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

Short answer

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

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

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

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

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.

Key concepts

Chemical Reactions

In the realm of chemistry, a chemical reaction describes a process where substances, known as reactants, are transformed into different substances called products. These transformations occur due to the breaking and forming of chemical bonds. This principle is fundamental to understanding how different elements and compounds interact in diverse environments. Regarding the given equation: \(2 \ \text{CuO}(s) + \text{C}(s) \rightarrow 2 \ \text{Cu}(s) + \text{CO}_2(g)\),

• This balanced equation shows that two moles of copper(II) oxide \((\text{CuO})\) react with one mole of carbon \((\text{C})\) to produce two moles of copper \((\text{Cu})\) and one mole of carbon dioxide \((\text{CO}_2)\).
• Balanced chemical equations are crucial as they ensure the law of conservation of mass is adhered to, meaning the reactants' atoms are accounted for in the products.
• In industrial processes, such reactions are used to extract metals from their oxides. For example, coke, which is a form of carbon, is used in reducing metal oxides to their base metals, as seen in the production of copper from copper(II) oxide.

Mole Concept

The mole concept is a critical component of stoichiometry and is used to express amounts of a chemical substance. It serves as a bridge between the atomic scale and the macro scale of laboratory practice. One mole contains exactly \(6.022 \times 10^{23}\) entities, typically atoms or molecules.

• In our reaction, we begin by converting the mass of copper(II) oxide (CuO) into moles, since stoichiometry calculations are based on mole ratios rather than mass ratios.
• To find moles, you divide the mass of a substance by its molar mass. In this exercise, 1 ton (or 1,000,000 g) of CuO is converted into moles by dividing by its molar mass of 79.5 g/mol, resulting in 12,579.75 moles of CuO.
• The balanced chemical equation provides the mole ratio needed to determine how many moles of carbon are required to react with the CuO. For every two moles of CuO, one mole of carbon is needed, making it 6,289.875 moles of carbon.

Mass Calculations

Mass calculations are essential in stoichiometry for determining the quantity of materials needed or produced in a chemical reaction. After establishing the amount of carbon needed in moles, the next step is converting these moles into mass.

• The mass of carbon is calculated by multiplying the number of its moles by its molar mass, which is about 12.01 g/mol. This gives the mass of carbon necessary for the reaction, calculated as 75,545.45125 g in our problem.
• However, the carbon source, coke, contains impurities. For practical applications, adjusting for purity is crucial, and in this case, only 95% of the coke's mass is carbon.
• To find the actual mass of coke needed, divide the required mass of pure carbon by the decimal equivalent of the percentage of carbon in coke, arriving at a necessary mass of 79,521 g (or 79.5 kg).

Carbon Chemistry

Carbon is a versatile element, central to many industrial processes due to its ability to form various allotropes and compounds. In carbon chemistry, understanding how carbon reacts and contributes to reactions is key.

• In the context of metallurgy, carbon acts as a reducing agent, meaning it helps to convert metal oxides into their metals by combining with the oxygen to form carbon dioxide.
• Coke, an impure form of carbon, is used extensively in this role in industries to facilitate large-scale chemical reductions, such as producing metals from oxides.
• This specific reaction showcases not only a fundamental concept in carbon chemistry but also highlights the importance of knowing the material specifications, such as purity levels, to ensure efficient and effective industrial processes.

By understanding these aspects of carbon chemistry, one can see why carbon, despite its simplicity, is incredibly valuable in both practical and theoretical applications.