Question

In aqueous solution, hydrogen sulfide reduces (a) \(\mathrm{Fe}^{3+}\) to \(\mathrm{Fe}^{2+},(\mathbf{b}) \mathrm{Br}_{2}\) to \(\mathrm{Br}^{-},(\mathbf{c}) \mathrm{MnO}_{4}^{-}\) to \(\mathrm{Mn}^{2+},(\mathbf{d}) \mathrm{HNO}_{3}\) to \(\mathrm{NO}_{2}\) . In all cases, under appropriate conditions, the product is elemental sulfur. Write a balanced net ionic equation for each reaction.

Short answer

The balanced net ionic equations for the given reactions are: Reaction a: \(2 H_2S(aq) + 2 Fe^{3+}(aq) \to 2 Fe^{2+}(aq) + 3 S(s) + 4 H^+(aq)\) Reaction b: \(H_2S(aq) + 2 Br_2(aq) \to 3 S(s) + 4 Br^-(aq) + 2 H^+(aq)\) Reaction c: \(5 H_2S(aq) + 2 MnO_4^-(aq) + 6 H^+(aq) \to 2 Mn^{2+}(aq) + 8 H_2O(l) + 5 S(s)\) Reaction d: \(3 H_2S(aq) + 4 H^+(aq) \to 3 NO_2(g) + 4 H_2O(l) + 5 S(s)\)

Step-by-step solution

Reaction a - Reduction of Fe³⁺ to Fe²⁺

Step 1 - Unbalanced chemical equation: H₂S(aq) + Fe³⁺(aq) -> Fe²⁺(aq) + S(s) Step 2 - Balancing the chemical equation: 2 H₂S(aq) + 2 Fe³⁺(aq) -> 2 Fe²⁺(aq) + 3 S(s) + 4 H⁺(aq) Step 3 - Total ionic equation: 2 H₂S(aq) + 2 Fe³⁺(aq) -> 2 Fe²⁺(aq) + 3 S(s) + 4 H⁺(aq) Step 4 - Net ionic equation (No spectator ions found in this reaction): 2 H₂S(aq) + 2 Fe³⁺(aq) -> 2 Fe²⁺(aq) + 3 S(s) + 4 H⁺(aq)

Reaction b - Reduction of Br₂ to Br⁻

Step 1 - Unbalanced chemical equation: H₂S(aq) + Br₂(aq) -> S(s) + Br⁻(aq) Step 2 - Balancing the chemical equation: H₂S(aq) + 2 Br₂(aq) -> 3 S(s) + 4 Br⁻(aq) + 2 H⁺(aq) Step 3 - Total ionic equation: H₂S(aq) + 2 Br₂(aq) -> 3 S(s) + 4 Br⁻(aq) + 2 H⁺(aq) Step 4 - Net ionic equation (No spectator ions found in this reaction): H₂S(aq) + 2 Br₂(aq) -> 3 S(s) + 4 Br⁻(aq) + 2 H⁺(aq)

Reaction c - Reduction of MnO₄⁻ to Mn²⁺

Step 1 - Unbalanced chemical equation: H₂S(aq) + MnO₄⁻(aq) -> Mn²⁺(aq) + S(s) Step 2 - Balancing the chemical equation: 5 H₂S(aq) + 2 MnO₄⁻(aq) + 6 H⁺(aq) -> 2 Mn²⁺(aq) + 8 H₂O(l) + 5 S(s) Step 3 - Total ionic equation: 5 H₂S(aq) + 2 MnO₄⁻(aq) + 6 H⁺(aq) -> 2 Mn²⁺(aq) + 8 H₂O(l) + 5 S(s) Step 4 - Net ionic equation (No spectator ions found in this reaction): 5 H₂S(aq) + 2 MnO₄⁻(aq) + 6 H⁺(aq) -> 2 Mn²⁺(aq) + 8 H₂O(l) + 5 S(s)

Reaction d - Reduction of HNO₃ to NO₂

Step 1 - Unbalanced chemical equation: H₂S(aq) + HNO₃(aq) -> NO₂(g) + S(s) Step 2 - Balancing the chemical equation: 3 H₂S(aq) + 4 HNO₃(aq) -> 3 NO₂(g) + 4 H₂O(l) + 5 S(s) Step 3 - Total ionic equation: 3 H₂S(aq) + 4 H⁺(aq) + 4 NO₃⁻(aq) -> 3 NO₂(g) + 4 H₂O(l) + 5 S(s) Step 4 - Net ionic equation (Canceling out spectator ions - 4 NO₃⁻): 3 H₂S(aq) + 4 H⁺(aq) -> 3 NO₂(g) + 4 H₂O(l) + 5 S(s) We have now written balanced net ionic equations for all 4 reactions involving hydrogen sulfide as the reducing agent and producing elemental sulfur.

Key concepts

Balancing Chemical Equations

Understanding how to balance chemical equations is fundamental in chemistry. It ensures that the law of conservation of mass is obeyed, meaning that atoms are neither created nor destroyed in a chemical reaction. For instance, in the reaction provided, when hydrogen sulfide reduces Fe³⁺ to Fe²⁺, the initial unbalanced equation is H₂S(aq) + Fe³⁺(aq) → Fe²⁺(aq) + S(s). To balance it, every atom on the left side of the equation must be accounted for on the right side.

Start by counting the number of each type of atom in the reactants and products. For the reaction mentioned, sulfur and iron must be balanced by ensuring that the number of iron and sulfur atoms in both the reactants and products are equal. Hydrogen atoms are balanced last since they are often found in multiple compounds. After applying stoichiometry, we arrive at a balanced equation of 2 H₂S(aq) + 2 Fe³⁺(aq) → 2 Fe²⁺(aq) + 3 S(s) + 4 H⁺(aq). This reflects that the mass and the charge are both conserved.

Remember to adjust the coefficients of the compounds accordingly and not to alter the chemical formulas of the reactants or products. Balancing equations allows us to predict the ratios in which chemicals will react and the amounts of substances produced or consumed in a reaction.

Net Ionic Equations

Net ionic equations provide a more straightforward depiction of a chemical reaction by focusing only on the entities that change in the course of the reaction. They exclude spectator ions, which are ions that do not participate in the reaction. The process of writing a net ionic equation involves three steps: writing the full ionic equation, identifying the spectator ions, and removing them to write the net ionic equation.

For instance, when writing the net ionic equation for the reduction of Br₂ to Br⁻ by hydrogen sulfide, you'll transform the balanced molecular equation, H₂S(aq) + 2 Br₂(aq) → 3 S(s) + 4 Br⁻(aq) + 2 H⁺(aq), into a total ionic equation. After that, examine this equation for spectator ions; however, in this particular reaction, there are no spectator ions. Therefore, the net ionic equation is the same as the total ionic equation.

A well-written net ionic equation makes understanding the changes that occur during the reaction easier and helps avoid the complexity that spectator ions can introduce.

Oxidation States

The concept of oxidation states is central to understanding redox reactions, where oxidation and reduction occur simultaneously. An oxidation state is an indicator that suggests how many electrons an atom has lost, gained, or shared when bonding with other atoms. During the process of balancing equations, changes in oxidation states can signal which atoms are oxidized and which are reduced.

For example, in the reaction where MnO₄⁻ is reduced to Mn²⁺, MnO₄⁻ has a higher oxidation state which decreases during the reaction, indicating that manganese is being reduced. To find the oxidation state, consider the known oxidation states of other atoms in the compound and the overall charge of the species. Oxygen typically has an oxidation state of -2, which helps in deducing the oxidation state of manganese in MnO₄⁻ as +7. This state changes to +2 in Mn²⁺ upon reduction.

Determining changes in oxidation state is pivotal in writing balanced chemical and net ionic equations for redox processes. Always assign oxidation numbers to all atoms in a reaction and track their changes to identify the oxidized and reduced species properly.