In the Bayer’s process of purification of red bauxite leaching agent is

NaOH is used as leaching agent in Bayer's process
In this process a suitable reagent [NaOH] is made to react with the ore and impurities can't react with NaOH. In red bauxite the impurity present is Fe₂O₃. Fe₂O₃ can't react with NaOH. The NaOH react with Al₂O₃ and form soluble NaAlO₂
$$\begin{gathered} {\mathrm{Al}}_2{\mathrm{O}}_3+2\mathrm{NaOH}\to 2{\mathrm{NaAlO}}_2+{\mathrm{H}}_2\mathrm{O} \\ {\mathrm{NaAlO}}_2+2{\mathrm{H}}_2\mathrm{O}\to \mathrm{Al}{\left(\mathrm{OH}\right)}_3\downarrow +\mathrm{NaOH} \\ 2\mathrm{Al}{\left(\mathrm{OH}\right)}_3\stackrel{∆}{\to }{\mathrm{Al}}_2{\mathrm{O}}_3+3{\mathrm{H}}_2\mathrm{O} \end{gathered}$$