Verified answer

[tex]\boxed{\bf Na \to Na_2O \to NaOH \to Na_2SO_4 \to NaCl \to NaNO_3}[/tex]
[tex]\tt 1)~2 Na + Na_2O_2 \to 2Na_2O.[/tex]
[tex]\tt 2)~Na_2O + H_2O \to 2NaOH.[/tex]
[tex]\tt 3)~2NaOH + H_2SO_4 \to Na_2SO_4 + 2H_2O.[/tex]
[tex]\tt 4) ~ Na_2SO_4 + BaCl_2 \to BaSO_4\downarrow + 2NaCl.[/tex]
[tex]\tt 5)~NaCl + AgNO_3 \to AgCl\downarrow + NaNO_3.[/tex]