Problem 93 - 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 is the theoretical yield of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) from \(3.00 \mathrm{kg}\) of \(\mathrm{Cu}_{2} \mathrm{S}\) ?

Step-by-Step Solution

Answer

The theoretical yield of \( \mathrm{H}_{2}\mathrm{SO}_{4} \) is 1.848 kg.

Step 1: Calculate the Molar Mass of Cu2S

First, determine the molar mass of cuprite, \( \mathrm{Cu}_{2}\mathrm{S} \). Copper (Cu) has a molar mass of 63.55 g/mol, and sulfur (S) has a molar mass of 32.07 g/mol. The molar mass of \( \mathrm{Cu}_{2}\mathrm{S} \) is calculated as: \((2 \times 63.55) + 32.07 = 159.17 \text{ g/mol}.\)

Step 2: Convert Mass of Cu2S to Moles

Use the mass of cuprite given (3.00 kg) and convert it to grams (3000 g) to find the number of moles. Use the formula \( \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \).\[\text{moles of } \mathrm{Cu}_{2}\mathrm{S} = \frac{3000 \text{ g}}{159.17 \text{ g/mol}} \approx 18.85 \text{ moles.}\]

Step 3: Calculate Moles of H2SO4 Produced

Since each S atom in \( \mathrm{Cu}_{2}\mathrm{S} \) produces one molecule of \( \mathrm{H}_{2}\mathrm{SO}_{4} \), the moles of \( \mathrm{H}_{2}\mathrm{SO}_{4} \) produced is equal to the moles of \( \mathrm{Cu}_{2}\mathrm{S} \). Therefore, \( 18.85 \text{ moles of } \mathrm{H}_{2}\mathrm{SO}_{4} \) are produced.

Step 4: Convert Moles of H2SO4 to Grams

Calculate the theoretical yield of \( \mathrm{H}_{2}\mathrm{SO}_{4} \) in grams. Use the molar mass of \( \mathrm{H}_{2}\mathrm{SO}_{4} \), which is \( 98.09 \text{ g/mol} \).\[\text{mass of } \mathrm{H}_{2}\mathrm{SO}_{4} = 18.85 \text{ moles} \times 98.09 \text{ g/mol} \approx 1848 \text{ g}.\]

Step 5: Convert Grams to Kilograms

Finally, convert the mass of \( \mathrm{H}_{2}\mathrm{SO}_{4} \) from grams to kilograms.\[1848 \text{ g} = 1.848 \text{ kg}.\]

Key Concepts

Sulfuric Acid

Sulfuric acid, with the chemical formula \( \mathrm{H}_2\mathrm{SO}_4 \), is one of the most important industrial chemicals in the world. It is a strong acid used in various applications, from manufacturing fertilizers to chemical synthesis. Understanding how it can be produced from raw materials like copper sulfide \( (\mathrm{Cu}_2\mathrm{S}) \) is essential for industrial chemistry.
When discussing production, we often refer to the process as the conversion of sulfur atoms from the raw material into sulfuric acid molecules. As each sulfur atom in \( \mathrm{Cu}_2\mathrm{S} \) can form one molecule of \( \mathrm{H}_2\mathrm{SO}_4 \), the material balance and understanding of stoichiometry come into play.
Producing sulfuric acid efficiently requires knowledge of multiple disciplines within chemistry, such as reactions, yields, and mass conservation during chemical processes.

Stoichiometry

Stoichiometry is the quantitative relationship between the reactants and products in a chemical reaction. It involves the use of balance and proportion to predict the quantity of products that will form in a reaction. This is crucial when calculating the theoretical yield of sulfuric acid from a given amount of a compound like \( \mathrm{Cu}_2\mathrm{S} \).
In this context, stoichiometry requires knowledge of the molecular or formula mass of each substance involved, allowing for the conversion between mass (in grams) and quantity (in moles). This conversion is vital because reactions at the molecular level happen between moles, not masses.
For example, understanding that each sulfur atom in \( \mathrm{Cu}_2\mathrm{S} \) contributes to one molecule of \( \mathrm{H}_2\mathrm{SO}_4 \) showcases how stoichiometry provides a blueprint for the expected interaction between elements in a given reaction.

Molar Mass Calculation

Calculating the molar mass is an essential skill when working with chemical equations and reactions. The molar mass is the mass of one mole of a substance, usually expressed in grams per mole, and it is calculated by summing the atomic masses of all atoms in a molecule.
For instance, to find the molar mass of cuprite, \( \mathrm{Cu}_2\mathrm{S} \), you add twice the atomic mass of copper (63.55 g/mol each) to the atomic mass of sulfur (32.07 g/mol), giving a total molar mass of 159.17 g/mol.
This calculated molar mass is then used as a conversion factor from grams to moles, which is the first crucial step in determining the theoretical yield of sulfuric acid from the initial mass of \( \mathrm{Cu}_2\mathrm{S} \).
This skill leads to accurate predictions in reaction outcomes.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products. They are characterized by the rearrangement of atoms and changes in chemical properties. In the case of \( \mathrm{Cu}_2\mathrm{S} \) reacting to form \( \mathrm{H}_2\mathrm{SO}_4 \), the sulfur atoms in the copper sulfide are key players, undergoing chemical change to produce sulfuric acid in certain industrial processes.
To understand these transformations, one must be familiar with the types of reactions, such as synthesis or decomposition, that occur. The balanced chemical equations represent the conservation of mass and energy, ensuring that all atoms present in the reactants are accounted for in the products.
This balance is essential when predicting the yield of reactions and allows chemists to determine the efficiency of industrial processes, helping to maximize product formation while minimizing waste.