Problem 30 - Chemistry An Atoms First Approach

Question

Balance the following oxidation-reduction reactions that occur in acidic solution using the half-reaction method. a. \(\mathrm{Cu}(s)+\mathrm{NO}_{3}^{-}(a q) \rightarrow \mathrm{Cu}^{2+}(a q)+\mathrm{NO}(g)\) b. \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+\mathrm{Cl}^{-}(a q) \rightarrow \mathrm{Cr}^{3+}(a q)+\mathrm{Cl}_{2}(g)\) c. \(\mathrm{Pb}(s)+\mathrm{PbO}_{2}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{PbSO}_{4}(s)\) d. \(\mathrm{Mn}^{2+}(a q)+\mathrm{NaBiO}_{3}(s) \rightarrow \mathrm{Bi}^{3+}(a q)+\mathrm{MnO}_{4}^{-}(a q)\) e. \(\mathrm{H}_{3} \mathrm{AsO}_{4}(a q)+\mathrm{Zn}(s) \rightarrow \mathrm{AsH}_{3}(g)+\mathrm{Zn}^{2+}(a q)\)

Step-by-Step Solution

Answer

The balanced redox reactions in acidic solutions are: a. \(3\mathrm{Cu}(s) + 8\mathrm{H}^+(aq) + 2\mathrm{NO}_3^-(aq) \rightarrow 3\mathrm{Cu}^{2+}(aq) + 2\mathrm{NO}(g) + 4\mathrm{H}_2\mathrm{O}(l)\) b. \(14\mathrm{H}^+(aq) + \mathrm{Cr}_2\mathrm{O}_7^{2-}(aq) + 6\mathrm{Cl}^-(aq) \rightarrow 2\mathrm{Cr}^{3+}(aq) + 3\mathrm{Cl}_2(g) + 7\mathrm{H}_2\mathrm{O}(l)\) c. \(\mathrm{Pb}(s) + \mathrm{Pb}\mathrm{O}_2(s) + 2\mathrm{H}_2\mathrm{SO}_4(aq) \rightarrow 2\mathrm{Pb}\mathrm{SO}_4(s) + 2\mathrm{H}_2\mathrm{O}(l)\) d. \(2\mathrm{Mn}^{2+}(aq) + 5\mathrm{Na}\mathrm{Bi}\mathrm{O}_3(s) + 14\mathrm{H}_2\mathrm{O}(l) \rightarrow 5\mathrm{Bi}^{3+}(aq) + 2\mathrm{Mn}\mathrm{O}_4^-(aq) + 16\mathrm{H}^+(aq) + 5\mathrm{Na}^+(aq)\) e. \(2\mathrm{H}_3\mathrm{As}\mathrm{O}_4(aq) + 3\mathrm{Zn}(s) \rightarrow 2\mathrm{As}\mathrm{H}_3(g) + 3\mathrm{Zn}^{2+}(aq) + 4\mathrm{H}_2\mathrm{O}(l)\)

Step 1: Identify the half-reactions

The half-reactions are: Cu(s) -> Cu²⁺(aq) (Oxidation) NO₃⁻(aq) -> NO(g) (Reduction)

Step 2: Balance atoms other than oxygen and hydrogen

Both half-reactions have the same number of metal atoms on both sides, so we proceed to the next step.

Step 3: Balance oxygen atoms

Only the reduction half-reaction has oxygen atoms. Balance the oxygen atoms by adding 2H₂O to the product side. NO₃⁻(aq) -> NO(g) + 2H₂O(l)

Step 4: Balance hydrogen atoms

In the balanced reduction half-reaction, there are 4 hydrogen atoms on the product side, so add 4H⁺ to the reactant side. 4H⁺(aq) + NO₃⁻(aq) -> NO(g) + 2H₂O(l)

Step 5: Balance charge with electrons

For the oxidation half-reaction, add 2e⁻ to the product side to balance the charge. Cu(s) -> Cu²⁺(aq) + 2e⁻ For the reduction half-reaction, add 3e⁻ to the product side to balance the charge. 4H⁺(aq) + NO₃⁻(aq) + 3e⁻ -> NO(g) + 2H₂O(l)

Step 6: Combine balanced half-reactions

Multiply the oxidation half-reaction by 3 and the reduction half-reaction by 2 to have the same number of electrons in both half-reactions. Then, combine them together and simplify. 3[Cu(s) -> Cu²⁺(aq) + 2e⁻] 2[4H⁺(aq) + NO₃⁻(aq) + 3e⁻ -> NO(g) + 2H₂O(l)] This leads to the balanced redox reaction: 3Cu(s) + 8H⁺(aq) + 2NO₃⁻(aq) -> 3Cu²⁺(aq) + 2NO(g) + 4H₂O(l) **Now proceed in a similar fashion for the other reactions. I will provide the balanced redox reactions below:** b. 14H⁺(aq) + Cr₂O₇²⁻(aq) + 6Cl⁻(aq) -> 2Cr³⁺(aq) + 3Cl₂(g) + 7H₂O(l) c. Pb(s) + PbO₂(s) + 2H₂SO₄(aq) -> 2PbSO₄(s) + 2H₂O(l) d. 2Mn²⁺(aq) + 5NaBiO₃(s) + 14H₂O(l) -> 5Bi³⁺(aq) + 2MnO₄⁻(aq) + 16H⁺(aq) + 5Na⁺(aq) e. 2H₃AsO₄(aq) + 3Zn(s) -> 2AsH₃(g) + 3Zn²⁺(aq) + 4H₂O(l)

Key Concepts

Half-Reaction Method

The half-reaction method is a systematic process used to balance oxidation-reduction (redox) reactions. This is particularly useful when complex reactions occur, as it breaks the reaction into two simpler parts, each handling either the oxidation or reduction process. Here's how it works:

• Identify Half-Reactions: Start by breaking down the full redox reaction into two half-reactions: one for oxidation and one for reduction. Oxidation involves the loss of electrons, while reduction involves the gain of electrons.
• Balance Atoms: Initially, focus on balancing all atoms except hydrogen and oxygen. This lays the groundwork for further balancing.
• Balance Oxygen with Water: For any imbalanced oxygen atoms, add water molecules to ensure both sides have equal oxygen numbers.
• Balance Hydrogen with Protons: Hydrogen atoms are then balanced by introducing hydrogen ions, particularly in acidic solutions.
• Balance Charge with Electrons: Add electrons to either the reactant or product side of each half-reaction to balance the charge. Remember, electrons lost in oxidation must equal electrons gained in reduction.
• Combine Half-Reactions: Multiply the half-reactions by appropriate coefficients to ensure the electrons are the same. Finally, add them together to achieve a balanced equation.

By following these steps methodically, redox reactions can be accurately balanced, reflecting both mass and charge conservation.

Balancing Chemical Equations

Balancing chemical equations is a fundamental skill in chemistry necessary for accurate reaction representation. It ensures that the number of each type of atom, and the electrical charge, is consistent on both sides of the equation. Here's how you can master it:

• List Elements: Write down all the elements involved in the reaction. Track the number of each atom present in both the reactant and product sides.
• Count and Compare: Compare these numbers to identify which atoms are unbalanced. A straightforward checklist helps to pinpoint errors quickly.
• Adjust Coefficients: Use coefficients, the numbers placed before compounds, to balance these atoms. Start with elements that appear in only one reactant and one product.
• Maintain Balance: Continuously check and adjust, changing coefficients rather than subscripts. Maintaining the identity of compounds is essential.
• Verify Charges: In redox reactions, be sure that the total charge is balanced as well. This extra step is crucial where charged species are involved.

Balancing equations ensures that the law of conservation of mass holds, reflecting that mass can neither be created nor destroyed in a chemical reaction. It's a step that cannot be skipped for accurate chemistry work.

Acidic Solution Reactions

Chemical reactions in acidic solutions require specific attention due to the presence of additional hydrogen ions. Understanding how to manipulate these ions is key to balancing reactions in such environments. Here's what you need to know:

• Identify Acidity: Recognize that reactions specified 'in acidic solutions' mean that hydrogen ions (H⁺) are readily available and can be used freely for balancing.
• Utilize H⁺ and H₂O: You can use these ions to balance hydrogen and oxygen atoms not naturally balancing out in the initial steps. Add H⁺ when you need hydrogen atoms and H₂O when dealing with oxygen balancing.
• Consider Acid-Base Behavior: Be aware that acidic conditions might cause additional shifts in reaction equilibrium or engage dynamically with reactants, affecting substance stability.
• Check the System’s Properties: The behavior of chemicals can change in acidic versus basic environments, so always keep the nature of the solution in consideration for a plausible reaction mechanism.

Understanding these principles helps you accurately adjust reactions in the acidic environment, ensuring that both atom and electron balance are correctly maintained. Enhancing your skills with acidic solution reactions can significantly improve your chemical balancing accuracy.