Question

The white pigment titanium oxide crystallizes with titanium ions in one-half of the octahedral holes in a closest-packed array of oxide ions. What is the formula of titanium oxide?

Short answer

The formula of titanium oxide is \({\rm{Ti}}{{\rm{O}}_2}\)

Step-by-step solution

Define the ionic compound features

A compound that crystallizes in a closest-packed array of anions with cations in the tetrahedral holes can have a maximum cation: anion ratio of 2:1; all of the tetrahedral holes are filled at this ratio. Examples include\({\rm{L}}{{\rm{i}}_2}{\rm{O}},{\rm{N}}{{\rm{a}}_2}{\rm{O}},{\rm{L}}{{\rm{i}}_2}\;{\rm{S}}\), and \({\rm{N}}{{\rm{a}}_2}\;{\rm{S}}\)Compounds with a ratio of less than 2:1 that may also crystallize in a closest-packed array of anions with cations in the tetrahedral holes if the ionic sizes fit.

 Identify the molecular formula.

In a closed packed crystal, The number of atoms, for the given case, is an oxide, per unit cell = Number of octahedral voids The possible molecule formula for titanium oxide is;

\(\begin{array}{l}{\rm{Ti}}:{\rm{O}} = \frac{{\frac{1}{2}}}{1}\\{\rm{Ti}}:{\rm{O}} = \frac{1}{2}\end{array}\)

Therefore, formula \( = {\rm{Ti}}{{\rm{O}}_2}\)