Question

Use the oxidation-number method to balance the following net ionic redox equations. \(\mathrm{Zn}+\mathrm{NO}_{3}^{-} \rightarrow \mathrm{Zn}^{2+}+\mathrm{NO}_{2}(\text { in acid solution })\)

Short answer

In order to balance the given redox equation in an acidic solution, follow these steps: 1. Assign oxidation numbers to each element and identify the half-reactions: Oxidation: \(Zn \rightarrow Zn^{2+}\) Reduction: \(NO_3^- \rightarrow NO_2\) 2. Balance the half-reactions by adding appropriate numbers of electrons, water molecules, and hydrogen ions (H+): Oxidation: \(Zn \rightarrow Zn^{2+} + 2e^-\) Reduction: \(NO_3^- + 1e^- + 2H^+ \rightarrow NO_2 + H_2 O\) 3. Balance the electrons in the half-reactions by multiplying the reduction half-reaction by 2: \(2(NO_3^- + 1e^- + 2H^+) \rightarrow 2(NO_2 + H_2 O)\) This results in: \(2NO_3^- + 2e^- + 4H^+ \rightarrow 2NO_2 + 2H_2 O\) 4. Combine the balanced half-reactions to obtain the balanced overall redox equation: \(Zn + 2NO_3^- + 4H^+ \rightarrow Zn^{2+} + 2NO_2 + 2H_2 O\)

Step-by-step solution

Assign the oxidation numbers of each element

First, assign the oxidation numbers of each element in the given redox equation: Zn: 0 \(NO_3^-\): N is assigned +5 \(Zn^{2+}\): Zn is assigned +2 \(NO_2\): N is assigned +4 The redox equation is now: \(Zn + NO_3^- \rightarrow Zn^{2+} + NO_2\)

Identify the half-reactions

Next, we should identify the half-reactions: an oxidation half-reaction representing the species that lose electrons and a reduction half-reaction representing the species that gain electrons. Oxidation half-reaction: \(Zn \rightarrow Zn^{2+}\) Reduction half-reaction: \(NO_3^- \rightarrow NO_2\)

Balance the half-reactions

Balance each half-reaction by adding appropriate numbers of electrons, water molecules, and hydrogen ions (H+). Oxidation half-reaction: \(Zn \rightarrow Zn^{2+} + 2e^-\) Reduction half-reaction: \(NO_3^- + 1e^- \rightarrow NO_2 + H_2 O\) Now we need to balance the hydrogen ions (H+): add two H+ ions to the reduction half-reaction. \(NO_3^- + 1e^- + 2H^+ \rightarrow NO_2 + H_2 O\)

Balance the electrons in the half-reactions

The number of electrons lost in the oxidation half-reaction should equal the number of electrons gained in the reduction half-reaction. In this case, we have: Oxidation half-reaction: \(2e^-\) lost Reduction half-reaction: \(1e^-\) gained To balance the electrons, multiply the reduction half-reaction by 2: \(2(NO_3^- + 1e^- + 2H^+) \rightarrow 2(NO_2 + H_2 O)\) Now the balanced reduction half-reaction is: \(2NO_3^- + 2e^- + 4H^+ \rightarrow 2NO_2 + 2H_2 O\)

Combine the balanced half-reactions

Combine the balanced oxidation and reduction half-reactions to obtain the balanced overall redox equation: \(Zn + 2NO_3^- + 2e^- + 4H^+ \rightarrow Zn^{2+} + 2e^- + 2NO_2 + 2H_2 O\) The electrons in the oxidation and reduction reactions cancel each other out: \(Zn + 2NO_3^- + 4H^+ \rightarrow Zn^{2+} + 2NO_2 + 2H_2 O\) This is the balanced net ionic redox equation for the reaction in an acidic solution.

Key concepts

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, are processes where electrons are transferred between reactants. These reactions are fundamental in chemistry because they involve changing the oxidation states of the compounds involved.
In a redox reaction:

• One reactant undergoes oxidation, meaning it loses electrons.
• Another reactant undergoes reduction, meaning it gains electrons.

Take, for example, the redox reaction: \(\mathrm{Zn} + \mathrm{NO}_3^- \rightarrow \mathrm{Zn}^{2+} + \mathrm{NO}_2\).
Here, zinc (\(\mathrm{Zn}\)) loses two electrons and is oxidized to \(\mathrm{Zn}^{2+}\). On the flip side, nitrate \((\mathrm{NO}_3^-)\) gains electrons and is reduced to nitrite \((\mathrm{NO}_2)\). This exchange of electrons is what defines this process as a redox reaction, making it integral in balancing chemical equations as well as understanding energetic changes in chemical processes.

Balancing Equations

Balancing equations is crucial because it ensures that the conservation of mass is respected, meaning the same number of each type of atom must exist on both sides of the equation. In the context of redox reactions, this process involves ensuring that both mass and charge are balanced.
Let's break it down:

• The first step is to assign oxidation numbers to each element to identify which atoms are oxidized and reduced.
• Then, identify and split the equation into two half-reactions—one for oxidation and another for reduction.

Each half-reaction is balanced separately:

• For the oxidation half-reaction, add electrons to balance the loss of electrons.
• For the reduction half-reaction, electrons are added to balance the gain of electrons.

Once the half-reactions are individually balanced, the next step is to equalize the electrons exchanged to ensure they cancel each other in the final combination. This often involves multiplying one or both of the half-reactions by appropriate integers.
Lastly, combine the half-reactions and simplify to get the overall balanced equation.
For example, in the redox reaction \(\mathrm{Zn} + 2\mathrm{NO}_3^- + 4\mathrm{H}^+ \rightarrow \mathrm{Zn}^{2+} + 2\mathrm{NO}_2 + 2\mathrm{H}_2\mathrm{O}\), you can see that both mass and charge are balanced.

Half-Reactions

Half-reactions are a method used to split a redox reaction into two components: one showing oxidation and the other showing reduction. This is particularly helpful in illustrating the transfer of electrons between chemical species.
Here’s how to understand them:

• Oxidation half-reaction: This involves the species that loses electrons. For \(\mathrm{Zn}\), the half-reaction is: \[\mathrm{Zn} \rightarrow \mathrm{Zn}^{2+} + 2e^-\]
• Reduction half-reaction: This involves the species that gains electrons. For \(\mathrm{NO}_3^-\), the half-reaction after balancing is: \[\mathrm{2NO}_3^- + 2e^- + 4\mathrm{H}^+ \rightarrow \mathrm{2NO}_2 + 2\mathrm{H}_2\mathrm{O}\]

In each half-reaction,
the conservation of mass and charge is maintained.
This step-by-step breakdown not only aids in balancing the overall redox equation but also offers a clear view of how electrons move between oxidants and reductants. Understanding half-reactions enhances your grasp of the processes accompanying redox reactions and their applications in electrochemistry, metabolism, and industrial practices.