Answer :
Theoretical yield of solid copper is 7.77 grams. Copper (II) sulfate is the limiting reactant in the reaction between aluminum and copper (II) sulfate.
To find the theoretical yield of solid copper and determine the limiting reactant, we'll follow these steps:
1. Write the balanced chemical equation:
[tex]\[ 2Al + 3CuSO_4 \rightarrow 3Cu + Al_2(SO_4)_3 \][/tex]
2. Calculate the molar masses of the reactants and products:
- Aluminum (Al): [tex]\( 26.98 \, \text{g/mol} \)[/tex]
- Copper (II) sulfate [tex](CuSO4): \( 63.55 + 32.07 + 4(16.00) = 159.60 \, \text{g/mol} \)[/tex]
- Copper (Cu): [tex]\( 63.55 \, \text{g/mol} \)[/tex]
3. Convert the given masses to moles:
- Moles of aluminum (Al): [tex]\( \frac{2.2 \, \text{g}}{26.98 \, \text{g/mol}} = 0.0815 \, \text{mol} \)[/tex]
- Moles of copper (II) sulfate[tex](CuSO4): \( \frac{14.4 \, \text{g}}{159.60 \, \text{g/mol}} = 0.0902 \, \text{mol} \)[/tex]
4. Determine the stoichiometric ratio between aluminum and copper (II) sulfate:
- From the balanced equation, 2 moles of aluminum react with 3 moles of copper (II) sulfate.
5. Calculate the theoretical yield of solid copper using the mole ratio:
[tex]\[ \text{Moles of Cu} = \text{Moles of Al} \times \left( \frac{3 \, \text{mol Cu}}{2 \, \text{mol Al}} \right) \][/tex]
[tex]\[ \text{Moles of Cu} = 0.0815 \, \text{mol} \times \left( \frac{3 \, \text{mol Cu}}{2 \, \text{mol Al}} \right) = 0.1223 \, \text{mol} \][/tex]
6. Convert moles of copper to grams using the molar mass of copper:
[tex]\[ \text{Mass of Cu} = \text{Moles of Cu} \times \text{Molar mass of Cu} \][/tex]
[tex]\[ \text{Mass of Cu} = 0.1223 \, \text{mol} \times 63.55 \, \text{g/mol} = 7.77 \, \text{g} \][/tex]
7. Determine the limiting reactant:
- Since aluminum is in excess (0.0815 mol) and copper (II) sulfate is completely consumed (0.0902 mol), copper (II) sulfate is the limiting reactant.
8. Summarize the results:
- The theoretical yield of solid copper is [tex]\( 7.77 \, \text{g} \).[/tex]
- Copper (II) sulfate is the limiting reactant.
The Correct question is:
How many grams of solid copper will theoretically be produced when 2.2G of aluminum is reacted with 14.4G of copper (II) sulfate? Which reactant is the limiting reactant? Show work. Be sure to include units. 2Al+3CuSo4→3Cu+Al2(SO4) 3
