Question

Balance the following oxidation-reduction reactions by the half-reaction method. (a) $$ \mathrm{FeI}_{3}(a q)+\mathrm{Mg}(s) \longrightarrow \mathrm{Fe}(s)+\mathrm{MgI}_{2}(a q) $$ (b) $$ \mathrm{H}_{2}(g)+\mathrm{Ag}^{+}(a q) \longrightarrow \mathrm{Ag}(s)+\mathrm{H}^{+}(a q) $$

Short answer

(a) The balanced equation is \(2 \mathrm{FeI}_{3} + 3 \mathrm{Mg} \rightarrow 2 \mathrm{Fe} + 3 \mathrm{MgI}_{2}\). (b) The balanced equation is \(\mathrm{H}_{2} + 2 \mathrm{Ag}^{+} \rightarrow 2 \mathrm{Ag} + 2 \mathrm{H}^{+}\).

Step-by-step solution

Identify Oxidation and Reduction Reactions (Part a)

For the equation \(\mathrm{FeI}_{3}(aq) + \mathrm{Mg}(s) \rightarrow \mathrm{Fe}(s) + \mathrm{MgI}_{2}(aq)\), determine the changes in oxidation states. \(\mathrm{Fe}^{3+}\) in \(\mathrm{FeI}_{3}\) is reduced to \(\mathrm{Fe}(s)\), and \(\mathrm{Mg}(s)\) is oxidized to \(\mathrm{Mg}^{2+}\) in \(\mathrm{MgI}_{2}\).

Write and Balance Half-Reactions for Part a

Write the reduction half-reaction and balance it: \( \mathrm{Fe}^{3+} + 3e^- \rightarrow \mathrm{Fe}(s)\). Write the oxidation half-reaction and balance it: \(\mathrm{Mg}(s) \rightarrow \mathrm{Mg}^{2+} + 2e^-\). Balance the electrons by multiplying the reduction reaction by 2 and the oxidation reaction by 3.

Combine and Balance Overall Reaction for Part a

Add the balanced half-reactions: \(2(\mathrm{Fe}^{3+} + 3e^- \rightarrow \mathrm{Fe}(s))\) and \(3(\mathrm{Mg}(s) \rightarrow \mathrm{Mg}^{2+} + 2e^-)\). Combined to form the balanced equation: \(2 \mathrm{FeI}_{3}(aq) + 3 \mathrm{Mg}(s) \rightarrow 2 \mathrm{Fe}(s) + 3 \mathrm{MgI}_{2}(aq)\).

Identify Oxidation and Reduction Reactions (Part b)

For the equation \(\mathrm{H}_{2}(g) + \mathrm{Ag}^{+}(aq) \rightarrow \mathrm{Ag}(s) + \mathrm{H}^{+}(aq)\), identify that \(\mathrm{H}_{2}(g)\) is oxidized to \(\mathrm{H}^{+}\) and \(\mathrm{Ag}^{+}\) is reduced to \(\mathrm{Ag}(s)\).

Write and Balance Half-Reactions for Part b

Write the oxidation half-reaction: \(\mathrm{H}_{2}(g) \rightarrow 2\mathrm{H}^{+}(aq) + 2e^-\). Write the reduction half-reaction: \(\mathrm{Ag}^{+}(aq) + e^- \rightarrow \mathrm{Ag}(s)\). Double the reduction half-reaction to balance the electrons: \(2\mathrm{Ag}^{+}(aq) + 2e^- \rightarrow 2\mathrm{Ag}(s)\).

Combine and Balance Overall Reaction for Part b

Add the balanced half-reactions: \(\mathrm{H}_{2}(g) \rightarrow 2\mathrm{H}^{+}(aq) + 2e^- \) and \(2\mathrm{Ag}^{+}(aq) + 2e^- \rightarrow 2\mathrm{Ag}(s)\). Combine to form the balanced equation: \(\mathrm{H}_{2}(g) + 2\mathrm{Ag}^{+}(aq) \rightarrow 2\mathrm{Ag}(s) + 2\mathrm{H}^{+}(aq)\).

Key concepts

Half-Reaction Method

The half-reaction method is a versatile technique employed in chemistry to balance redox reactions. A redox reaction involves the transfer of electrons between species, consisting of two intertwined processes: oxidation and reduction. In this method, the reaction is dissected into two "half-reactions," each signifying either oxidation or reduction. One of the main goals is to ensure that the number of electrons lost in oxidation equals the number of electrons gained in reduction.

To use the half-reaction method effectively:

• Determine which elements in the reaction are oxidized and which are reduced by analyzing changes in oxidation states.
• Write separate half-reactions for the oxidation and reduction processes. This helps in clearly identifying electron transfer.
• Balance each half-reaction in terms of atoms and charge, often involving adding water molecules, hydrogen ions, or hydroxide ions as needed based on the reaction's environment (acidic or basic).
• Ensure the electrons in each half-reaction cancel out by appropriately multiplying the half-reactions, then add them together to form the overall balanced reaction.

By methodically addressing each half, the half-reaction method guides chemists through complex balancing with clarity and structure.

Balancing Chemical Equations

Balancing chemical equations is an essential skill in chemistry. It involves ensuring that the number of atoms for each element is equal on both sides of the equation. This practice arises from the law of conservation of mass, which states that matter cannot be created or destroyed.

To balance a chemical equation, follow these steps:

• Write the unbalanced equation with reactants on the left and products on the right.
• Count the number of atoms for each element in both reactants and products.
• Add coefficients before the chemical formulas to balance the number of atoms for each element. Begin with the most complex molecules.
• Double-check each type of atom to ensure the same number is present on both sides of the equation.
• Recalculate each element's atoms as coefficients affect more than one substance in the equation.

Balancing chemical equations ensures no discrepancies occur in stoichiometric calculations, preserving mass and conforming to the constraints of physical laws. It's crucial in predicting reaction products and understanding reaction mechanisms.

Redox Chemistry

Redox chemistry revolves around the processes of reduction (gain of electrons) and oxidation (loss of electrons). At its core, a redox reaction comprises both these processes happening simultaneously. Each part of this reaction is a mirror image of the other's electron movement, making them inseparable.

Core aspects of redox chemistry include:

• Oxidation: When a substance loses electrons, its oxidation state increases. An example from everyday life is the rusting of iron.
• Reduction: A gain of electrons by a substance results in a decrease in oxidation state. This can be seen in the formation of metallic silver from silver ions.
• Oxidizing and Reducing Agents: The substance that is reduced (gains electrons) is referred to as the oxidizing agent, while the substance that is oxidized (loses electrons) is called the reducing agent. They facilitate electron transfer.

Understanding redox reactions is vital in numerous applications, from industrial processes and energy generation to biological systems. Recognizing these electron transfers allows chemists to manipulate reactions for desired outcomes, such as energy storage in batteries or detoxification processes in biochemistry.