## Input interpretation

We are given a chemical equation to balance:

*P2O5 + BaO → Ba3(PO4)2*

Barium oxide is one of the reactants.

## Balanced equation

To balance the equation algebraically, we need to add stoichiometric coefficients, c;, to the reactants and products:

*c1 P2O5 + c2 BaO → c3 Ba3(PO4)2*

We then set the number of atoms in the reactants equal to the number of atoms in the products for P, O, and Ba:

*P: 2c1 = 2c3*

*O: 5c1 + c2 = 8c3*

*Ba: c2 = 3c3*

As the coefficients are relative quantities and underdetermined, we choose a coefficient to set arbitrarily. To keep the coefficients small, we usually set the arbitrary value to one. For instance, we can set c1 = 1 and solve the system of equations for the remaining coefficients:

*c1 = 1*

*c2 = 3*

*c3 = 1*

We substitute the coefficients into the chemical reaction to obtain the balanced equation:

*P2O5 + 3BaO → Ba3(PO4)2*

## Answer

The balanced chemical equation is

* P2O5 + 3BaO → Ba3(PO4)2*

where barium oxide (BaO) and phosphorus pentoxide (P2O5) react to form barium phosphate (Ba3(PO4)2).