Problem 6 - Chemistry The Molecular Science

Question

In this reaction, assign an oxidation number to each atom in reactants and products. Identify which substance is oxidized and which is reduced. Identify the oxidizing agent and the reducing agent. $$ \begin{aligned} 8 \mathrm{H}^{+}(\mathrm{aq})+\mathrm{MnO}_{4}^{-}(\mathrm{aq})+& 5 \mathrm{Fe}^{2+}(\mathrm{aq}) \longrightarrow \\ & 5 \mathrm{Fe}^{3+}(\mathrm{aq})+\mathrm{Mn}^{2+}(\mathrm{aq})+4 \mathrm{H}_{2} \mathrm{O}(\ell) \end{aligned} $$

Step-by-Step Solution

Answer

\( \text{Fe}^{2+} \) is oxidized; \( \text{MnO}_4^- \) is reduced. \( \text{Fe}^{2+} \) is the reducing agent; \( \text{MnO}_4^- \) is the oxidizing agent.

Step 1: Assign Oxidation Numbers to Each Atom in Reactants

For the reactants:- **Hydrogen in \( \text{H}^+ \)** has an oxidation number of +1 since it is a proton.- **Manganese in \( \text{MnO}_4^- \):** Oxygen typically has an oxidation number of -2. Since there are four oxygen atoms, the total is -8. The compound \( \text{MnO}_4^- \) has a charge of -1, so manganes holds an oxidation number of +7 (since +7 - 8 = -1).- **Iron in \( \text{Fe}^{2+} \)** has an oxidation number of +2 due to its charge.

Step 2: Assign Oxidation Numbers to Each Atom in Products

For the products:- **Iron in \( \text{Fe}^{3+} \)** has an oxidation number of +3 due to its charge.- **Manganese in \( \text{Mn}^{2+} \)** has an oxidation number of +2 due to its charge.- **Water \( \text{H}_2\text{O} \):** Oxygen is -2 and hydrogen is +1 in water.

Step 3: Determine Changes in Oxidation Numbers

Comparing reactants and products, we observe:- **Iron \( \text{Fe} \)**: changes from +2 in \( \text{Fe}^{2+} \) to +3 in \( \text{Fe}^{3+} \). This is an increase of oxidation number, indicating oxidation.- **Manganese \( \text{Mn} \)**: changes from +7 in \( \text{MnO}_4^- \) to +2 in \( \text{Mn}^{2+} \). This is a decrease of oxidation number, indicating reduction.

Step 4: Identify the Oxidizing Agent and Reducing Agent

- **Substance oxidized (reducing agent):** \( \text{Fe}^{2+} \) is oxidized to \( \text{Fe}^{3+} \), hence it acts as the reducing agent.- **Substance reduced (oxidizing agent):** \( \text{MnO}_4^- \) is reduced to \( \text{Mn}^{2+} \), thus it acts as the oxidizing agent.

Key Concepts

Oxidation Numbers

Oxidation numbers are essential in understanding redox reactions. They represent the hypothetical charges atoms would have if the compound was composed of ions.
They help identify how electrons are transferred in a reaction. Here’s how you assign them:

• For single atoms: The oxidation number is the charge of the atom.
• Hydrogen generally has an oxidation number of +1.
• Oxygen usually has an oxidation number of -2.
• For ions, the oxidation number equals the charge of the ion.

You can identify which atom is oxidized (loses electrons) or reduced (gains electrons) by examining changes in oxidation numbers. A higher oxidation number in products compared to reactants indicates oxidation. Conversely, a lower number indicates reduction.

Oxidizing Agent

In redox reactions, the oxidizing agent is the substance that accepts electrons. As it gains electrons, it is reduced. This might seem opposite of what one might expect, but remember that by accepting electrons, the oxidizing agent drives the oxidation of another substance.
How to identify it:

• Look for the substance whose atoms get reduced, showing a decrease in oxidation number.

In the reaction given, ext{MnO}_4^- is reduced to ext{Mn}^{2+} , making it the oxidizing agent. It causes the oxidation of ext{Fe}^{2+} by accepting electrons and reducing itself.

Reducing Agent

The reducing agent is responsible for donating electrons in a redox reaction. By losing electrons, it causes another substance to be reduced. Since it donates electrons, the reducing agent itself undergoes oxidation.
To spot a reducing agent:

• Identify the substance whose atoms show an increase in oxidation number.

In the given reaction, ext{Fe}^{2+} changes to ext{Fe}^{3+} , which is an increase in oxidation state, indicating they are losing electrons. Thus, ext{Fe}^{2+} serves as the reducing agent, driving the reduction of ext{MnO}_4^- by donating electrons.