Question

Coke is an impure form of carbon that is often used in the industrial production of metals from their oxides. If a sample of coke is \(95 \%\) carbon by mass, determine the mass of coke needed to react completely with \(1.0\) ton of copper(II) oxide. $$ 2 \mathrm{CuO}(s)+\mathrm{C}(s) \longrightarrow 2 \mathrm{Cu}(s)+\mathrm{CO}_{2}(g) $$

Short answer

The mass of coke needed to react completely with 1.0 ton of copper(II) oxide is 79,424.81 grams.

Step-by-step solution

Convert the mass of copper(II) oxide to moles

First, we need to convert the mass of copper(II) oxide, which is 1.0 ton, to moles. To do this, we use the molar mass of copper(II) oxide, which is the sum of the molar masses of its elements: Cu (63.55 g/mol) and O (16.00 g/mol). The molar mass of CuO is 63.55 + 16.00 = 79.55 g/mol. Now, we can convert the mass of copper(II) oxide to moles: 1 ton = 1000 kg, so we have 1000 kg or 1,000,000 g of copper(II) oxide. Number of moles = Mass/Molar mass Number of moles of CuO = \(\frac{1,000,000}{79.55}\) = 12,568.67 moles

Use stoichiometry to find the moles of carbon needed for the reaction

According to the balanced chemical equation, 2 moles of CuO react with 1 mole of C. Hence, we need half the number of moles of carbon to react completely with the moles of CuO. Number of moles of C needed = \(\frac{12,568.67}{2}\) = 6,284.33 moles

Convert the moles of carbon to mass

Now, using the molar mass of carbon (12.01 g/mol), we can convert the moles of carbon needed into mass. Mass of carbon needed = Number of moles * Molar mass Mass of carbon needed = 6,284.33 * 12.01 = 75,454.07 g

Calculate the mass of coke needed

We know that the coke sample is 95% carbon by mass. To find the mass of coke needed, we can set up a proportion: \(\frac{Mass \ of \ carbon \ needed}{Mass \ of \ coke \ needed}\) = \(\frac{95}{100}\) Cross-multiplying and solving for the mass of coke needed, we get: Mass of coke needed = \(\frac{100 \times 75,454.07}{95}\) = 79,424.81 g Thus, the mass of coke needed to react completely with 1.0 ton of copper(II) oxide is 79,424.81 grams.