### This is an **oxidation-reduction** (redox) reaction:

* 3* **Mg**0 - *6* **e**- → *3* **Mg**II *(oxidation)*

* 3* **N**V + *3* **e**- → *3* **N**IV *(reduction)*

** Fe**III + *3* **e**- → **Fe**0 *(reduction)*

*Mg* is a **reducing** agent, *Fe(NO3)3* is an **oxidizing** agent, *Fe(NO3)3* is an **oxidizing** agent.

*Mg*

*Fe(NO3)3*

*Fe(NO3)3*

### Word equation

* magnesium + ferric nitrate → magnesium nitrate + iron*

### Input interpretation

* Mg + Fe(NO3)3 → Mg(NO3)2 + Fe*

** Magnesium ferric nitrate magnesium nitrate iron**

### Balanced equation

Balance the chemical equation algebraically:

* Mg + Fe(NO3)3 → Mg(NO3)2 + Fe*

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

* c1 Mg + c2 Fe(NO3)3 → c3 Mg(NO3)2 + c4 Fe*

Set the number of atoms in the reactants equal to the number of atoms in the products for **Mg, Fe, N **and **O:**

* Mg: c1=c3*

* Fe: c2=c4*

* N: 3c2=2c3*

*0: 9c2=6c3*

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 **c2 = 1 **and solve the system of equations for the remaining coefficients:

* c1 = 3/2 c2 = 1*

* c3 = 3/2 c4 = 1*

Multiply by the least common denominator, 2, to eliminate fractional coefficients:

* c1 = 3 c2 = 2*

* c3 = 3 c4 = 2*

Substitute the coefficients into the chemical reaction to obtain the balanced equation:

**Answer:**

* Mg + Fe(NO3)3 → Mg(NO3)2 + Fe*