Problem 111 - Introductory Chemistry Atoms First

Question

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 \(=2000 \mathrm{lb} ; 1 \mathrm{~kg}=2.205 \mathrm{lb}]\)

Step-by-Step Solution

Answer

The balanced chemical equation for the reaction between copper(I) oxide and solid carbon is: Cu₂O + C → 2Cu + CO₂ To react completely with 1 ton of copper(I) oxide, 80.12 kg of coke (which is 95% carbon by mass) is required.

Step 1: Write the balanced chemical equation

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

Step 2: Calculate the mass of coke required

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.

Key Concepts

Chemical Reactions

Chemical reactions are processes where reactants are transformed into products. They are the heart of chemistry, showing how substances change and interact to form new materials. In our reaction, copper(I) oxide ( Cuₗ O) reacts with solid carbon ( C ) to form copper metal ( Cu ) and carbon dioxide gas ( CO₂ ). This is an example of a redox reaction, where electrons are transferred between the reactants, leading to the formation of new bonds and distinct products. Such reactions are essential in industries and laboratories, driving processes from metal extraction to everyday combustion.

Balanced Chemical Equations

A balanced chemical equation ensures that the number of each type of atom is the same on both sides of the equation. This adheres to the law of conservation of mass, stating that mass cannot be created or destroyed in a chemical reaction. In the equation for our reaction:
Cu₂O + C → 2Cu + CO₂
We see that:

• There are 2 copper (Cu) atoms on both sides.
• There is 1 oxygen (O) atom on both sides.
• There is 1 carbon (C) atom on both sides.

Balancing a reaction involves adjusting the coefficients (the numbers in front of the reactants and products) until each element has the same number of atoms on both sides. Balanced equations are crucial for calculating the precise amounts of reactants and products involved in the reaction.

Molar Mass Calculations

Molar mass is a key concept in stoichiometry, representing the mass of one mole of a substance. It links the microscopic world of atoms and molecules to the macroscopic scale of grams and kilograms used in the laboratory. For copper(I) oxide, the molar mass is calculated by adding the atomic masses of its constituent atoms:

• Cu: 63.55 g/mol (two atoms of copper in Cu₂O = 2 x 63.55 g/mol)
• O: 16 g/mol

Total for Cu₂O: 143.10 g/mol
This value is used to convert weights (like kilograms of copper(I) oxide) into moles, which is crucial for determining how much of other substances will react. Understanding molar mass allows chemists to measure ingredients accurately and predict product yields.

Reaction Stoichiometry

Reaction stoichiometry involves the quantitative relationships between the quantities of reactants and products in a chemical reaction. Through stoichiometry, we can predict the amounts of substances consumed and produced. In our problem, stoichiometry is employed to find how much coke, which is mostly carbon, is required to fully react with a certain amount of copper(I) oxide. Since the balanced equation tells us that 1 mole of Cu₂O reacts with 1 mole of C, we can use the molar masses:

• Copper(I) oxide is 143.10 g/mol
• Carbon is 12.01 g/mol

By converting the given mass of copper(I) oxide to moles, we can determine the exact moles of carbon needed. Considering that coke is 95% pure carbon, we adjust for impurities to find the real amount required. Reaction stoichiometry lets us accurately calculate and plan chemical processes and is foundational in both practical and theoretical chemistry.