Question

Silver is sometimes found in nature as large nuggets; more often it is found mixed with other metals and their ores. Cyanide ion is often used to extract the silver by the following reaction that occurs in basic solution: $$\mathrm{Ag}(s)+\mathrm{CN}^{-}(a q)+\mathrm{O}_{2}(g) \stackrel{\mathrm{Basic}}{\longrightarrow} \mathrm{Ag}(\mathrm{CN})_{2}^{-}(a q)$$ Balance this equation by using the half-reaction method.

Short answer

The balanced chemical equation for the given reaction using the half-reaction method in a basic solution is: \(2 \mathrm{Ag}(s) + \mathrm{O}_{2}(g) + \mathrm{CN}^{-}(a q) + 4 \mathrm{OH}^{-}(a q) \rightarrow 2 \mathrm{Ag}(\mathrm{CN})_{2}^{-}(a q) + 2 \mathrm{H}_{2}\mathrm{O}(l)\)

Step-by-step solution

1. Identify the oxidation and reduction half-reactions

Oxidation half-reaction: Ag(s) → Ag(CN)₂⁻(aq) Reduction half-reaction: O₂(g) + CN⁻(aq) → Ag(CN)₂⁻(aq)

2. Balance atoms other than O and H in each half-reaction

Both half-reactions are already balanced for atoms other than O and H: Oxidation half-reaction: Ag(s) → Ag(CN)₂⁻(aq) Reduction half-reaction: O₂(g) + CN⁻(aq) → Ag(CN)₂⁻(aq)

3. Balance O atoms by adding H2O molecules

In the reduction half-reaction, we will add 2 H₂O molecules in the product side to balance the O atoms: Reduction half-reaction: O₂(g) + CN⁻(aq) → Ag(CN)₂⁻(aq) + 2 H₂O(l)

4. Balance H atoms by adding H+ ions (but since it's a basic solution, we need to use OH- ions)

Since the reaction occurs in a basic solution, we will balance H atoms using OH⁻ ions instead of H⁺ ions. In the reduction half-reaction, add 4 OH⁻ ions to the reactant side to balance the H atoms: Reduction half-reaction: O₂(g) + CN⁻(aq) + 4 OH⁻(aq) → Ag(CN)₂⁻(aq) + 2 H₂O(l)

5. Balance charges by adding electrons

Balance charges by adding electrons to the respective half-reactions: Oxidation half-reaction: Ag(s) → Ag(CN)₂⁻(aq) + \(\underline{e⁻}\) Reduction half-reaction: O₂(g) + CN⁻(aq) + 4 OH⁻(aq) + \(\underline{2 e⁻}\) → Ag(CN)₂⁻(aq) + 2 H₂O(l)

6. Equalize the electrons in both half-reactions

Since the oxidation half-reaction has 1 electron and the reduction half-reaction has 2 electrons, we need to multiply the oxidation half-reaction by 2 to have the same number of electrons in both half-reactions: Oxidation half-reaction: \(2\) [Ag(s) → Ag(CN)₂⁻(aq) + \(e⁻\)] Resulting half-reaction: 2 Ag(s) → 2 Ag(CN)₂⁻(aq) + 2 \(e⁻\) Now, both half-reactions have the same number of electrons: Oxidation half-reaction: 2 Ag(s) → 2 Ag(CN)₂⁻(aq) + 2 \(e⁻\) Reduction half-reaction: O₂(g) + CN⁻(aq) + 4 OH⁻(aq) + 2 \(e⁻\) → Ag(CN)₂⁻(aq) + 2 H₂O(l)

7. Add the balanced half-reactions and cancel any common terms

Add both half-reactions and cancel common terms (2 \(e⁻\), Ag(CN)₂⁻): 2 Ag(s) + O₂(g) + CN⁻(aq) + 4 OH⁻(aq) → 2 Ag(CN)₂⁻(aq) + 2 H₂O(l) This is the balanced chemical equation for the given reaction.

Key concepts

Half-Reaction Method

The half-reaction method is a systematic approach to balancing chemical equations, particularly useful for oxidation-reduction reactions. This method breaks down the overall reaction into two parts: the oxidation half-reaction, where a substance loses electrons, and the reduction half-reaction, where another substance gains those electrons, maintaining the principle of charge conservation. In the process of balancing:

• Identify and separate the oxidation and reduction half-reactions.
• Balance all elements except oxygen and hydrogen first.
• Balance oxygen atoms by adding water ( H₂O ) molecules.
• Balance hydrogen atoms afterward, using protons ( H⁺ ) if in acidic solution, but in basic solutions, OH⁻ ions are used instead.
• Finally, balance the charge by adding electrons ( e⁻ ), ensuring both half-reactions have equal electron counts to be combined back into one equation.

This comprehensive technique allows one to address various complexities found in redox reactions by ensuring both mass and charge balance in the reaction equation, crucial for accurate chemical representations in academic and professional chemistry.

Oxidation-Reduction Reactions

Oxidation-reduction reactions, or redox reactions, are chemical processes in which electrons transfer from one reactant to another. These reactions are characterized by the simultaneous occurrence of oxidation (loss of electrons) and reduction (gain of electrons). In any redox reaction:

• The substance undergoing oxidation increases its oxidation state, while the substance reduced sees a decrease in its oxidation state.
• The electron transfer is often evident when tracking changes in oxidation numbers of the elements involved.
• These reactions are integral to numerous biological and chemical systems, playing roles in everything from energy cycles in cells to industrial processes such as metal extraction and corrosion.

Understanding redox reactions through their half-reactions helps provide finer insights into the electron transfer's direction and rate, essential for balancing and evaluating reactions that might appear spontaneously or be driven under specific conditions.

Basic Solution Reactions

Reactions occurring in basic solutions have special characteristics because they take place with an abundance of hydroxide ions ( OH⁻ ) available. In the context of balancing these reactions, it is essential to account for these conditions:

• Hydroxide ions often play a critical role in balancing hydrogen atoms in these reactions, instead of protons ( H⁺ ).
• When balancing redox reactions in a basic solution, it is necessary to add electrons and hydroxide ions strategically to both sides of the equation—especially when hydrogen atoms need balancing.
• Water molecules can also be used to balance oxygen and sometimes hydrogen atoms as well.

Mastering the balance of chemical reactions in a basic environment enables the accurate depiction of naturally occurring processes, as seen in certain extractions and biochemical transformations, such as those occurring in alkaline batteries or specific types of ore extraction.