Copper(I) oxide reacts with solid carbon to form copper metal. Carbon dioxide gas is the other product of this reaction. (a) Write the balanced chemical equation for this reaction. (b) Coke is a cheap, impure form of solid carbon that is often used industrially. If a sample of coke is \(95 \%\) C by mass, determine the mass in kilograms of coke needed to react completely with \(1.000\) ton of copper(I) oxide. \([1\) ton \(=2000 \mathrm{lb} ; 1 \mathrm{~kg}=2.205 \mathrm{lb}]\)

We are given that copper(I) oxide reacts with solid carbon to form copper metal and carbon dioxide. The unbalanced equation for this reaction is: Cu₂O + C → Cu + CO₂ To balance this equation, the number of atoms of each element on both sides should be equal. From the given equation, we see that we have 2 Cu atoms on the left and only 1 Cu atom on the right; thus we must put a 2 in front of Cu on the right side: Cu₂O + C → 2Cu + CO₂ Now, we observe that all elements are balanced correctly: - 2 Cu atoms on both sides, - 1 O atom on both sides, - 1 C atom on both sides. The balanced chemical equation is: Cu₂O + C → 2Cu + CO₂

We need to find the mass of coke required to completely react with 1 ton of Cu₂O. First, we need to convert 1 ton of Cu₂O to kg and then to moles. Given that 1 ton = 2000 lb and 1 kg = 2.205 lb, we have: \(1.000\, ton = 1.000 \times 2000\, lb = 2000\, lbs\) \(2000\, lb \times \frac{1\, kg}{2.205\, \text{lb}} = 907.217\, kg\) Now let's find the molar mass of Cu₂O: Cu₂O = (2 × Molar\, mass\, of\, Cu) + Molar\, mass\, of\, O = \(2 \times 63.55 \text{ g/mol} + 16 \text{ g/mol} = 143.10 \text{ g/mol}\) Now, we find the number of moles of Cu₂O in 907.217 kg: \(\frac{907,217 \,g}{143.10 \,\text{g/mol}} = 6,340\, moles\) From the balanced chemical equation, we know that 1 mole of Cu₂O reacts with 1 mole of C, so we need 6,340 moles of C to react with 1 ton of Cu₂O. The molar mass of C is: Molar\, mass\, of\, C = 12.01 \text{ g/mol} So, 6,340 moles of C weigh: \(6,340\, moles \times 12.01\, \text{g/mol} = 76,118.4 \text{ g}\) Now, we know that coke is 95% carbon by mass. Therefore, to get 76,118.4 g of carbon, we need: \(\frac{76,118.4 \text{ g}}{0.95} = 80,123.6 \text{ g}\) Finally, convert the mass of coke to kilograms: \(80,123.6 \text{ g} \times \frac{1 \text{ kg}}{1,000 \text{ g}} = 80.12 \text{ kg}\) Hence, 80.12 kg of coke is needed to react completely with 1 ton of copper(I) oxide.