A pure metal M crystallizes in a face-centered cubic (fcc) lattice. A sample of this metal is found to contain 3.612 10²⁴ tetrahedral voids. If the atomic mass of the metal is 27 g mol ⁻¹ , the mass of the metal sample in grams is _____. (Given N_A = 6.02 10²³ mol ⁻¹ )

Step-by-step solution

In a face-centered cubic (fcc) lattice, the number of tetrahedral voids is twice the number of atoms. Let the number of atoms in the sample be N . Number of tetrahedral voids = 2N = 3.612 10²⁴ N = 3.612 10²⁴ 2 = 1.806 10²⁴ atoms Number of moles of metal M = N N_A = 1.806 10²⁴ 6.02 10²³ = 3 mol Mass of the sample = moles atomic mass = 3 27 = 81 g Answer: 81