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Chapter 3: Problem 119

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(Il) oxide. $$ 2 \mathrm{CuO}(s)+\mathrm{C}(s) \longrightarrow 2 \mathrm{Cu}(s)+\mathrm{CO}_{2}(g) $$

Short Answer

Expert verified
To react completely with 1.0 ton of copper(II) oxide, we need 79.5 kg of coke, which contains 95% carbon by mass. This is achieved through the stoichiometry of the balanced chemical equation, mole ratios, and mass calculations as follows: Conversion of 1.0 ton CuO to moles, finding the moles of carbon needed using the 2:1 mole ratio, calculating mass of pure carbon, and finally calculating the mass of coke required.

Step by step solution

01

1. Convert the mass of copper(II) oxide to moles

First, we need to convert the mass of copper(II) oxide to moles. The molar mass of copper(II) oxide (CuO) is: Molar mass of CuO = (63.5 + 16.0) g/mol = 79.5 g/mol As 1 ton is equal to 1000 kg, we first convert the mass of copper(II) oxide to grams: 1.0 ton = 1000 kg = 1,000,000 g Now, we can find the number of moles of CuO: Number of moles of CuO = (mass of CuO) / (molar mass of CuO) = (1,000,000 g) / (79.5 g/mol) = 12,579.75 moles
02

2. Find the number of moles of carbon needed

Using the balanced chemical equation, we can determine the number of moles of carbon needed to react with the given moles of CuO: 2 CuO(s) + C(s) → 2 Cu(s) + CO₂(g) The mole ratio of CuO to C is 2:1, so we will need half of the moles of CuO in moles of carbon: Number of moles of carbon = 1/2 × number of moles of CuO = 1/2 × 12,579.75 moles = 6,289.875 moles
03

3. Find the mass of pure carbon needed

Now that we have the number of moles of carbon needed, we can find the mass of carbon required for the reaction using the molar mass of carbon, which is 12.01 g/mol: Mass of carbon = (number of moles of carbon) × (molar mass of carbon) = (6,289.875 moles) × (12.01 g/mol) = 75,545.45125 g
04

4. Calculate the mass of coke needed

As the coke is 95% carbon by mass, we need to find the mass of coke that contains the required amount of carbon: Mass of coke = (Mass of carbon) / (percentage of carbon in coke) = (75,545.45125 g) / 0.95 = 79,521 g or 79.5 kg Therefore, 79.5 kg of coke is needed to react completely with 1.0 ton of copper(II) oxide.

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Most popular questions from this chapter

A 1.500 -g sample of a mixture containing only \(\mathrm{Cu}_{2} \mathrm{O}\) and CuO was treated with hydrogen to produce 1.252 \(\mathrm{g}\) of pure cupper metal. Calculate the mass percent of \(\mathrm{Cu}_{2} \mathrm{O}\) in the original mixture.

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A compound contains only \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{N}\) . Combustion of 35.0 \(\mathrm{mg}\) of the compound produces 33.5 $\mathrm{mg} \mathrm{CO}_{2}\( and 41.1 \)\mathrm{mg}\( \)\mathrm{H}_{2} \mathrm{O}$ . What is the empirical formula of the compound?

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