This is an oxidation-reduction (redox) reaction:

*2 P0 + 6 e- → 2 P-III (reduction)*

*3 Mg0 - 6 e- → 3 MgII (oxidation)*

**P **is an oxidizing agent, **Mg **is a reducing agent.

### Word equation

*magnesium + red phosphorus → magnesium phosphide*

### Input interpretation

*3Mg + P2 → Mg3P2*

*Magnesium red phosphorus magnesium phosphide*

### Balanced equation

Balance the chemical equation algebraically:

*3Mg + P2 → Mg3P2*

Add stoichiometric coefficients, **c1**, to the reactants and products:

*c13Mg + c2P2 → c3Mg3P2*

Set the number of atoms in the reactants equal to the number of atoms in the products for ** Mg **and

*P:**Mg: c1 = 3c3*

*P: c2 = 2c3*

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** c3 = 1** and solve the system of equations for the remaining coefficients:

* c1 = 3 c2=2*

*c3=1*

Substitute the coefficients into the chemical reaction to obtain the balanced

equation:

**Answer**:

*3Mg + P2 → Mg3P2*