Given the reaction: Cu + 2AgNO_3 → Cu(NO_3)_2 + 2Ag, how many moles of copper (Cu) are required to produce 3.50 mol of silver (Ag)?

• A. 3.50 mol
• B. 0.875 mol
• C. 1.75 mol
• D. 7.00 mol

Answer: (C)

Verified step by step guidance

1. Write down the balanced chemical equation: \(\mathrm{Cu} + 2\mathrm{AgNO}_3 \rightarrow \mathrm{Cu}(\mathrm{NO}_3)_2 + 2\mathrm{Ag}\).
2. Identify the mole ratio between copper (Cu) and silver (Ag) from the balanced equation. For every 1 mole of Cu, 2 moles of Ag are produced.
3. Set up a proportion using the mole ratio to find the moles of Cu needed to produce 3.50 moles of Ag: \(\frac{1\ \mathrm{mol\ Cu}}{2\ \mathrm{mol\ Ag}} = \frac{x\ \mathrm{mol\ Cu}}{3.50\ \mathrm{mol\ Ag}}\).
4. Solve for \(x\) (moles of Cu) by cross-multiplying and dividing: \(x = \frac{1}{2} \times 3.50\).
5. Interpret the result as the number of moles of copper required to produce 3.50 moles of silver.