Problem 70 - Chemistry Matter and Change

Question

Balance the following redox chemical equation. Rewrite the equation in full ionic form, then derive the net ionic equation and balance by the half- reaction method. Give the final answer as it is shown below but with the balancing coefficients. $$\begin{array}{l}{\mathrm{KMnO}_{4}(\mathrm{aq})+\mathrm{FeSO}_{4}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) \rightarrow} \\ {\quad \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}(\mathrm{aq})+\mathrm{MnSO}_{4}(\mathrm{aq})+} \\\ \quad {\mathrm{K}_{2} \mathrm{SO}_{4}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l})}\end{array}$$

Step-by-Step Solution

Answer

The balanced molecular equation is: \(2\text{KMnO}_{4} + 10\text{FeSO}_{4} + 8\text{H}_{2}\text{SO}_{4} \rightarrow 5\text{Fe}_{2}(\text{SO}_{4})_{3} + 2\text{MnSO}_{4} + \text{K}_{2} \text{SO}_{4} + 8\text{H}_{2}\text{O}\).

Step 1: Write the Full Ionic Equation

The first step is to write the full ionic equation for the reaction. Dissociate all strong electrolytes into their ions:\[\text{KMnO}_{4} + \text{FeSO}_{4} + \text{H}_{2}\text{SO}_{4} \rightarrow \text{Fe}_{2}(\text{SO}_{4})_{3} + \text{MnSO}_{4} + \text{K}_{2} \text{SO}_{4} + \text{H}_{2}\text{O}\]Becomes:\[\text{K}^+ + \text{MnO}_{4}^- + \text{Fe}^{2+} + \text{SO}_{4}^{2-} + 2\text{H}^+ + \text{SO}_{4}^{2-} \rightarrow 2\text{Fe}^{3+} + 3\text{SO}_{4}^{2-} + \text{Mn}^{2+} + \text{SO}_{4}^{2-} + 2\text{K}^+ + \text{SO}_{4}^{2-} + \text{H}_{2}\text{O}\]

Step 2: Derive the Net Ionic Equation

Identify the spectator ions that do not change during the reaction and remove them. The spectator ions in this reaction are \(\text{K}^+\) and \(\text{SO}_{4}^{2-}\):\[\text{MnO}_{4}^- + 5\text{Fe}^{2+} + 8\text{H}^+ \rightarrow 5\text{Fe}^{3+} + \text{Mn}^{2+} + 4\text{H}_{2}\text{O}\]

Step 3: Balance the Half-reactions

Now, separate the net ionic equation into two half-reactions:1. \(\text{MnO}_{4}^- \rightarrow \text{Mn}^{2+}\): Reduce the permanganate ion to manganese ion.2. \(\text{Fe}^{2+} \rightarrow \text{Fe}^{3+}\): Oxidize iron(II) ion to iron(III) ion.Balance each half-reaction:- For the reduction half-reaction: \[\text{MnO}_{4}^- + 8\text{H}^+ + 5e^- \rightarrow \text{Mn}^{2+} + 4\text{H}_{2}\text{O}\]- For the oxidation half-reaction: \[\text{Fe}^{2+} \rightarrow \text{Fe}^{3+} + e^-\]

Step 4: Combine and Balance Electrons

Multiply the oxidation half-reaction by 5 to balance the electrons with the reduction half-reaction:\[5\text{Fe}^{2+} \rightarrow 5\text{Fe}^{3+} + 5e^-\]Combine both half-reactions to get the balanced net ionic equation:\[\text{MnO}_{4}^- + 5\text{Fe}^{2+} + 8\text{H}^+ \rightarrow \text{Mn}^{2+} + 5\text{Fe}^{3+} + 4\text{H}_{2}\text{O}\]

Step 5: Verify and Convert to Full Equation

Verify that both mass and charge are balanced in the net ionic equation:- Charge: Left side = +8 (4+1) from electrons, Right side = +8 from ions.- Mass: Same number of each type of atom on both sides.Convert back to the molecular equation:\[2\text{KMnO}_{4} + 10\text{FeSO}_{4} + 8\text{H}_{2}\text{SO}_{4} \rightarrow 5\text{Fe}_{2}(\text{SO}_{4})_{3} + 2\text{MnSO}_{4} + \text{K}_{2} \text{SO}_{4} + 8\text{H}_{2}\text{O}\]

Key Concepts

Balancing Equations

Balancing chemical equations is an essential skill in chemistry. It ensures that the number of atoms for each element is the same on both sides of the equation, thus obeying the Law of Conservation of Mass. In a redox reaction, you need to balance not just the atoms but also the charges. By doing this, you can ensure that your equation accurately represents what happens when reactants turn into products.
To start balancing, list out all the elements involved in the reaction. Count how many of each type of atom you have on both sides of the equation.

• Identify the atoms that are not balanced.
• Adjust coefficients—never subscripts—to balance each element one by one.

It's usually helpful to begin with the most complex molecule. Remember, when working with redox reactions, balancing the charge is as critical as balancing the atoms.

Half-Reaction Method

The half-reaction method is a systematic approach used to balance redox reactions. Redox, short for reduction-oxidation, reactions involve the transfer of electrons from one species to another. By using the half-reaction method, you can separately balance oxidation and reduction processes. In this method, the equation is split into two parts: one for oxidation and one for reduction.
Each half-reaction contains:

• The reactant and product involved in the electron transfer.
• Electrons to be added or removed, which help balance the charges.

For example, you start by writing the oxidation state changes and balance each half for mass and charge using electrons, protons, and water. Then, adjust each half-reaction so that they have the same number of electrons, enabling them to cancel out when combined. Always test your final equation for both balanced mass (atoms) and charge.

Net Ionic Equations

Net ionic equations highlight the essence of the chemical reaction by focusing only on the ions and molecules directly involved in the reaction. They are derived from the full ionic equations by removing the spectator ions, which are ions that do not participate in the chemical change. To obtain a net ionic equation, follow these steps:

• Write down the complete ionic equation, separating all strong electrolytes into their ions.
• Identify and eliminate the spectator ions from both sides of the equation.

This process simplifies the equation, showing only the components that undergo chemical change. It offers clearer insight into the underlying chemical process and is particularly useful for aqueous reactions.

Oxidation-Reduction

Oxidation and reduction, often abbreviated as redox, are two complementary processes. In every redox reaction, one reactant is oxidized while the other is reduced. **Oxidation** refers to the loss of electrons from a substance. This process can increase the oxidation state of an element. **Reduction**, on the other hand, is the gain of electrons, which decreases its oxidation state.
To identify redox reactions in an equation:

• Determine the oxidation states of each atom present in the reactants and the products.
• Identify the change in oxidation states to locate the atoms gaining or losing electrons.

Recognizing where and how oxidation and reduction occur helps you understand the flow of electrons, which is fundamental in many chemical processes, including energy production in cells and industrial applications.