### Input interpretation

* (NH4)3PO4 **→ ** H2O + NH3 + HPO3*

** water ammonia metaphosphoric acid**

### Balanced equation

Balance the chemical equation algebraically:

* (NH4)3PO4 **→ ** H2O + NH3 + HPO3*

Add stoichiometric coefficients, c, to the reactants and products:

* C1 (NH4)3PO4 **→ ** C2 H2O + C3 NH3 + C4 HPO3*

Set the number of atoms in the reactants equal to the number of atoms in the products for ** N, H, P **and

*O:**N: 3c1 = c3*

*H: 12c1 = 2c2 + 3c3 + c4*

*P: c1 = c4*

*O: 4c1 = c2 + 3 c4*

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

*c1=1*

*c2 = 1*

*c3 = 3*

*c4=1*

Substitute the coefficients into the chemical reaction to

equation:

**Answer:**

* (NH4)3PO4 **→ ** H2O + NH3 + HPO3*