A cube of gold that is 1.00 cm on a side has a mass of 19.3 g. A single gold atom has a mass of 197.0 u. (a) How many gold atoms are in the cube?

Key Concepts

Density and Mass

Density is defined as mass per unit volume and is a crucial property of materials. In this case, the density of gold can be calculated using the mass of the cube (19.3 g) and its volume (1.00 cm³). Understanding how to relate mass and volume through density is essential for determining the number of atoms in the cube.

Molar Mass and Avogadro's Number

The molar mass of a substance is the mass of one mole of its entities, typically expressed in grams per mole. For gold, the molar mass is approximately 197.0 g/mol. Avogadro's number, 6.022 x 10²³, represents the number of atoms in one mole of a substance, allowing us to convert between mass and the number of atoms.

Calculating Number of Atoms

To find the number of atoms in a sample, one can use the formula: number of atoms = (mass of the sample / molar mass) x Avogadro's number. This calculation combines the concepts of mass, molar mass, and Avogadro's number to determine how many individual atoms are present in a given mass of a substance.