Question

Balance these redox reactions by inspection. a) \(\mathrm{Fe}_{2} \mathrm{~S}_{3}+\mathrm{O}_{2} \rightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}+\mathrm{S}\) b) \(\mathrm{Cu}_{2} \mathrm{O}+\mathrm{H}_{2} \rightarrow \mathrm{Cu}+\mathrm{H}_{2} \mathrm{O}\)

Short answer

a) 2Fe_2S_3 + 9O_2 → 2Fe_2O_3 + 6S; b) Cu_2O + H_2 → 2Cu + H_2O.

Step-by-step solution

Identify Oxidation and Reduction Parts for Reaction (a)

For the reaction \( \mathrm{Fe}_{2} \mathrm{~S}_{3}+\mathrm{O}_{2} \rightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}+\mathrm{S} \), iron \((Fe)\) is being oxidized from \(+2\) to \(+3\) in \( \mathrm{Fe}_{2} \mathrm{O}_{3} \), and sulfur \((S)\) is being reduced from \(-2\) in \( \mathrm{Fe}_{2} \mathrm{S}_{3} \) to \(0\). \( \mathrm{O}_{2} \) is reduced to \(-2\) in \( \mathrm{Fe}_{2} \mathrm{O}_{3} \).

Balance Iron and Sulfur Atoms for Reaction (a)

Ensure that both the number of iron and sulfur atoms are the same on both sides of the equation: starting with \( \mathrm{Fe}_{2} \mathrm{~S}_{3} \rightarrow 2\mathrm{Fe}_{2} \mathrm{O}_{3} \) balances iron, and \(3\mathrm{S}\) balances sulfur.

Balance Oxygen Atoms for Reaction (a)

Oxygen atoms in reactions need balancing. \( \mathrm{Fe}_{2} \mathrm{O}_{3} \) has 3 oxygen atoms, so from \( \mathrm{O}_2\), you'll need 9 oxygen atoms in total: \(4.5\mathrm{O}_{2} \). Hence, whole numbers, use: \( \mathrm{Fe}_{2} \mathrm{S}_{3}+\frac{9}{2} \mathrm{O}_{2} \rightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}+3\mathrm{S} \).

Identify Oxidation and Reduction Parts for Reaction (b)

For the reaction \( \mathrm{Cu}_{2} \mathrm{O}+\mathrm{H}_{2} \rightarrow \mathrm{Cu}+\mathrm{H}_{2} \mathrm{O} \), copper \((Cu)\) is reduced from \(+1\) to \(0\), and hydrogen \((H)\) is oxidized from \(0\) in \(H_{2}\) to \(+1\) in water \(\mathrm{H}_{2}\mathrm{O}\).

Balance Copper and Hydrogen Atoms for Reaction (b)

Balance the number of atoms: start with copper \(\mathrm{Cu}_{2} \rightarrow 2 \mathrm{Cu}\) and balance hydrogen so two hydrogen molecules give two water molecules: \(\mathrm{Cu}_{2} \mathrm{~O}+\mathrm{H}_{2} \rightarrow 2\mathrm{Cu}+\mathrm{H}_{2} \mathrm{O}\).

Confirm Final Balanced Equations

Rewrite both reactions ensuring all atoms are balanced:(a) \( \mathrm{2Fe}_{2} \mathrm{~S}_{3}+9 \mathrm{O}_{2} \rightarrow 4\mathrm{Fe}_{2} \mathrm{O}_{3}+6\mathrm{S} \)(b) \( \mathrm{Cu}_{2} \mathrm{~O}+\mathrm{H}_{2} \rightarrow 2\mathrm{Cu}+\mathrm{H}_{2} \mathrm{O} \)

Key concepts

Oxidation States

Understanding oxidation states is key to balancing redox reactions. An oxidation state, also known as an oxidation number, represents the degree of oxidation of an atom within a molecule. It's the hypothetical charge that an atom would have if all bonds to atoms of different elements were completely ionic.

• In a chemical compound, each atom is assigned an oxidation state. For instance, in the compound \(\mathrm{Fe}_{2} \mathrm{S}_{3}\), iron \((Fe)\) has an oxidation state of \(+3\) and sulfur \((S)\) has \(-2\).
• Changes in an atom's oxidation state during a reaction indicate whether it has been oxidized or reduced. If the oxidation state increases, as with iron in the initial example, it is oxidized. If it decreases, as seen with sulfur, it is reduced.

Understanding these variations helps identify the reduction and oxidation parts of a redox reaction.

Reduction Reactions

Reduction reactions are a vital portion of redox reactions. They occur when an atom or molecule gains electrons, thereby reducing its oxidation state.

• In reaction (a), sulfur \((S)\) is reduced because its oxidation state goes from \(-2\) in \(\mathrm{Fe}_{2} \mathrm{S}_{3}\) to \(0\) in \(S\).
• Reduction results in a decrease in oxidation state, often associated with gaining electrons. This is mirrored in chemical equations when the atom gains hydrogen or loses oxygen.

The ability to identify which element is reduced helps balance chemical equations accurately.

Inspection Method

The inspection method is a straightforward approach to balance redox reactions. It involves manually adjusting coefficients to ensure the number of atoms and charge are balanced on both sides.

Steps to Balance by Inspection

• Identify which atoms need balancing in both the reactants and products.
• Adjust coefficients to balance the atoms that have different amounts on either side. Start with elements that appear in only one reactant and product first.
• Iterate through until the total charge and atom counts are equal.

This method is effective but can require trial and error, especially with complex equations.

Chemical Equations

Chemical equations represent the reactants and products in a chemical reaction. They must be balanced to reflect the law of conservation of mass, which means the same number of each type of atom appears on both sides.

• In redox reactions, balance atoms by first identifying elements that are reduced or oxidized. Adjust their coefficients, and then balance the rest of the atoms.
• For instance, in reaction (b), copper changes and needs to be balanced first \(\mathrm{Cu}_{2} \mathrm{O} + \mathrm{H}_{2} \rightarrow 2 \mathrm{Cu} + \mathrm{H}_{2} \mathrm{O}\). Copper and hydrogen atoms are adjusted to balance both sides.

Viewing a chemical equation like a mathematical equation will help ensure that no atoms are lost or created, keeping the reaction coherent.