A number of metal oxides are known to form “nonstoichiometric” compounds, in which the ratios of atoms that make up the compound cannot be expressed in small whole numbers. In the crystal structure of a nonstoichiometric compound, some of the lattice points where one would have expected to find atoms are vacant. Transition metals most easily form nonstoichiometric compounds because of the number of oxidation states that they can have. For example, a titanium oxide with formula TiO_1.18 is known.

(a) Calculate the average oxidation number of titanium in this compound.

(b) If the compound has both Ti²⁺ and Ti³⁺ ions present, what fraction of the titanium ions will be in each oxidation state?