Problem 113 - Chemistry The Science in Context

Question

The solubilities of Fe and Mn in freshwater streams are affected by changes in their oxidation states. Complete and balance the following redox equation in which soluble \(\mathrm{Mn}^{2+}\) becomes solid MnO \(_{2}\) \(\mathrm{Fe}(\mathrm{OH})_{2}+(a q)+\mathrm{Mn}^{2+}(a q) \rightarrow \mathrm{MnO}_{2}(s)+\mathrm{Fe}^{2+}(a q)\)

Step-by-Step Solution

Answer

Question: Identify the net ionic equation representing the transformation of soluble Mn²⁺ to solid MnO₂ and the formation of Fe²⁺ ions. Explain the process in terms of oxidation states and electron transfer. Answer: The net ionic equation for this reaction is Fe(OH)₂(aq) + Mn²⁺(aq) → MnO₂(s) + Fe²⁺(aq). In this process, Mn²⁺ is oxidized to Mn in MnO₂, losing 2 electrons and changing its oxidation state from +2 to +4. Meanwhile, the oxidation state of Fe remains unchanged at +2.

Step 1: Identify the oxidation states

In this equation, we have the following oxidation states: - Fe in Fe(OH)₂: +2 - Mn²⁺ in reactants: +2 - Mn in MnO₂: +4 - Fe²⁺ in products: +2

Step 2: Determine electron transfer

Mn²⁺ is oxidized to Mn in MnO₂, which means it goes from an oxidation state of +2 to +4. The change in oxidation state is +2, so Mn loses 2 electrons in this process. Fe remains in the same oxidation state, so there is no redox change for Fe.

Step 3: Balance atoms and charges in half-reactions

We can write the half-reactions for the redox process: Oxidation: Mn²⁺(aq) → MnO₂(s) + 2e⁻ Reduction: Fe remains unchanged, so there is no reduction half-reaction.

Step 4: Balance oxygen atoms using water molecules

The oxygen atoms are already balanced in both half-reactions. There are 2 oxygen atoms in Mn²⁺(aq) and 2 oxygen atoms in MnO₂(s). We don't need to add water molecules.

Step 5: Balance hydrogen atoms using H⁺ ions

In the oxidation half-reaction, there are no hydrogen atoms, so there's no need to balance using H⁺ ions.

Step 6: Reconstruct the balanced equation

Put the two half-reactions back together and balance the electrons: Fe(OH)₂(aq) + Mn²⁺(aq) → MnO₂(s) + 2e⁻ + Fe²⁺(aq) Reinserting the 2 electrons balanced in the equation, we have: Fe(OH)₂(aq) + 2e⁻ + Mn²⁺(aq) → MnO₂(s) + Fe²⁺(aq) The net ionic equation is thus: Fe(OH)₂(aq) + Mn²⁺(aq) → MnO₂(s) + Fe²⁺(aq)

Key Concepts

Oxidation States

Oxidation states are a way to keep track of how many electrons are lost or gained by an atom in a chemical reaction. In redox reactions, the oxidation state of an element can change, indicating that electrons have been transferred. This is essential for understanding which atoms are oxidized and which are reduced.

• The oxidation state of iron in Fe(OH)₂ is +2, which doesn't change as it remains Fe²⁺ in the products.
• The oxidation state of manganese changes: Mn²⁺ becomes MnO₂, changing from +2 to +4.

By determining the oxidation states, we can identify the reducing and oxidizing agents within the reaction.

Electron Transfer

Electron transfer is the key process in redox reactions, which involves the movement of electrons from one species to another. When an atom's oxidation state increases, it loses electrons (oxidation), while a reduction in oxidation state means it gains electrons.
In the given reaction:

• Manganese (Mn²⁺) is oxidized to MnO₂. This means Mn goes from an oxidation state of +2 to +4, losing 2 electrons in the process.
• Iron (Fe) does not participate in electron transfer in this reaction, as its oxidation state remains unchanged.

Understanding electron transfer helps us see how elements change during the reaction and which element actually gives up or gains electrons.

Half-Reactions

Relying on half-reactions provides a clearer perspective of the redox process, breaking it down into separate oxidation and reduction events. By considering each half-reaction separately, we can better understand the specific electron transfer involved.

• Oxidation half-reaction: Mn²⁺(aq) → MnO₂(s) + 2e⁻. Here, manganese loses electrons, highlighting its oxidation.
• There is no reduction half-reaction for iron, as there's no change in its oxidation state.

Half-reactions help balance the overall redox equation by clearly showing how electrons are transferred in the various components of the reaction.

Balancing Chemical Equations

Balancing chemical equations is essential for accurately representing the quantities of reactants and products involved. This balance reflects the conservation of mass and charge in the reaction.
To balance the redox equation, the number of each type of atom and charge must be the same on both sides of the equation. In this reaction:

• Atom balance: There are equivalent numbers of manganese, iron, oxygen, and hydrogen atoms on each side.
• Charge balance: The charges are the same on both sides, ensuring the stability of the reaction.

By carefully balancing the equation, we confirm that electrons lost in oxidation are equal to those gained in reduction, maintaining the equation's integrity.