Question

one of the various titanium oxides crystallizes with a cubic unit cell that contains titanium ions at the corners and in the center. oxide ions are located at the center of each edge of the unit cell. what is the formula of the compound?

Answer 1

The formula of the titanium oxide with the described unit cell structure is Ti2O3, consisting of two titanium ions and three oxide ions per unit cell.

Step-by-step explanation:

The formula of the titanium oxide that crystallizes with a cubic unit cell with titanium ions at the corners and in the center, and oxide ions at the center of each edge, can be deduced by examining the contributions of each ion to the unit cell.

Each corner atom contributes 1/8 of its presence to the unit cell, and with 8 corners, you get 1 titanium ion (8 * 1/8). The titanium ion at the center contributes fully, adding another whole titanium ion.

This totals to 2 titanium ions per unit cell (Ti2+). There are 12 edges, and each oxide ion contributes 1/4 of its presence to the unit cell (12 * 1/4), yielding 3 oxide ions (O2-). Therefore, the formula of this compound is Ti2O3.