12.91P - Chemistry: Molecular Nature Of Matter And Change

Question

Calcium sulfide adopts the sodium chloride crystal structure (Figure). How many ${\mathbf{S}}^{\mathbf{2}\mathbf{-}}$ ions are in the CaS unit cell?

Step-by-Step Solution

Answer

Four ${\mathbf{S}}^{\mathbf{2}\mathbf{-}}$ ions are present in the CaS unit cell

Step 1: Sodium chloride structure

Sodium chloride structure is an anion-occupied face-centered array with cations occupying interpenetrating FCC lattice.

Step 2: Ions in the unit cell

The face-centered cubic unit cell consists of 8 anions in the corner, thus one anion contributing $\frac{\mathbf{1}}{\mathbf{8}}$ to the unit cell. Along with that, anions are present in the center of the six respective faces of the cell. Hereby, each anion contributing $\frac{\mathbf{1}}{\mathbf{2}}$ to the unit cell.

Thus, each unit cell consists of $\mathbf{8}\mathbf{\times }\left(\frac{1}{8}\right)\mathbf{+}\mathbf{6}\mathbf{\times }\left(\frac{1}{2}\right)\mathbf{=}\mathbf{4}$, i.e., four anions in the unit cell.

Similarly, for cations, the ions are arranged in an FCC array, thus four cations in the unit cell.