text{CO}_2)=6.60\ \text{g}\), and the equality of total mass before and after the reaction in a sealed flask demonstrates that matter cannot be created or destroyed.