An unknown metal with an fcc structure has a density of 10.5 g/cm³, and the edge length of the unit cell is 409 pm.What is the probable identity of the metal?

Question

Quizplus · Accepted Answer

The face-centered cubic (fcc) structure has 4 atoms per unit cell. The density (ρ) can be used with the formula ρ = (Z*M)/(a^3*N_A), where Z is the number of atoms per unit cell (4 for fcc), M is the molar mass, a is the edge length in cm (409 pm = 4.09 x 10^-8 cm), and N_A is Avogadro's number (6.022 x 10^23 mol^-1). Rearranging to solve for M gives M = ρ*a^3*N_A/Z. Substituting the given values (ρ = 10.5 g/cm^3, a = 4.09 x 10^-8 cm), we find M closely matches the molar mass of Silver (Ag), which is approximately 107.87 g/mol, identifying the metal as Silver.

An Unknown Metal with an Fcc Structure Has a Density