Problem 64 - Chemistry and Chemical Reactivity

Question

Sulfuric acid can be prepared starting with the sulfide ore, cuprite \(\left(\mathrm{Cu}_{2} \mathrm{S}\right) .\) If each \(\mathrm{S}\) atom in \(\mathrm{Cu}_{2} \mathrm{S}\) leads to one molecule of \(\mathrm{H}_{2} \mathrm{SO}_{4},\) what mass of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) can be produced from \(3.00 \mathrm{kg}\) of \(\mathrm{Cu}_{2} \mathrm{S} ?\)

Step-by-Step Solution

Answer

1.85 kg of \( \text{H}_2\text{SO}_4 \) can be produced.

Step 1: Molar Mass Calculation of Cu2S

Calculate the molar mass of cuprite, \( \text{Cu}_2\text{S} \). The atomic mass of copper (Cu) is approximately 63.55 g/mol and sulfur (S) is about 32.07 g/mol. Therefore, the molar mass of \( \text{Cu}_2\text{S} \) is calculated as follows: \( 2 \times 63.55 + 32.07 = 159.17 \) g/mol.

Step 2: Convert Mass of Cu2S to Moles

Convert the given mass of \( \text{Cu}_2\text{S} \) into moles. Given mass is 3,000 g (since 3.00 kg = 3,000 g). Use the formula \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \). So, the number of moles of \( \text{Cu}_2\text{S} \) is \( \frac{3000}{159.17} \approx 18.85 \) moles.

Step 3: Determine Moles of H2SO4 Produced

Each sulfur atom in \( \text{Cu}_2\text{S} \) leads to one molecule of \( \text{H}_2\text{SO}_4 \). Since there are 18.85 moles of \( \text{Cu}_2\text{S} \), there are also 18.85 moles of \( \text{H}_2\text{SO}_4 \) produced.

Step 4: Calculate Mass of H2SO4

Calculate the mass of \( \text{H}_2\text{SO}_4 \) using its molar mass. The molar mass of \( \text{H}_2\text{SO}_4 \) is \( 2 \times 1.01 + 32.07 + 4 \times 16.00 = 98.09 \) g/mol. Thus, the mass of \( \text{H}_2\text{SO}_4 \) produced is \( 18.85 \times 98.09 \approx 1,848.08 \) g, or 1.85 kg.

Key Concepts

Understanding Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It is essential in determining how much product you can obtain from given amounts of reactants. In this exercise, we start with cuprite, \( \text{Cu}_2\text{S} \), and aim to find out how much sulfuric acid, \( \text{H}_2\text{SO}_4 \), can be produced. Through stoichiometry, we predict the quantity of product formed in chemical reactions based on the balanced chemical equations. This means knowing that each sulfur atom in cuprite will form one molecule of sulfuric acid, emphasizing a 1:1 mole ratio in this scenario. This directly relates the moles of the reactant to the moles of the product, allowing for the conversion calculations necessary for any further steps.

Calculating Molar Mass

Molar mass is a crucial concept in chemistry, needed to convert mass into moles. It refers to the mass of one mole of a substance and is usually expressed in grams per mole (g/mol).The exercise provides us with one compound, \( \text{Cu}_2\text{S} \), for which we calculate the molar mass as follows:- Copper (Cu) has an atomic mass of approximately 63.55 g/mol.- Sulfur (S) has an atomic mass of about 32.07 g/mol.Combining these, the molar mass of cuprite is:- \( 2 \times 63.55 + 32.07 = 159.17 \) g/mol.Calculating the molar mass is pivotal for determining how many moles are present in a given mass of a compound, setting the stage for stoichiometric conversions.

Interpreting Chemical Reactions

Chemical reactions illustrate how substances transform into different compounds. They are represented through balanced equations where the number of atoms of each element is the same on both sides. In the context of this exercise, although no explicit reaction was given, the information highlights the transformation from \( \text{Cu}_2\text{S} \) to \( \text{H}_2\text{SO}_4 \). Understanding that each sulfur atom in \( \text{Cu}_2\text{S} \) transforms into one molecule of \( \text{H}_2\text{SO}_4 \) emphasizes the importance of the chemical formula in predicting products. This is useful in determining the proportion or yield we can expect when carrying out a chemical reaction, helping to calculate the possible mass of products formed.

Converting Mass to Moles

Converting mass to moles is a fundamental skill in chemistry that facilitates stoichiometric calculations. Given a mass, you use the molar mass of the substance to determine how many moles it represents.In the exercise, we started with \( 3.00 \) kg of \( \text{Cu}_2\text{S} \). This can be converted to g (3000 g) for easier calculation:

• Use the formula: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \).
• Plug the values: \( \frac{3000}{159.17} \approx 18.85 \) moles.

This calculation is vital because it tells us how much reactant we have in terms of moles, which is directly used in the stoichiometric calculations to find out the moles and subsequently the mass of the product formed.