Question 17.6: Balance the equation Sn + HNO3 → SnO2 + NO2 + H2O (unbalanc...

Use the Change in Oxidation Number Problem-Solving Strategy

1. Assign oxidation numbers to each element to identify the elements being oxidized and those being reduced. Write the oxidation numbers below each element to avoid confusing them with ionic charge:

Note that the oxidation numbers of Sn and N have changed.

2. Now write two new equations (half-reactions), using only the elements that change in oxidation number. Then add electrons to bring the equations into electrical balance. One equation represents the oxidation step; the other represents the reduction step. Remember: Oxidation produces electrons; reduction uses electrons.

Sn^0→Sn^{4+} + 4 e^-    (oxidation)

Sn^0 loses 4 electrons

N^{5+} + 1 e^-→N^{4+}   (reduction)

N^{5+} gains 1 electron

3. Multiply the two equations by the smallest whole numbers that will make the electrons lost by oxidation equal to the number of electrons gained by reduction. In this reaction the oxidation step is multiplied by 1 and the reduction step by 4. The equations become

Sn^0→Sn^{4+} + 4 e^-  (oxidation)

Sn^0 loses 4 electrons

4 N^{5+} + 4 e^-→4 N^{4+}      (reduction)

4N^{5+} gains 4 electrons

We have now established the ratio of the oxidizing to the reducing agent as being four atoms of N to one atom of Sn.

4. Transfer the coefficient in front of each substance in the balanced
oxidation–reduction equations to the corresponding substance in the
original equation. We need to use 1 Sn, 1 SnO_2 , 4HNO_3 ,   and    4NO_2:

Sn + 4 HNO_3→SnO_2 + 4 NO_2 + H_2O  (unbalanced)

5. In the usual manner, balance the remaining elements that are not oxidized or reduced to give the final balanced equation:

Sn + 4 HNO_3→SnO_2 + 4 NO_2 + 2 H_2O (balanced)

6. Finally, check to ensure that both sides of the equation have the same number of atoms of each element. The final balanced equation contains 1 atom of Sn 4 atoms of N , 4 atoms of H and 12 atoms of O on each side.

Because each new equation presents a slightly different problem and because proficiency in balancing equations requires practice, let’s work through two more examples.