Here's how to balance the equation for the reaction between aluminum chloride (AlCl₃) and sodium phosphate (Na₃PO₄):

1. Write the unbalanced equation:

AlCl₃ + Na₃PO₄ → AlPO₄ + NaCl

2. Balance the elements one at a time:

* Aluminum (Al): There's one Al on each side, so it's balanced.

* Phosphorus (P): There's one P on each side, so it's balanced.

* Chlorine (Cl): There are three Cl on the left and only one on the right. Add a coefficient of 3 in front of NaCl.

* Sodium (Na): There are three Na on the left and now three on the right.

3. The balanced equation:

AlCl₃ + Na₃PO₄ → AlPO₄ + 3 NaCl

Explanation:

This reaction is a double displacement reaction. The aluminum and sodium ions switch places, forming aluminum phosphate (AlPO₄), which is a solid precipitate, and sodium chloride (NaCl), which remains in solution.