Problem 26 - Chemistry: The Central Science

Question

Complete and balance the following equations, and identify the oxidizing and reducing agents. (Recall that the \(\mathrm{O}\) atoms in hydrogen peroxide, \(\mathrm{H}_{2} \mathrm{O}_{2}\), have an atypical oxidation state.) (a) \(\mathrm{NO}_{2}^{-}(a q)+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q) \longrightarrow \mathrm{Cr}^{3+}(a q)+\mathrm{NO}_{3}^{-}(a q)\) (acidic solution) (b) \(\mathrm{S}(s)+\mathrm{HNO}_{3}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{3}(a q)+\mathrm{N}_{2} \mathrm{O}(g)\) (acidic solution) Exercises 901 (c) \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+\mathrm{CH}_{3} \mathrm{OH}(a q) \longrightarrow \mathrm{HCO}_{2} \mathrm{H}(a q)+\) \(\mathrm{Cr}^{3+}(a q)\) (acidic solution) (d) \(\mathrm{BrO}_{3}{\underline{\phantom{xx}}}^{-}(a q)+\mathrm{N}_{2} \mathrm{H}_{4}(g) \longrightarrow \mathrm{Br}^{-}(a q)+\mathrm{N}_{2}(g)\) (acidic solution) (e) \(\mathrm{NO}_{2}{\underline{\phantom{xx}}}^{-}(a q)+\mathrm{Al}(s) \longrightarrow \mathrm{NH}_{4}^{+}(a q)+\mathrm{AlO}_{2}{\underline{\phantom{xx}}}^{-}(a q)\) (basic solution) (f) \(\mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{ClO}_{2}(a q) \longrightarrow \mathrm{ClO}_{2}^{-}(a q)+\mathrm{O}_{2}(g)\) (basic solution) Voltaic Cells (Section 20.3)

Step-by-Step Solution

Answer

For equation (a), the balanced redox equation is: \(2\mathrm{NO}_{2}^{-} + 2\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-} + 14\mathrm{H}^{+} \longrightarrow 2\mathrm{NO}_{3}^{-} + 4\mathrm{Cr}^{3+} + 7\mathrm{H}_{2}\mathrm{O}\) The oxidizing agent is \(\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}\) and the reducing agent is \(\mathrm{NO}_{2}^{-}\).

Step 1: Write the oxidation and reduction half-reactions.

Oxidation half-reaction: \(\mathrm{NO}_{2}^{-} \longrightarrow \mathrm{NO}_{3}^{-}\) Reduction half-reaction: \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} \longrightarrow \mathrm{Cr}^{3+}\) Step 2: Balance the half-reactions

Step 2: Balance the atoms and charges in each half-reaction.

Balanced oxidation half-reaction: \(2\mathrm{NO}_{2}^{-} + \mathrm{H}_{2}\mathrm{O} \longrightarrow 2\mathrm{NO}_{3}^{-} + 2\mathrm{H}^{+}\) Balanced reduction half-reaction: \(2\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-} + 14\mathrm{H}^{+} + 6\mathrm{e}^{-} \longrightarrow 4\mathrm{Cr}^{3+} + 7\mathrm{H}_{2}\mathrm{O}\) Step 3: Combine the half-reactions

Step 3: Add the balanced half-reactions together.

Add the balanced half-reactions together and cancel common species on both sides of the equation to find the balanced redox equation: \(2\mathrm{NO}_{2}^{-} + \mathrm{H}_{2}\mathrm{O} + 2\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-} + 14\mathrm{H}^{+} + 6\mathrm{e}^{-} \longrightarrow 2\mathrm{NO}_{3}^{-} + 2\mathrm{H}^{+} + 4\mathrm{Cr}^{3+} + 7\mathrm{H}_{2}\mathrm{O} + 6\mathrm{e}^{-}\) The final balanced redox equation is: \(2\mathrm{NO}_{2}^{-} + 2\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-} + 14\mathrm{H}^{+} \longrightarrow 2\mathrm{NO}_{3}^{-} + 4\mathrm{Cr}^{3+} + 7\mathrm{H}_{2}\mathrm{O}\) Step 4: Identify the oxidizing and reducing agents

Step 4: Identify the oxidizing and reducing agents.

The oxidizing agent is the species that gets reduced: \(\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}\) The reducing agent is the species that gets oxidized: \(\mathrm{NO}_{2}^{-}\) Next, balance equation (b) and determine oxidizing and reducing agents. Repeat this process for the remaining equations (c) to (f).

Key Concepts

Oxidation Half-Reaction

In redox reactions, oxidation is the process where an element loses electrons. This is demonstrated in the oxidation half-reaction, a crucial part of understanding redox equations. In the original exercise, the oxidation half-reaction involves the conversion of nitrite, \(\mathrm{NO}_2^{-}\), to nitrate, \(\mathrm{NO}_3^{-}\).

During this process, nitrite loses electrons, contributing to its oxidation. To work with oxidation half-reactions, you should:

• Identify the species that lose electrons.
• Write the chemical equation that represents this loss.
• Balance the equation by ensuring the number of atoms and the charge are equal on both sides.

Reduction Half-Reaction

Reduction refers to the gain of electrons by a substance. In the original problem, the reduction half-reaction is the transformation of dichromate, \(\mathrm{Cr}_2\mathrm{O}_7^{2-}\), into chromium ions, \(\mathrm{Cr}^{3+} \). During this transition, dichromate gains electrons, undergoing a reduction process. You can understand a reduction half-reaction by:

• Determining which species gain electrons in the redox process.
• Writing the chemical equation indicating electron gain.
• Balancing it to match atoms and charge balance on both sides of the reaction.

Balanced Redox Equation

Once you have detailed the oxidation and reduction half-reactions, the next step is to combine them into a balanced redox equation. The balanced redox equation ensures that the total number of electrons lost in oxidation equals those gained in reduction.

For example, the combined equation from the exercise is: \[2\mathrm{NO}_2^{-} + 2\mathrm{Cr}_2\mathrm{O}_7^{2-} + 14\mathrm{H}^{+} \rightarrow 2\mathrm{NO}_3^{-} + 4\mathrm{Cr}^{3+} + 7\mathrm{H}_2\mathrm{O}\]This balanced equation is important because:

• It reflects the conservation of mass and charge.
• Ensures no excess electrons appear on either side.
• Represents the full chemical change through oxidation and reduction.

Oxidizing Agent

In any redox reaction, the oxidizing agent is crucial because it gains electrons and gets reduced in the process. In the exercise, this is the dichromate ion, \(\mathrm{Cr}_2\mathrm{O}_7^{2-} \). The oxidizing agent:

• Facilitates the oxidation of another species by accepting electrons.
• Undergoes reduction itself.
• Plays a vital role in driving the redox process forward.

To identify the oxidizing agent, look for the species that reduces its oxidation state throughout the reaction.

Reducing Agent

The reducing agent is equally important as it loses electrons and gets oxidized during a redox reaction. In the given problem, nitrite, \(\mathrm{NO}_2^{-}\), serves as the reducing agent. It is responsible for:

• Donating electrons to the oxidizing agent.
• Increasing its oxidation state due to electron loss.
• Initiating the reduction of another species through electron supply.

Identifying the reducing agent involves looking for the species that exhibits an increase in oxidation state, signaling it has been oxidized.