Titanium oxide crystallizes in the following cubic unit cell:
(b) What is the formula of titanium oxide?

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Identify the positions of the titanium (Ti) and oxygen (O) atoms in the unit cell. In the given diagram, the blue spheres represent Zn atoms and the red spheres represent F atoms. For this problem, assume Zn represents Ti and F represents O.

Determine the number of Ti atoms in the unit cell. Ti atoms are located at the corners and the center of each face of the cubic unit cell. Each corner atom is shared by 8 unit cells, and each face-centered atom is shared by 2 unit cells.

Calculate the total contribution of Ti atoms in the unit cell. There are 8 corner atoms, each contributing 1/8 of an atom, and 6 face-centered atoms, each contributing 1/2 of an atom.

Determine the number of O atoms in the unit cell. O atoms are located entirely within the unit cell, so each O atom counts fully.

Calculate the total number of O atoms in the unit cell. There are 4 O atoms inside the unit cell. Combine the contributions of Ti and O atoms to determine the empirical formula of titanium oxide.

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주요 개념

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Unit Cell Structure

A unit cell is the smallest repeating unit in a crystal lattice that reflects the overall symmetry and structure of the entire crystal. In the case of titanium oxide, understanding the arrangement of atoms within the cubic unit cell is crucial for determining the stoichiometry and formula of the compound. The face-centered cubic structure indicates how atoms are positioned at the corners and the centers of the faces of the cube.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions, based on the conservation of mass. For titanium oxide, knowing the ratio of titanium to oxygen atoms in the unit cell allows us to derive its chemical formula. This concept is essential for understanding how different elements combine in fixed ratios to form compounds.

Ionic Compounds

Ionic compounds are formed through the electrostatic attraction between positively and negatively charged ions. In the case of titanium oxide, titanium typically forms a cation (Ti^4+) while oxygen forms an anion (O^2-). The balance of these charges is critical in determining the empirical formula, which reflects the simplest whole-number ratio of the constituent ions.

Titanium oxide crystallizes in the following cubic unit cell: (b) What is the formula of titanium oxide?