To determine how many moles of copper (Cu) need to react to form 0.854 mol of silver (Ag), we can use the stoichiometric relationships from the balanced chemical equation provided:
[tex]\[ \text{Cu} + 2 \text{AgNO}_3 \rightarrow 2 \text{Ag} + \text{Cu(NO}_3\text{)}_2 \][/tex]
1. Identify the given value and what we need to find:
- Given: 0.854 mol of Ag.
- Find: moles of Cu needed to react.
2. Analyze the balanced chemical equation:
- According to the equation, 1 mole of Cu reacts with 2 moles of AgNO3 to form 2 moles of Ag.
- This means that the mole ratio of Cu to Ag is 1:2.
[tex]\[\text{1 mole of Cu} \rightarrow \text{2 moles of Ag}\][/tex]
3. Determine the stoichiometric ratio to use:
- Since the mole ratio is 1:2, we need half as many moles of Cu as we have moles of Ag.
4. Calculate the required moles of Cu:
- We are given 0.854 mol of Ag.
- To find the number of moles of Cu, we use the ratio:
[tex]\[
\text{Moles of Cu} = \frac{\text{Moles of Ag}}{2}
\][/tex]
Substituting the given value:
[tex]\[
\text{Moles of Cu} = \frac{0.854 \, \text{mol of Ag}}{2} = 0.427 \, \text{mol of Cu}
\][/tex]
5. Conclusion:
- Therefore, 0.427 moles of copper (Cu) must react to form 0.854 mol of silver (Ag).
