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Answer :
To determine how many grams of copper are produced when 38.1 g of [tex]\( \text{Cu}_2\text{O} \)[/tex] reacts with [tex]\( \text{Cu}_2\text{S} \)[/tex], follow these steps:
1. Write the Balanced Equation:
[tex]\[
2 \text{Cu}_2\text{O} + \text{Cu}_2\text{S} \rightarrow 6 \text{Cu} + \text{SO}_2
\][/tex]
2. Find Molar Masses:
- Molar mass of [tex]\( \text{Cu}_2\text{O} \)[/tex] = [tex]\( 2 \times 63.55 + 16 = 143.1 \, \text{g/mol} \)[/tex]
- Molar mass of Cu = 63.55 g/mol
3. Calculate Moles of [tex]\( \text{Cu}_2\text{O} \)[/tex]:
- Mass of [tex]\( \text{Cu}_2\text{O} \)[/tex] is 38.1 g.
- Moles of [tex]\( \text{Cu}_2\text{O} = \frac{38.1 \, \text{g}}{143.1 \, \text{g/mol}} = 0.2662 \, \text{mol} \)[/tex]
4. Use the Stoichiometry of the Reaction:
- From the balanced equation, 2 moles of [tex]\( \text{Cu}_2\text{O} \)[/tex] produce 6 moles of Cu.
- Therefore, 1 mole of [tex]\( \text{Cu}_2\text{O} \)[/tex] produces 3 moles of Cu.
5. Calculate Moles of Cu Produced:
- Moles of Cu produced = [tex]\( 0.2662 \, \text{mol} \times 3 = 0.7987 \, \text{mol} \)[/tex]
6. Calculate Mass of Cu Produced:
- Mass of Cu = [tex]\( 0.7987 \, \text{mol} \times 63.55 \, \text{g/mol} = 50.76 \, \text{g} \)[/tex]
Therefore, 50.76 grams of copper are produced.
1. Write the Balanced Equation:
[tex]\[
2 \text{Cu}_2\text{O} + \text{Cu}_2\text{S} \rightarrow 6 \text{Cu} + \text{SO}_2
\][/tex]
2. Find Molar Masses:
- Molar mass of [tex]\( \text{Cu}_2\text{O} \)[/tex] = [tex]\( 2 \times 63.55 + 16 = 143.1 \, \text{g/mol} \)[/tex]
- Molar mass of Cu = 63.55 g/mol
3. Calculate Moles of [tex]\( \text{Cu}_2\text{O} \)[/tex]:
- Mass of [tex]\( \text{Cu}_2\text{O} \)[/tex] is 38.1 g.
- Moles of [tex]\( \text{Cu}_2\text{O} = \frac{38.1 \, \text{g}}{143.1 \, \text{g/mol}} = 0.2662 \, \text{mol} \)[/tex]
4. Use the Stoichiometry of the Reaction:
- From the balanced equation, 2 moles of [tex]\( \text{Cu}_2\text{O} \)[/tex] produce 6 moles of Cu.
- Therefore, 1 mole of [tex]\( \text{Cu}_2\text{O} \)[/tex] produces 3 moles of Cu.
5. Calculate Moles of Cu Produced:
- Moles of Cu produced = [tex]\( 0.2662 \, \text{mol} \times 3 = 0.7987 \, \text{mol} \)[/tex]
6. Calculate Mass of Cu Produced:
- Mass of Cu = [tex]\( 0.7987 \, \text{mol} \times 63.55 \, \text{g/mol} = 50.76 \, \text{g} \)[/tex]
Therefore, 50.76 grams of copper are produced.
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