Question

Balance the equation for each of the following oxidation-reduction chemical reactions. a. \(\mathrm{Na}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{Na}_{2} \mathrm{O}_{2}(s)\) b. \(\operatorname{Fe}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{FeSO}_{4}(a q)+\mathrm{H}_{2}(g)\) c. \(\mathrm{Al}_{2} \mathrm{O}_{3}(s) \rightarrow \mathrm{Al}(s)+\mathrm{O}_{2}(g)\) d. \(\mathrm{Fe}(s)+\mathrm{Br}_{2}(l) \rightarrow \mathrm{FeBr}_{3}(s)\) e. \(\mathrm{Zn}(s)+\mathrm{HNO}_{3}(a q) \rightarrow \mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{H}_{2}(g)\)

Short answer

The balanced redox equations for the given reactions are: a. 2Na(s) + O₂(g) → 2Na₂O₂(s) b. Fe(s) + H₂SO₄(aq) → FeSO₄(aq) + H₂(g) c. 2Al₂O₃(s) → 4Al(s) + 3O₂(g) d. Fe(s) + 3Br₂(l) → 2FeBr₃(s) e. Zn(s) + 2HNO₃(aq) → Zn(NO₃)₂(aq) + H₂(g)

Step-by-step solution

Identify the oxidation states of elements involved

For each reaction, identify the oxidation states of the elements involved in both the reactants and products side. Remember that oxidation state represents the effective charge on an atom in a chemical species. a. Na(s) + O₂(g) → Na₂O₂(s) Oxidation states: Na (0) and O₂ (0) b. Fe(s) + H₂SO₄(aq) → FeSO₄(aq) + H₂(g) Oxidation states: Fe (0), H₂ (0), SO₄²⁻ (-2 for each S and +6 for O) c. Al₂O₃(s) → Al(s) + O₂(g) Oxidation states: Al (+3), O (-2), and O₂ (0) d. Fe(s) + Br₂(l) → FeBr₃(s) Oxidation states: Fe (0) and Br₂ (0) e. Zn(s) + HNO₃(aq) → Zn(NO₃)₂(aq) + H₂(g) Oxidation states: Zn (0), H (+1), N (+5), and O (-2)

Identify the changes in oxidation states

Determine the increase and decrease in oxidation states for the species involved in each reaction. The increase in oxidation state indicates oxidation (loss of electrons), while the decrease indicates reduction (gain of electrons). a. Na is oxidized from 0 to +1, and O is reduced from 0 to -1. b. Fe is oxidized from 0 to +2, and H is reduced from +1 to 0. c. Al is reduced from +3 to 0, and O is oxidized from -2 to 0. d. Fe is oxidized from 0 to +3, and Br is reduced from 0 to -1. e. Zn is oxidized from 0 to +2, and H is reduced from +1 to 0.

Balance the atoms of elements undergoing changes in oxidation states

Adjust the coefficients of the species to achieve a balanced equation in terms of atoms of elements that are undergoing changes in oxidation states. a. Na(s) + O₂(g) → 2Na₂O₂(s) Balancing Na atoms: 2 Na on both sides. b. Fe(s) + H₂SO₄(aq) → FeSO₄(aq) + H₂(g) Balancing Fe atoms: 1 Fe on both sides. c. 2Al₂O₃(s) → 4Al(s) + 3O₂(g) Balancing Al and O atoms: 4 Al and 6 O on both sides. d. Fe(s) + Br₂(l) → 2FeBr₃(s) Balancing Fe and Br atoms: 2 Fe and 6 Br on both sides. e. Zn(s) + 2HNO₃(aq) → Zn(NO₃)₂(aq) + H₂(g) Balancing Zn, N, and H atoms: 1 Zn, 2 N, and 2 H on both sides.

Check the oxidation states and balance for remaining atoms

Ensure that the oxidation states have been balanced and check the balance for the remaining atoms in each of the reactions. a. 2Na(s) + O₂(g) → 2Na₂O₂(s) is already balanced in terms of oxidation states and remaining atoms (Na and O). b. Fe(s) + H₂SO₄(aq) → FeSO₄(aq) + H₂(g) is already balanced in terms of oxidation states and remaining atoms (Fe, H, and SO₄). c. 2Al₂O₃(s) → 4Al(s) + 3O₂(g) is already balanced in terms of oxidation states and remaining atoms (Al and O). d. Fe(s) + 3Br₂(l) → 2FeBr₃(s) is already balanced in terms of oxidation states and remaining atoms (Fe and Br). e. Zn(s) + 2HNO₃(aq) → Zn(NO₃)₂(aq) + H₂(g) is already balanced in terms of oxidation states and remaining atoms (Zn, H, N, and O). Thus, the balanced redox equations for the given reactions are: a. 2Na(s) + O₂(g) → 2Na₂O₂(s) b. Fe(s) + H₂SO₄(aq) → FeSO₄(aq) + H₂(g) c. 2Al₂O₃(s) → 4Al(s) + 3O₂(g) d. Fe(s) + 3Br₂(l) → 2FeBr₃(s) e. Zn(s) + 2HNO₃(aq) → Zn(NO₃)₂(aq) + H₂(g)

Key concepts

Balancing Chemical Equations

Balancing chemical equations is a fundamental skill in chemistry that ensures the law of conservation of mass is followed. This law states that matter cannot be created or destroyed in an isolated system. Hence, the number of atoms for each element must be the same on both sides of a chemical equation.

In the context of oxidation-reduction (redox) reactions, balancing chemical equations involves more than just matching the number of atoms; it also requires ensuring that the transfer of electrons is accounted for.
For instance, in the reaction:

• Fe(s) + H₂SO₄(aq) → FeSO₄(aq) + H₂(g)

The iron (Fe) atom, starts as a neutral atom (oxidation state 0) and ends as Fe²⁺ in FeSO₄. This change necessitates ensuring that electron loss by Fe is matched by an electron gain by another species in the reaction.

To balance such reactions, chemists often use methods like half-reaction balance or systematic trial and error. In essence, balancing redox equations ensures that both mass and charge are conserved.

Oxidation States

The concept of oxidation states, or oxidation numbers, is crucial for identifying which elements are oxidized and which are reduced in a redox reaction. Oxidation states provide a book-keeping tool to track the transfer of electrons in a reaction.

An oxidation state is essentially the "charge" an atom would have if all bonds to its neighboring atoms were purely ionic. Here's a step-by-step approach to determining oxidation states:

• The oxidation state of a pure element is always zero, such as Na in Na(s) or O₂ in O₂(g).
• For ions, the oxidation state is equal to the charge of the ion, e.g., Fe²⁺ in FeSO₄, where Fe has an oxidation state of +2.
• In compounds, some atoms have common oxidation states: for instance, hydrogen is typically +1 and oxygen is typically -2, unless in peroxides or when bound to fluorine.

Using these guidelines allows one to assign oxidation states accurately and hence, facilitates the identification of redox changes in any given reaction.

For example, in the reaction of Zn with HNO₃:

• Zn is oxidized from 0 in Zn to +2 in Zn(NO₃)₂,
• H is reduced from +1 in HNO₃ to 0 in H₂.

Determining these changes is the first critical step toward efficiently balancing redox reactions.

Redox Balancing Methods

Balancing redox reactions is all about ensuring that the number of electrons lost in the process of oxidation is equal to the number of electrons gained during reduction.

There are two main methods for balancing redox reactions: the oxidation number method and the half-reaction method. Each method systematically accounts for electron transfer.

• The Oxidation Number Method:
  • This involves assigning oxidation numbers to the reactants and products, calculating the changes in oxidation numbers, and using these changes to identify the oxidation and reduction parts of the reaction.
  • The equations are balanced by ensuring that the increase in oxidation numbers is matched with an equal decrease.
• The Half-Reaction Method:
  • This splits the overall redox reaction into two half-reactions: one representing oxidation and the other reduction.
  • Each half-reaction is balanced separately (for atoms and charge) and then combined to give the overall balanced equation.

For example, in the reduction of Al₂O₃ → Al + O₂, using either method helps clarify the electron movements. Aluminum is reduced from +3 to 0, while oxygen is oxidized from -2 to 0. Choosing a method often depends on the complexity of the reaction or the user's comfort with a particular technique.

Understanding these methods is vital for anyone working with chemical reactions, as they underscore the delicate balance of electron transfer that drives redox processes.