Cryolite, $N{a}_{3}Al{F}_6(s),$ an ore used in the production of aluminum, can be synthesized using aluminum oxide.

Balance the equation for the synthesis of cryolite.

equation:

$A{l}_2{O}_3(s)+$NaOH$(l)+HF(g)longrightarrowN{a}_{3}Al{F}_6+H_{2}O(g)$

If $15\mathrm{.}0kg$ of $A{l}_2{O}_3(s),53\mathrm{.}4kg$ of NaOH$(l),$ and $53\mathrm{.}4kg$ of $HF(g)$ react completely, how many kilograms of cryolite are produced?

mass of cryolite produced:

$kgNaAl{F}_6$

Which reactants are in excess?

$HF$