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## Q. 3.13

Copper was among the first metals to be refined from minerals collected by ancient metalworkers. The production of copper was already an industry by $3500_{BCE}$. Cuprite is a copper mineral commonly found near Earth’s surface, making it a likely resource for Bronze Age coppersmiths. Cuprite has the formula $Cu_{2}O$ and can be converted to copper metal by reacting it with charcoal:

$2 Cu_{2}O(s) + C(s) → 4 Cu(s) + CO_{2}(g)$

How much cuprite and how much carbon are needed to prepare a 256 g copper bracelet such as the one shown in Figure 3.21?

Collect and Organize We are given a balanced chemical equation and the mass of product. We are asked to find the masses of the reactants. Because the chemical equation relates moles, not masses, of reactants and products, we need to find the molar mass of each substance in the reaction.

Analyze The balanced chemical equation tells us that for every 4 moles of copper we produce, 2 moles of $Cu_{2}O$ and 1 mole of C must react. To use these mole ratios, we first need to convert the mass of copper to the equivalent number of moles of Cu by using the molar mass of Cu. We then work a separate conversion for each reactant: the first conversion uses the mole ratio of $Cu_{2}O$ to Cu (2:4) from the balanced equation, and the second uses the mole ratio of C to Cu (1:4). Finally, we use the molar masses of $Cu_{2}O$ and C to find the mass of each required for the reaction.

## Verified Solution

Carrying out the steps described in the analysis of the problem:

$256 \sout{g Cu} \times \frac{1 \sout{mol Cu}}{63.55 \sout{ g Cu}} \times \frac{2 \sout{ mol Cu_{2}O}}{4 \sout{mol Cu}} \times \frac{143.09 g Cu_{2}O}{1 \sout{mol Cu_{2}O}} =288 g Cu_{2}O$

$256 \sout{g Cu} \times \frac{1 \sout{mol Cu}}{63.55 \sout{g Cu}} \times \frac{1 \sout{mol C}}{4 \sout{mol Cu}} \times \frac{12.01 g C}{1 \sout{ mol C}} =12.1 g C$

We are allowed only three significant figures in our answer, so the final masses of the reactants we need are 288 g of $Cu_{2}O$ and 12.1 g of C.

Think About It To prepare a given mass of copper, we must have sufficient amounts of both copper ore and charcoal. Usually there is a limited supply of ore and more than enough charcoal.