Brass is a substitutional alloy consisting of a solution of copper and zinc. A particular sample of red brass consisting of 80.0 % Cu and 20.0 % Zn by mass has a density of 8750 kg/m³. (a) What is the molality of Zn in the solid solution?

Verified step by step guidance

1. Calculate the mass of zinc in 1 kg of the brass sample. Since the sample is 20.0% Zn by mass, the mass of Zn is 0.20 kg.
2. Calculate the mass of copper in 1 kg of the brass sample. Since the sample is 80.0% Cu by mass, the mass of Cu is 0.80 kg.
3. Determine the number of moles of Zn using its molar mass (65.38 g/mol). Convert the mass of Zn from kg to g before using the formula: moles = mass (g) / molar mass (g/mol).
4. Determine the number of moles of Cu using its molar mass (63.55 g/mol). Convert the mass of Cu from kg to g before using the formula: moles = mass (g) / molar mass (g/mol).
5. Calculate the molality of Zn in the solution using the formula: molality (m) = moles of solute (Zn) / mass of solvent (Cu) in kg.

Key Concepts

Molality

Molality is a measure of the concentration of a solute in a solution, defined as the number of moles of solute per kilogram of solvent. It is particularly useful in situations where temperature changes may affect volume, as it is based on mass rather than volume. In this case, calculating the molality of zinc (Zn) in the brass alloy requires knowing the mass of the solvent, which is the copper (Cu) in the alloy.

Density

Density is defined as mass per unit volume and is a critical property for understanding the composition of materials. In the context of the brass alloy, the given density allows for the conversion between mass and volume, which is essential for determining the amounts of copper and zinc present in the sample. Knowing the density helps in calculating the total mass of the alloy, which is necessary for further calculations.

Alloy Composition

An alloy is a mixture of two or more elements, where at least one is a metal, and its properties differ from those of its constituent elements. In this case, brass is a substitutional alloy of copper and zinc, meaning that zinc atoms replace some of the copper atoms in the metallic lattice. Understanding the composition of the alloy is crucial for calculating the molality, as it directly influences the amounts of each metal present in the sample.