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

To react completely with 1.0 ton of copper(II) oxide, about 79.374 kg of the given coke sample will be needed.

Step-by-step solution

1. Calculate the number of moles of copper(II) oxide in 1 ton

One ton is equal to 1000 kg. Start by converting the given mass of copper(II) oxide to moles. The molar mass of CuO is calculated as \(Cu (63.546g/mol) + O (16g/mol)\), which is 79.546 g/mol. Moles of CuO = \(\frac{Mass_{CuO}}{Molar\_mass_{CuO}}\) Moles of CuO = \(\frac{1000\,\mathrm{kg}}{79.546\,\mathrm{g/mol}} = 12567.312\,\mathrm{moles}\)

2. Determine the moles of carbon needed for this reaction

According to the balanced chemical equation: $$ 2 \mathrm{CuO}(s)+\mathrm{C}(s) \longrightarrow 2 \mathrm{Cu}(s)+\mathrm{CO}_{2}(g) $$ 2 moles of CuO react completely with 1 mole of carbon. Find the moles of carbon needed. Moles of C = \(\frac{1}{2} * Moles_{CuO}\) Moles of C = \(\frac{1}{2} * 12567.312 = 6283.656\,\mathrm{moles}\)

3. Calculate the mass of carbon required

Now, convert the moles of carbon to mass using the molar mass of carbon (12 g/mol). Mass of C = \(Moles_C * Molar\_mass_C\) Mass of C = \(6283.656 * 12 = 75,403.87\, \mathrm{g}\) or \(75.40387\,\mathrm{kg}\)

4. Determine the mass of coke required

Since we know that the coke sample has 95% carbon by mass, we need to find how much coke is necessary to obtain 75.40387 kg of carbon. Let the mass of coke be x. Then, \(95 \%\) of x should equal to the mass of carbon required. Solve for x: \(x * 0.95 = 75.40387\, \mathrm{kg}\) Mass of coke (x) = \(\frac{75.40387}{0.95} = 79.374\, \mathrm{kg}\)

Conclusion

To react completely with 1.0 ton of copper(II) oxide, about 79.374 kg of the given coke sample will be needed.

Key concepts

Carbon Properties

Carbon is a non-metal element that boasts several unique properties making it highly versatile. Its atomic number is 6, and it has an atomic mass of approximately 12 g/mol. Carbon can form various compounds because of its 4 valence electrons, allowing strong covalent bonds with other elements.

The allotropes of carbon, such as graphite and diamond, have distinct structures and properties. Graphite is soft and conducts electricity, while diamond is hard and insulating. These variations highlight carbon's flexibility.

In industrial processes, coke is an impure form of carbon that consists mostly of carbon along with small amounts of other elements. Coke is used primarily in metal extraction processes because of its ability to act as a reducing agent. Being able to donate electrons, carbon is excellent for reducing metal oxides to metals during extraction.

Metal Extraction

Metal extraction is an essential industrial process for obtaining metals from their natural ore forms. Most metals occur naturally in their oxide forms, such as copper(II) oxide, requiring reduction to be converted into pure metals.

Reduction is achieved by heating the metal oxide with a reducing agent, like carbon. During the process, carbon reacts with the metal oxide to form metal and carbon dioxide.

• The metal extraction process removes oxygen from the metal oxide.
• Carbon as a reducing agent plays a key role in changing oxides into metals.
• This extraction is vital for manufacturing metals used in everyday objects and industrial applications.

Understanding the metal extraction process facilitates comprehension of how raw materials transform into usable products.

Copper(II) Oxide

Copper(II) oxide (CuO) is a black solid compound used predominantly in metallurgy. It possesses a molar mass of 79.546 g/mol, calculated by summing the atomic masses of copper (63.546 g/mol) and oxygen (16 g/mol).

CuO acts as a reagent for reactions, such as metal extraction. In the given reaction: \[2\ \mathrm{CuO}(s)+\ \mathrm{C}(s) \longrightarrow 2\ \mathrm{Cu}(s)+\ \mathrm{CO}_{2}(g)\]

• Copper(II) oxide provides copper through reduction by carbon.
• This reaction helps to purify copper for industrial and commercial use.
• It continues to be fundamental in the production of copper in large quantities.

The understanding of CuO and its role is critical for industries utilizing copper in various applications.

Molar Mass Calculations

Molar mass is the mass of one mole of a substance expressed in grams per mole (g/mol). It is fundamental for translating between grams and moles in chemical calculations:

Calculating Molar Mass

Begin by identifying the atomic masses of each element in the compound from the periodic table. For CuO, copper's atomic mass is 63.546 g/mol, and oxygen's is 16 g/mol, totaling 79.546 g/mol.

Moles and Mass Conversion

Utilize the formula: Moles = \(\frac{\text{Mass}}{\text{Molar Mass}}\) to convert mass to moles. This step is vital for quantitatively assessing chemical reactions, like determining how much of each substance to use or expect.

• Molar mass helps in predicting product amounts formed in reactions.
• Proper calculations ensure efficient and optimized use of materials.
• These calculations are crucial for scaling up reactions for industrial applications.

Mastery of molar mass calculations is a cornerstone for effective chemical process management.