Question

Write complete balanced half-reactions for (a) reduction of nitrate ion to $\mathrm{NO}$ in acidic solution, (b) oxidation of ${\mathrm{HNO}}_2$ to ${\mathrm{NO}}_2$ in acidic solution.

Short answer

(a) The balanced reduction half-reaction for the reduction of nitrate ion to nitric oxide in acidic solution is: $N{O}_3^{-}+4H^{+}+3e^{-}\to NO+2H_{2}O$ (b) The balanced oxidation half-reaction for the oxidation of nitrous acid to nitrogen dioxide in acidic solution is: $HN{O}_2+H_{2}O+3e^{-}\to N{O}_2+3H^{+}$

Step-by-step solution

Write the unbalanced half-reaction

First, write the unbalanced reduction half-reaction: NO3⁻ → NO

Balance atoms that aren't oxygen or hydrogen

In this case, nitrogen atoms are already balanced. So we don't need to do anything here.

Balance oxygen atoms using water (H2O) molecules

There are three oxygen atoms in NO3⁻ and only one in NO. Therefore, we need to add two water molecules on the right side to balance the oxygen atoms. NO3⁻ → NO + 2H2O

Balance hydrogen atoms using protons (H⁺)

Now we have four hydrogen atoms on the right side, but none on the left. So we need to add four protons (H⁺) on the left side to balance. NO3⁻ + 4H⁺ → NO + 2H2O

Balance charge using electrons (e⁻)

Finally, we need to balance the charge. The left side has a charge of +3 (+1 for each of the 4 protons, and -1 for the nitrate ion), and the right side has a charge of 0. Therefore, we need to add 3 electrons (e⁻) to the right side to balance the charges: NO3⁻ + 4H⁺ + 3e⁻ → NO + 2H2O So the balanced reduction half-reaction is: NO3⁻ + 4H⁺ + 3e⁻ → NO + 2H2O (b) Oxidation of nitrous acid to nitrogen dioxide in acidic solution

Write the unbalanced half-reaction

First, write the unbalanced oxidation half-reaction: HNO2 → NO2

Balance atoms that aren't oxygen or hydrogen

In this case, nitrogen atoms are already balanced. So we don't need to do anything here.

Balance oxygen atoms using water (H2O) molecules

There are two oxygen atoms in NO2 and only one in HNO2. Therefore, we need to add one water molecule on the left side to balance the oxygen atoms. HNO2 + H2O → NO2

Balance hydrogen atoms using protons (H⁺)

Now, we have 3 hydrogen atoms on the left side and none on the right side, so we need to add 3 protons (H⁺) on the right side to balance. HNO2 + H2O → NO2 + 3H⁺

Balance charge using electrons (e⁻)

Finally, we need to balance the charge. The left side has a charge of 0, and the right side has a charge of +3. Therefore, we need to add 3 electrons (e⁻) to the left side to balance the charges: HNO2 + H2O + 3e⁻ → NO2 + 3H⁺ So the balanced oxidation half-reaction is: HNO2 + H2O + 3e⁻ → NO2 + 3H⁺

Key concepts

Half-Reactions

Understanding half-reactions is crucial in solving problems involving redox (reduction-oxidation) reactions. A redox reaction can be split into two separate parts called half-reactions: one for oxidation and one for reduction. Oxidation involves the loss of electrons, while reduction involves the gain of electrons. Each half-reaction shows either the oxidation or reduction process solely, along with the electrons that are lost or gained. This makes it easier to balance complex redox equations by focusing on each process independently.

For instance, the reduction half-reaction for the conversion of nitrate ion to nitrogen monoxide in the acidic solution is NO3⁻ + 4H⁺ + 3e⁻ → NO + 2H2O. This demonstrates the gain of electrons (e⁻) by nitrate ions, while the oxidation half-reaction for the conversion of nitrous acid to nitrogen dioxide is HNO2 + H2O + 3e⁻ → NO2 + 3H⁺, showing the loss of electrons from nitrous acid.

Oxidation States

The oxidation state, often called oxidation number, is an indicator of the degree of oxidation of an atom in a chemical compound. It is a theoretical charge that an atom would have if all bonds to atoms of different elements were 100% ionic. Balancing redox reactions requires a clear understanding of oxidation states because these reactions involve changes in oxidation states. Atoms in a molecule or ion either increase or decrease their oxidation state when oxidized or reduced, respectively.

To correctly balance the half-reactions, identifying the change in oxidation states helps in determining the number of electrons gained or lost. For example, in the reduction of nitrate ion (NO3⁻) to NO, the nitrogen atom’s oxidation state decreases, meaning it gains electrons. Conversely, in the oxidation of HNO2 to NO2, the nitrogen’s oxidation state increases as it loses electrons.

Stoichiometry

Stoichiometry is the area of chemistry that involves the calculation of the quantities of reactants and products in a chemical reaction. It is vital for balancing reactions, including redox reactions, to ensure that the law of conservation of mass is obeyed. In stoichiometry, the coefficients of the reactants and products are adjusted to have the same number of atoms of each element on both sides of the equation.

In redox reactions, additional steps are taken to balance the charge as well as the atoms. This may involve adding water molecules to balance oxygen, protons (H⁺) to balance hydrogen in acidic solutions, and electrons to balance the charges. In the balanced half-reactions provided above, stoichiometry ensures that, in addition to having the same types and numbers of atoms on each side, the overall charge is also the same on both sides of the equation.

Acidic Solution Chemistry

In the context of balancing redox reactions, it is important to note the environment in which the reaction occurs. Redox reactions can take place in either acidic or basic solutions, and this affects how the balancing is approached. When dealing with acidic solution chemistry, H⁺ ions (protons) are available in the solution and are used to balance hydrogen atoms in the half-reactions. Water (H2O) is also commonly used to balance oxygen atoms.

This differs from basic solution chemistry, where OH⁻ ions would be used instead. The presence of H⁺ in the balancing of the reactions illustrated above is specific to acidic solutions. These reactions are tailored to this environment, underscoring the adaptability of balancing techniques depending on the solution's acidity or basicity.