A copper wire having a mass of 2.196 g was allowed to react with an excess of sulfur. The excess sulfur was then burned, yielding SO2 gas. The mass of the copper sulfide produced was 2.748 g. (c) Calculate the number of copper ions per cubic centimeter if the density of the copper sulfide is 5.6 g/cm3.

Verified step by step guidance

1. Determine the mass of sulfur that reacted by subtracting the mass of copper from the mass of copper sulfide: \( \text{mass of sulfur} = \text{mass of copper sulfide} - \text{mass of copper} \).
2. Calculate the moles of copper using its molar mass: \( \text{moles of copper} = \frac{\text{mass of copper}}{\text{molar mass of copper}} \).
3. Calculate the moles of sulfur using its molar mass: \( \text{moles of sulfur} = \frac{\text{mass of sulfur}}{\text{molar mass of sulfur}} \).
4. Determine the empirical formula of the copper sulfide by finding the simplest whole number ratio of moles of copper to moles of sulfur.
5. Calculate the number of copper ions per cubic centimeter using the density of copper sulfide and Avogadro's number: \( \text{number of copper ions} = \frac{\text{density} \times \text{Avogadro's number} \times \text{volume}}{\text{molar mass of copper sulfide}} \).

Key Concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows us to calculate the amounts of substances involved based on balanced chemical equations. In this question, stoichiometry is essential for determining the moles of copper sulfide produced from the mass of copper reacted.

Density

Density is defined as the mass of a substance per unit volume, typically expressed in grams per cubic centimeter (g/cm³). It is a crucial property that helps in converting mass to volume and vice versa. In this problem, the density of copper sulfide is used to find the volume of the produced compound, which is necessary for calculating the concentration of copper ions.

Molarity and Ion Concentration

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. To find the number of copper ions per cubic centimeter, we need to relate the mass of copper sulfide to the number of moles and then to the volume. Understanding how to convert between mass, moles, and volume is essential for determining the concentration of ions in a given volume.