Iridium metal, Ir, crystallizes in a face-centered cubic...

Iridium metal, Ir, crystallizes in a face-centered cubic (close-packed) structure. The edge length of the unit cell was found by $x$ -ray diffraction to be $383.9 \mathrm{pm} .$ The density of iridium is $22.42 \mathrm{~g} / \mathrm{cm}^{3}$. Calculate the mass of an iridium atom. Use Avogadro's number to calculate the atomic mass of iridium.

Key Concepts

Avogadro's Number

Avogadro's number is a fundamental constant that represents the number of atoms or molecules in one mole of a substance. It provides the essential conversion between the microscopic scale (individual atoms) and the macroscopic scale (grams per mole), allowing one to calculate the mass of a single atom from the atomic mass determined experimentally.

Density in Crystalline Solids

Density is defined as the mass per unit volume of a substance and is a central concept bridging the microscopic and macroscopic properties of materials. In crystalline solids, the density is calculated using the total mass of the atoms in a unit cell divided by the cell’s volume. By knowing the density and the number of atoms per unit cell, one can work out the mass of a single atom.

Face-Centered Cubic Structure

A face-centered cubic (FCC) structure is a type of crystal lattice where atoms are located at each corner of the cube as well as at the centers of all cube faces. A key consequence of this arrangement is that each FCC unit cell effectively contains four atoms, which is crucial when relating the measured density and cell dimensions to the mass of individual atoms.

Unit Cell Volume Calculation

The unit cell volume is a fundamental geometric concept in crystallography and is computed by cubing the edge length of the cell. In the context of using crystallographic data, accurately calculating the volume is essential since it is directly used in density calculations to determine how mass is packed within the crystal lattice.

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