In the process of extracting alumina from bauxite, a key step involves the leaching of the ore with a solution of sodium hydroxide (NaOH). The bauxite ore typically consists of various impurities like silica (\( \text{SiO}_2 \)), titanium dioxide (\( \text{TiO}_2 \)), iron(III) oxide (\( \text{Fe}_2\text{O}_3 \)), and other oxides. The goal is to separate alumina (\( \text{Al}_2\text{O}_3 \)) from these impurities.
In this context, let us analyze the behavior of each component when reacted with NaOH:
Silica reacts with NaOH to form sodium silicate (\( \text{Na}_2\text{SiO}_3 \)), which is soluble in water and can be leached out. The reaction is:
\(SiO_2 + 2\,NaOH \rightarrow Na_2SiO_3 + H_2O\)
Titanium dioxide does not react with NaOH and remains insoluble in the leaching process.
Fe2O3 does not dissolve in NaOH under normal conditions and also remains as residue.
Though zinc oxide can react with strong bases, it is not typically present in significant amounts in bauxite ores for this process and is unrelated in the context given.
Thus, the correct answer is silica (\( \text{SiO}_2 \)), as it is the component that reacts with NaOH to form a soluble product that can be leached out during the extraction of alumina from bauxite.
Therefore, the correct option is: SiO_2