Problem 38 - General Chemistry: Principles and Modern Applications

Question

Balance these equations for redox reactions occurring in acidic solution. (a) \(\mathrm{P}_{4}(\mathrm{s})+\mathrm{NO}_{3}^{-} \longrightarrow \mathrm{H}_{2} \mathrm{PO}_{4}^{-}+\mathrm{NO}(\mathrm{g})\) (b) \(\mathrm{S}_{2} \mathrm{O}_{3}^{2-}+\mathrm{MnO}_{4}^{-} \longrightarrow \mathrm{SO}_{4}^{2-}+\mathrm{Mn}^{2+}\) (c) \(\mathrm{HS}^{-}+\mathrm{HSO}_{3}^{-} \longrightarrow \mathrm{S}_{2} \mathrm{O}_{3}^{2-}\) (d) \(\mathrm{Fe}^{3+}+\mathrm{NH}_{3} \mathrm{OH}^{+} \longrightarrow \mathrm{Fe}^{2+}+\mathrm{N}_{2} \mathrm{O}(\mathrm{g})\)

Step-by-Step Solution

Answer

The balanced redox reactions are: (a) \(P_4 + 20 NO_3^- + 24 H^+ \rightarrow 4 H_2PO_4^- + 20 NO\) (b) \(3 S_2O_3^{2-} + 2 MnO_4^- + 8 H^+ \rightarrow 3 SO_4^{2-} + 2 Mn^{2+} + 5 H_2O\) (c) \(HS^- + 2 HSO_3^- \rightarrow S_2O_3^{2-} + 2 H_2O\) (d) \(8 Fe^{3+} + 10 NH_3OH^+ \rightarrow 8 Fe^{2+} + 5 N_2O + 25 H_2O\)

Step 1: Split the reaction into half-reactions

This allows us to focus on balancing the oxidation and reduction processes separately. Each half reaction should include the reactant being oxidized or reduced, the product of that process, and electrons showing the gain for reduction or loss for oxidation.

Step 2: Balance atoms in half-reactions

Start by balancing the atoms that are not hydrogen or oxygen in the half-reactions, followed by oxygen atoms, which can be balanced using water molecules (\(H_2O\)), and finally balance hydrogen atoms using \(H^+\) ions.

Step 3: Balance charges in half-reactions

This can be achieved by adding electrons which themselves carry charge. If in reduction half-reaction, add the electrons to the left side of the equation, and if in oxidation half-reaction, add the electrons to the right side of the equation.

Step 4: Equalize electron transfer

Make sure the number of electrons lost in the oxidation half-reaction equals the number gained in the reduction half-reaction. If they are not equal, multiply each equation by an appropriate factor so the number of electrons will cancel out when the equations are added together.

Step 5: Combine the half-reactions

Add the half-reactions together and simplify to get the balanced redox reaction.

Key Concepts

Half-Reaction Method

Balancing redox reactions can be daunting, but the half-reaction method simplifies the process. This method breaks down a complex redox reaction into two separate half-reactions: one for oxidation and one for reduction. Each half-reaction focuses on the transfer of electrons, either gained or lost. This makes it easier to account for the atoms and charge changes occurring during the reaction.

Here's the step-by-step breakdown:

• **Separate into two half-reactions**: Identify the substances being oxidized and reduced. Insert electrons into each half-reaction based on the electron loss or gain during the transformation.
• **Balance the atoms in each half-reaction**: Start with elements other than hydrogen and oxygen. Follow by balancing oxygen atoms, which can be done by adding water molecules ( H_2O ). Finally, balance hydrogen atoms by adding protons ( H^+ ).
• **Balance the charges**: Adjust the number of electrons to ensure each half-reaction has neutral charge. Add electrons to the appropriate side based on whether the half-reaction involves oxidation or reduction.
• **Equalize electron transfer**: Make the number of electrons in the oxidation reaction equal to those in the reduction reaction by multiplying the reactions by appropriate coefficients.

By following these steps, the half-reaction method systematically simplifies the task of balancing a redox equation, ensuring accuracy and understanding.

Acidic Solution Redox Balance

Balancing redox equations in acidic solutions is crucial for achieving accurate chemical reactions, particularly when reaction mediums are acidic environments. Here's how you can ensure your redox equations are correctly balanced in these settings:

**Acidic Environment**: It's important to remember that in acidic solutions, hydrogen ions (H^+) and water (H_2O) are freely available. These can be utilized to balance hydrogen and oxygen atoms when needed.

**Process:**

• **Balance all atoms except hydrogen and oxygen initially**: This helps to set up the framework of the half-reactions without the immediate complexity.
• **Balance oxygen atoms by adding H_2O molecules**: This step adjusts the oxygen count effectively, as water contributes additional oxygen atoms.
• **Balance hydrogen atoms by adding H^+ ions**: Since H^+ ions are abundant in acidic solutions, they serve as a helpful tool for balancing hydrogen.

This approach, commonly required for reactions such as `\( \mathrm{P}_{4}(\mathrm{s})+\mathrm{NO}_{3}^{-} \longrightarrow \mathrm{H}_{2} \mathrm{PO}_{4}^{-}+\mathrm{NO}(\mathrm{g}) \)`, ensures that all elements and charges are balanced effectively without disrupting the acidic nature of the solution.

By following this method, you can confidently manage the intricacies of redox balance in an acidic environment.

Oxidation-Reduction Process

Understanding the oxidation-reduction process—or redox reactions—is fundamental in mastering balance equations in chemistry. Redox reactions entail the transfer of electrons between chemical species, often involving energy changes that are important in both living organisms and industrial processes.

**Key Points of Redox Reactions**:

• **Oxidation** is the loss of electrons from a substance. This increases the oxidation state of the molecule, atom, or ion involved. Think of it as giving away electrons.
• **Reduction** is the gain of electrons. This process reduces the oxidation state when a substance accepts electrons. Imagine it as receiving additional electrons.
• The substance that loses electrons is called the **reducing agent** because it reduces another component by donating electrons. Conversely, the **oxidizing agent** is the one that accepts electrons, causing the other component to lose electrons.
• In a balanced redox reaction, the total number of electrons lost in oxidation should equal the electrons gained in reduction. This ensures mass and charge balance within the reaction.

Understanding the basic concept of electron transfer allows you to see the larger picture of how energy flows and how reactions drive biological and chemical processes. With this comprehension, balancing equations like `\( \mathrm{Fe}^{3+}+\mathrm{NH}_{3} \mathrm{OH}^{+} \longrightarrow \mathrm{Fe}^{2+}+\mathrm{N}_{2} \mathrm{O}(\mathrm{g}) \)` becomes more intuitive since you better grasp the roles of each component involved in the reaction.