Question

Balance these redox reactions by the half reaction method. a) \(\mathrm{Na}+\mathrm{Hg}_{2} \mathrm{Cl}_{2} \rightarrow \mathrm{NaCl}+\mathrm{Hg}\) b) \(\mathrm{Al}_{2} \mathrm{O}_{3}+\mathrm{C} \rightarrow \mathrm{Al}+\mathrm{CO}_{2}\)

Short answer

a) \(2\mathrm{Na} + \mathrm{Hg}_2\mathrm{Cl}_2 \rightarrow 2\mathrm{NaCl} + 2\mathrm{Hg}\); b) \(2\mathrm{Al}_2\mathrm{O}_3 + 3\mathrm{C} \rightarrow 4\mathrm{Al} + 3\mathrm{CO}_2\).

Step-by-step solution

Identify Oxidation and Reduction Half-Reactions - (a)

In the reaction \(\mathrm{Na} + \mathrm{Hg}_{2}\mathrm{Cl}_{2} \rightarrow \mathrm{NaCl} + \mathrm{Hg}\), identify the species that are oxidized and reduced. Sodium \((\mathrm{Na})\) is oxidized to sodium chloride \((\mathrm{NaCl})\), and \(\mathrm{Hg}_2\mathrm{Cl}_2\) is reduced to mercury \((\mathrm{Hg})\).

Write Oxidation and Reduction Half-Reactions - (a)

Write the half-reactions:1. \(\mathrm{Na} \rightarrow \mathrm{Na}^+ + e^-\)2. \(\mathrm{Hg}_2^{2+} + 2e^- \rightarrow 2\mathrm{Hg}\) after splitting \(\mathrm{Hg}_2\mathrm{Cl}_2\) to \(\mathrm{Hg}_2^{2+} + 2\mathrm{Cl}^-\).

Balance the Electrons - (a)

Balance the electrons in both half-reactions. The sodium half-reaction needs 2 electrons, so multiply by 2:1. \(2\mathrm{Na} \rightarrow 2\mathrm{Na}^+ + 2e^-\)2. \(\mathrm{Hg}_2^{2+} + 2e^- \rightarrow 2\mathrm{Hg}\)

Combine the Balanced Half-Reactions - (a)

Add the balanced half-reactions together and include the spectator ions (chloride ions) to form the complete balanced equation:\(2\mathrm{Na} + \mathrm{Hg}_2\mathrm{Cl}_2 \rightarrow 2\mathrm{NaCl} + 2\mathrm{Hg}\).

Identify Oxidation and Reduction Half-Reactions - (b)

In the reaction \(\mathrm{Al}_{2}\mathrm{O}_3 + \mathrm{C} \rightarrow \mathrm{Al} + \mathrm{CO}_2\), aluminum oxide \((\mathrm{Al}_{2} \mathrm{O}_3)\) is reduced to aluminum \((\mathrm{Al})\). Carbon \((\mathrm{C})\) is oxidized to carbon dioxide \((\mathrm{CO}_2)\).

Write Oxidation and Reduction Half-Reactions - (b)

Write the half-reactions:1. \(\mathrm{Al}_2\mathrm{O}_3 + 6e^- \rightarrow 2\mathrm{Al} + 3\mathrm{O}^{2-}\)2. \(\mathrm{C} + 2\mathrm{O}^{2-} \rightarrow \mathrm{CO}_2 + 4e^-\).

Balance the Electrons - (b)

Balance the electrons in both half-reactions. Multiply the aluminum half-reaction by 2 and the carbon half-reaction by 3 to match the number of electrons:1. \(2(\mathrm{Al}_2\mathrm{O}_3 + 6e^- \rightarrow 2\mathrm{Al} + 3\mathrm{O}^{2-})\)2. \(3(\mathrm{C} + 2\mathrm{O}^{2-} \rightarrow \mathrm{CO}_2 + 4e^-)\).

Combine the Balanced Half-Reactions - (b)

Combine the balanced half-reactions and simplify:\(2\mathrm{Al}_2\mathrm{O}_3 + 3\mathrm{C} \rightarrow 4\mathrm{Al} + 3\mathrm{CO}_2\).

Key concepts

Half Reaction Method

The half reaction method is a powerful tool used to balance redox reactions in chemistry. By breaking down a full chemical equation into its oxidation and reduction components, one can better understand how electrons transfer between the reactants. This method simplifies the complex redox equations by focusing on electron flow.
To use the half reaction method, start by identifying the species undergoing oxidation and reduction. For instance, in the reaction between sodium (Na) and mercury chloride (\(\mathrm{Hg}_{2}\mathrm{Cl}_{2}\)), sodium is oxidized, meaning it loses electrons, while mercury is reduced, meaning it gains electrons.

• Oxidation refers to the loss of electrons, while reduction refers to the gain of electrons.
• Writing separate half reactions for oxidation and reduction helps in balancing both mass and charge separately.

Once the half reactions are written, balance the electrons lost in oxidation with those gained in reduction by multiplying the half reactions by appropriate coefficients. Finally, recombine these balanced half reactions to form the complete balanced redox equation. This systematic procedure simplifies balancing by offering clear steps ensuring no atoms or charges are overlooked.

Balancing Chemical Equations

Balancing chemical equations is essential in chemistry to reflect the law of conservation of mass. It ensures that the mass and charge are the same on both sides of a chemical reaction equation. This process involves adjusting the coefficients of reactants and products until a balance is achieved.
When using the half reaction method, balancing becomes more focused on electrons particularly for redox reactions. The goal is to make sure that the number of electrons lost in oxidation equals the number gained in reduction:

• Balance each element in the half reactions first, ensuring that the number of atoms for each element is equal on both sides.
• Add electrons to balance the charge in each half reaction.
• Adjust coefficients in the half reactions to equalize the electron transfer.

In the reaction between sodium and mercury chloride, balancing involved adjusting the sodium half reaction by multiplying it by 2 to equalize the electrons with the mercury half reaction. This adjustment brings harmony to the original complex equation, ensuring mass and charge conservation.

Oxidation and Reduction

Oxidation and reduction are core concepts in chemistry representing the transfer of electrons between species. Understanding these concepts is critical for grasping how redox reactions operate, as they involve changes in the oxidation states of the reacting species.
Oxidation is characterized by the loss of electrons. In redox equations, the oxidation state of the element that loses electrons increases. Conversely, reduction involves a gain of electrons, resulting in a decrease in the oxidation state of the reduced component:

• Any species that causes another to undergo oxidation is called an oxidizing agent. Meanwhile, the species undergoing oxidation is called a reducing agent.
• In the given reaction \(\mathrm{Na} + \mathrm{Hg}_{2}\mathrm{Cl}_{2} \rightarrow \mathrm{NaCl} + \mathrm{Hg}\), sodium (\(\mathrm{Na}\)) is oxidized and acts as the reducing agent.
• Mercury (\(\mathrm{Hg}_{2}\mathrm{Cl}_{2}\)) is reduced and behaves as the oxidizing agent.

Oxidation and reduction can occur simultaneously during a redox reaction, and comprehending these changes helps in elaborately writing and balancing half reactions. It ultimately connects the theoretical and practical aspects of chemical reactions, highlighting the interplay of electron transfer in chemical processes.