Final answer:
To find how much copper is produced, convert 3.06 metric tons of bornite to grams, calculate the moles of bornite, use the reaction stoichiometry to determine the moles of copper expected, apply the 89.0% actual yield, and then convert this amount back to grams and metric tons.
Step-by-step explanation:
To calculate the amount of copper produced from the heating of bornite (Cu₃FeS₃), we start by converting metric tons to grams to work with standard chemical equations. We know that 1 metric ton is equal to 1,000,000 grams. Thus, 3.06 metric tons of bornite is equivalent to 3,060,000 grams of bornite. From the stoichiometry of the reaction given, 2 moles of bornite produce 6 moles of copper. We need the molar mass of bornite to convert grams to moles. The molar mass of bornite (calculated as 342.23 g/mol) allows us to find out the moles of bornite. Then we use the stoichiometry to find the moles of copper produced.
Here, for every 2 moles of bornite, we get 6 moles of copper, so we can set up a direct proportion. With the actual yield being 89.0%, we apply this percentage to determine the actual amount of copper produced in grams. This process involves mole-to-mole conversions and the application of the percentage yield. Finally, we convert grams of copper to metric tons by dividing by 1,000,000. The step-by-step calculation includes:
- Converting 3.06 metric tons of bornite to grams: 3.06 metric tons × 1,000,000 g/metric ton = 3,060,000 g.
- Calculating moles of bornite using its molar mass: moles of bornite = mass (g) / molar mass (g/mol).
- Using stoichiometry to find moles of copper produced: (6 mol Cu / 2 mol Cu₃FeS₃) × moles of bornite.
- Calculating the actual yield of copper: moles of copper produced × 89.0%.
- Converting moles of actual copper produced to grams, then to metric tons.
Final calculations will yield the amount of copper produced from the reaction.