a)
\((1)\,\,4Al + 3{O_2}\buildrel {{t^o}} \over\longrightarrow 2A{l_2}{O_3}\)
\((2)\,\,A{l_2}{O_3} + 6HCl \to 2AlC{l_3} + 3{H_2}O\)
\((3)\,\,\,AlC{l_3} + 3NaOH \to Al{(OH)_3} \downarrow + 3NaCl\)
\((4)\,\,2Al{(OH)_3}\buildrel {{t^o}} \over\longrightarrow A{l_2}{O_3} + 3{H_2}O\)
\((5)\,\,2Al + 3S\buildrel {{t^o}} \over\longrightarrow A{l_2}{S_3}\)
b)
\((1)\,\,2A{l_2}{O_3}\mathrel{\mathop{\kern0pt\longrightarrow}\limits_{criolit}^{đpnc}} 4Al + 3{O_2}\)
\((2)\,\,2Al + 3{H_2}S{O_{4(l)}} \to A{l_2}{(S{O_4})_3} + 3{H_2} \uparrow \)
\((3)\,\,A{l_2}{(S{O_4})_3} + 3BaC{l_2} \to 3BaS{O_4} \downarrow + 2AlC{l_3}\)
\((4)\,\,AlC{l_3} + 3NaOH \to Al{(OH)_3} \downarrow + 3NaCl\)
\((5)\,\,2Al{(OH)_3}\buildrel {{t^o}} \over\longrightarrow A{l_2}{O_3} + 3{H_2}O\)