Write the valency of the following radicals and represent them by a putting a positive or a negative sign. 

${\mathrm{CO}}_3, {\mathrm{SO}}_4, \mathrm{Cl}, {\mathrm{PO}}_4, \mathrm{Al}, \mathrm{Na}, \mathrm{Ca}, \mathrm{Mg}.$

Balance the following chemical equation:

$\mathrm{Al} +{\mathrm{O}}_2\to {\mathrm{Al}}_2{\mathrm{O}}_3$

Balance the following chemical equation:

$\mathrm{NaOH} +{\mathrm{H}}_2{\mathrm{SO}}_4 \to {\mathrm{Na}}_2{\mathrm{SO}}_4 +2{\mathrm{H}}_2\mathrm{O}$

Balance the following chemical equation:

${\mathrm{MnO}}_2+\mathrm{HCl} \to {\mathrm{MnCl}}_2 +{\mathrm{Cl}}_2\uparrow +{\mathrm{H}}_2\mathrm{O}$

Balance the following chemical equation:

${\mathrm{KClO}}_3\to \mathrm{KCl} +{\mathrm{O}}_2\uparrow$

Balance the following chemical equation:

${\mathrm{KMnO}}_4+\mathrm{HCl}\to \mathrm{KCl}+{\mathrm{MnCl}}_2+{\mathrm{Cl}}_2\uparrow +{\mathrm{H}}_2\mathrm{O}$