Problem 2 - Chemistry and Chemical Reactivity

Question

Write balanced equations for the following half-reactions. Specify whether each is an oxidation or reduction. (a) \(\mathrm{H}_{2} \mathrm{O}_{2}(\mathrm{aq}) \longrightarrow \mathrm{O}_{2}(\mathrm{g}) \quad\) (in acid) (b) \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(\mathrm{aq}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g}) \quad\) (in acid) (c) \(\mathrm{NO}_{3}^{-}(\mathrm{aq}) \longrightarrow \mathrm{NO}(\mathrm{g})\) (in acid) (d) \(\mathrm{MnO}_{4}^{-}(\mathrm{aq}) \longrightarrow \mathrm{MnO}_{2}(\mathrm{s})\) (in base)

Step-by-Step Solution

Answer

(a) Oxidation; (b) Oxidation; (c) Reduction; (d) Reduction.

Step 1: Understand Half-Reaction Fundamentals

In a redox reaction, a half-reaction shows either oxidation (loss of electrons) or reduction (gain of electrons). Balancing a half-reaction involves making sure both the atoms and the charge are balanced, often in acidic or basic solutions.

Step 2: Write and Balance Oxygen for Reaction (a)

Begin with the unbalanced reaction: \(\mathrm{H}_2\mathrm{O}_2(\mathrm{aq}) \rightarrow \mathrm{O}_2(\mathrm{g})\). Balance the oxygen atoms by adding water: \(\mathrm{H}_2\mathrm{O}_2 \rightarrow \mathrm{O}_2 + 2\mathrm{H}_2\mathrm{O}\). This reaction involves the conversion of one molecule of hydrogen peroxide into one molecule of oxygen.

Step 3: Balance Hydrogen and Charge for Reaction (a)

Since we're in an acidic solution, add protons to balance hydrogen: \(\mathrm{H}_2\mathrm{O}_2 \rightarrow \mathrm{O}_2 + 2 \mathrm{H}_2\mathrm{O} + 2\mathrm{H}^+\). Then add electrons to balance the charge: \(\mathrm{H}_2\mathrm{O}_2 \rightarrow \mathrm{O}_2 + 2 \mathrm{H}^+ + 2e^-\). This half-reaction is an oxidation reaction because electrons are on the product side.

Step 4: Write and Balance for Reaction (b)

Begin with the unbalanced reaction: \(\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4 \rightarrow \mathrm{CO}_2\). Each molecule of oxalic acid produces two CO2 molecules: \(\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4 \rightarrow 2\mathrm{CO}_2\).

Step 5: Balance Charge for Reaction (b)

Add protons to balance the hydrogen: \(\mathrm{H}_2\mathrm{C}_2\mathrm{O}_4 \rightarrow 2\mathrm{CO}_2 + 2\mathrm{H}^+ + 2e^-\). This is a two-electron oxidation reaction.

Step 6: Write and Balance for Reaction (c)

For the unbalanced reaction: \(\mathrm{NO}_3^- \rightarrow \mathrm{NO}\), balance nitrogen and oxygen by adding water and protons: \(\mathrm{NO}_3^- + 2\mathrm{H}^+ + e^- \rightarrow \mathrm{NO} + \mathrm{H}_2\mathrm{O}\). This half-reaction is a reduction reaction as it acquires electrons.

Step 7: Write and Balance for Reaction (d)

For the reaction \(\mathrm{MnO}_4^- \rightarrow \mathrm{MnO}_2\), in a basic medium balance it by adding hydroxide ions and water: \(\mathrm{MnO}_4^- + 2\mathrm{H}_2\mathrm{O} + 3e^- \rightarrow \mathrm{MnO}_2 + 4\mathrm{OH}^-\). This is a reduction reaction as it involves gain of electrons.

Key Concepts

Oxidation and Reduction

Oxidation and reduction are the core processes in redox reactions that involve the transfer of electrons. In simpler terms:

• Oxidation refers to the loss of electrons. This means that during an oxidation reaction, a molecule passes electrons onto another, effectively losing them. For example, in the unbalanced half-reaction of hydrogen peroxide (\[\text{H}_2\text{O}_2 \longrightarrow \text{O}_2\]), hydrogen peroxide loses electrons, making it an oxidation process.
• Reduction entails the gaining of electrons. In this scenario, a molecule receives electrons, added to its own count. As seen in the nitrate ion example (\[\text{NO}_3^- \longrightarrow \text{NO}\]), it gains electrons, meaning a reduction is occurring.

These two processes are always paired in a reaction. One cannot happen without the other. As electrons are neither created nor destroyed, their loss in one half-reaction means a gain in another.

Acidic and Basic Solutions

A key factor in balancing redox reactions is whether they occur in acidic or basic solutions. The environment affects which additional ions are used to balance the reactions.

• In acidic solutions, protons (\[\text{H}^+\]) are readily available. These are used to help balance the hydrogen atoms in the equation. For example, when balancing the half-reaction for hydrogen peroxide, \[\text{H}_2\text{O}_2 \rightarrow \text{O}_2 + 2\text{H}_2\text{O} + 2\text{H}^+\], the added protons come from the acidic solution.
• In basic solutions, hydroxide ions (\[\text{OH}^-\]) are predominant. These are employed to ensure that the equation balances with respect to oxygen and charge. In the reaction for permanganate ion to manganese dioxide, the balanced equation becomes \[\text{MnO}_4^- + 2\text{H}_2\text{O} + 3e^- \rightarrow \text{MnO}_2 + 4\text{OH}^-\].

Balancing these components helps ensure that all atoms and charges are correctly managed in the reactions.

Redox Reactions

Redox reactions are a type of chemical process where reduction and oxidation occur simultaneously. During these reactions, one species loses electrons (is oxidized), and another gains electrons (is reduced). This can occur both in simple systems and complex biochemical pathways.The key points to remember when working with redox reactions are:

• Recognize that two pairs of different half-reactions will always constitute a full redox reaction.
• The manner of balancing these reactions depends heavily on the medium, whether it is acidic or basic, which will determine the presence of \[\text{H}^+\]or \[\text{OH}^-\]ioans assisting in maintaining balanced equations.
• Balancing involves ensuring that the number of atoms for each element and the net charges are the same on both the reactant and product sides of the equations.

Understanding redox reactions and the balance of hydroxide or protons provides essential insights into numerous chemical processes, not just theoretical, but also in practical real-world applications.