Problem 56 - Chemistry The Central Science

Question

Write complete balanced half-reactions for (a) reduction of nitrate ion to NO in acidic solution, (b) oxidation of HNO \(_{2}\) to \(\mathrm{NO}_{2}\) in acidic solution.

Step-by-Step Solution

Answer

(a) Reduction of nitrate ion to NO in acidic solution: \(NO_3^- + 4 H^+ + 3 e^- \rightarrow NO + 2 H_2O \) (b) Oxidation of HNO₂ to NO₂ in acidic solution: \( HNO_2 + e^- \rightarrow NO_2 + H_2O + 2 H^+ \)

Step 1: Write the Unbalanced Half Reaction

First, let's write down the unbalanced half-reactions for each process. (a) Reduction of nitrate ion (NO₃⁻) to NO: NO₃⁻ → NO (b) Oxidation of HNO₂ to NO₂: HNO₂ → NO₂

Step 2: Balance Atoms besides Oxygen and Hydrogen

In this case, nitrogen is already balanced in both half-reactions. (a) NO₃⁻ → NO (b) HNO₂ → NO₂

Step 3: Balance Oxygen Atoms with H₂O

Add the appropriate number of H₂O molecules to balance the oxygen atoms in the reaction. (a) NO₃⁻ → NO + 2 H₂O (b) HNO₂ → NO₂ + H₂O

Step 4: Balance Hydrogen Atoms with H⁺ ions

Add the appropriate number of H⁺ ions to balance the hydrogen atoms. (a) NO₃⁻ + 4 H⁺ → NO + 2 H₂O (b) HNO₂ → NO₂ + H₂O + 2 H⁺

Step 5: Balance the Charge with e⁻ (electrons)

Add electrons to the half-reaction with a lower overall charge to ensure the charges on both sides of the reaction are equal. (a) NO₃⁻ + 4 H⁺ + 3 e⁻ → NO + 2 H₂O (b) HNO₂ + e⁻ → NO₂ + H₂O + 2 H⁺ Now, we have the complete balanced half-reactions for each process: (a) Reduction of nitrate ion to NO in acidic solution: NO₃⁻ + 4 H⁺ + 3 e⁻ → NO + 2 H₂O (b) Oxidation of HNO₂ to NO₂ in acidic solution: HNO₂ + e⁻ → NO₂ + H₂O + 2 H⁺

Key Concepts

Understanding the Half-Reaction Method

The half-reaction method is a systematic approach for balancing redox reactions. Redox reactions involve the transfer of electrons between substances, and these reactions are split into two parts: reduction and oxidation. The half-reaction method separates these parts so that they can be balanced individually, making the overall process more manageable.

To balance a half-reaction, one must ensure that the number of atoms of each element and the total charge is the same on both sides of the reaction. This involves adding appropriate coefficients and, where necessary, water molecules, hydrogen ions (H⁺), and electrons (e⁻). Once both half-reactions are balanced, they can be combined to give the balanced overall redox reaction.

This process often requires an understanding of the conditions of the reaction, such as whether it occurs in an acidic or basic solution, as this affects the balancing agents used (H⁺ in acidic conditions and OH⁻ in basic conditions).

Reduction of Nitrate Ion

In the context of balancing redox reactions, understanding the process for the reduction of nitrate ion is crucial. The nitrate ion (NO₃⁻) is a common oxidizing agent and can be reduced to a variety of products depending on the conditions. In this case, we are focusing on the reduction of nitrate to nitrogen monoxide (NO) in an acidic solution.

The balancing of this reaction begins by writing the unbalanced half-reaction: NO₃⁻ → NO. Next, we balance the oxygen atoms by adding water molecules. To balance the hydrogen atoms in an acidic solution, we use H⁺ ions. Finally, we add electrons to balance the charge, as the nitrate ion starts with a negative charge, and the resulting products must have a neutral charge. The balanced half-reaction retains the conservation of mass and charge, which states that matter is neither created nor destroyed, and the total charge must be the same on both sides of the equation.

Oxidation of Nitrous Acid

The oxidation state of an atom within a compound can change through chemical reactions. When we discuss the oxidation of nitrous acid (HNO₂), we are referring to a process where the nitrogen in nitrous acid is increasing its oxidation state. In the reaction that was outlined, nitrous acid is oxidized to form nitrogen dioxide (NO₂), which has a higher oxidation state of nitrogen.

The initial step is to write the skeleton reaction, then balance the atoms other than oxygen and hydrogen. In an acidic environment, water and hydrogen ions are used to balance the oxygen and hydrogen atoms, respectively. Lastly, electrons are added to balance the charge because oxidation involves the loss of electrons. A key aspect of this process is ensuring that the electrons lost in the oxidation half-reaction are the same as those gained in the reduction half-reaction, allowing them to cancel each other out when combined to give the overall balanced redox equation.