How many atoms are in a 2.0 cm×2.0 cm×2.0 cm cube of aluminum?

Verified step by step guidance

1. Determine the volume of the aluminum cube using the formula for the volume of a cube, V = a^3, where 'a' is the length of a side of the cube.
2. Convert the volume from cubic centimeters to cubic meters by using the conversion factor (1 m = 100 cm).
3. Calculate the mass of the aluminum cube using the density formula, \( \rho = \frac{m}{V} \), where \( \rho \) is the density of aluminum (approximately 2700 kg/m^3). Rearrange the formula to find the mass (m = \( \rho \times V \)).
4. Use Avogadro's number and the molar mass of aluminum to find the number of moles of aluminum in the cube. The molar mass of aluminum is approximately 26.98 g/mol.
5. Multiply the number of moles by Avogadro's number (approximately 6.022 \times 10^{23} atoms/mol) to find the total number of aluminum atoms in the cube.

Key Concepts

Atomic Structure

Atoms are the basic building blocks of matter, consisting of protons, neutrons, and electrons. In a solid like aluminum, atoms are arranged in a closely packed structure, which influences the material's properties. Understanding atomic structure is essential for calculating the number of atoms in a given volume.

Density

Density is defined as mass per unit volume and is a critical property for determining how many atoms are present in a specific volume of material. For aluminum, the density is approximately 2.7 g/cm³. By knowing the density, one can calculate the mass of the aluminum cube and subsequently the number of atoms it contains.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10²³, is the number of atoms or molecules in one mole of a substance. This concept is vital for converting the mass of aluminum into moles and then determining the total number of atoms. It provides a bridge between macroscopic measurements and atomic-scale quantities.