Question

\(\mathrm{Cu}^{+}(\mathrm{aq})\) is unstable in solution and undergoes simultaneous oxidation and reduction according to the reaction, \(2 \mathrm{Cu}^{+}(\mathrm{aq}) \rightleftharpoons-\mathrm{Cu}^{2+}(\mathrm{aq})+\mathrm{Cu}(\mathrm{s})\) choose correct \(E^{\circ}\) for above reaction if \(E^{\circ}\left(\mathrm{Cu}^{2+} / \mathrm{Cu}\right)=0.34 \mathrm{~V}\) and \(E^{\circ}\left(\mathrm{Cu}^{2+} / \mathrm{Cu}^{+}\right)=0.15 \mathrm{~V}\) (a) \(-0.38 \mathrm{~V}\) (b) \(+0.49 \mathrm{~V}\) (c) \(+0.38 \mathrm{~V}\) (d) \(-0.19 \mathrm{~V}\)

Short answer

Option (d): \(-0.19 \mathrm{~V}\) is correct.

Step-by-step solution

Understanding the Reaction

The given reaction is a redox reaction where simultaneously, copper(I) ions are oxidized to copper(II) ions and reduced to copper metal. This type of reaction is known as a disproportionation reaction, where an element in one oxidation state is simultaneously oxidized and reduced, resulting in different products.

Identify the Half-Reactions

For the disproportionation reaction \(2 \mathrm{Cu}^+(\mathrm{aq}) \rightarrow \mathrm{Cu}^{2+}(\mathrm{aq}) + \mathrm{Cu}(\mathrm{s})\), we need to split it into two half-reactions. The oxidation half-reaction is:\(\mathrm{Cu}^+ \rightarrow \mathrm{Cu}^{2+} + e^-\)and the reduction half-reaction is:\(\mathrm{Cu}^+ + e^- \rightarrow \mathrm{Cu}\).

Key concepts

Redox Reaction

Redox reactions are chemical processes where the oxidation states of elements change during the reaction. The term 'redox' stands for reduction-oxidation, as these reactions involve both reduction and oxidation processes. Reduction refers to the gain of electrons by an element, while oxidation involves the loss of electrons.
In a redox reaction, two half-reactions occur: one representing the oxidation process and the other for reduction. This balance between oxidation and reduction is crucial as electrons lost in the oxidation half must be gained in the reduction half. Such reactions occur frequently in nature and are fundamental to processes like respiration, combustion, and photosynthesis.

Electrochemistry

Electrochemistry is a branch of chemistry that studies the interaction between chemical reactions and electricity. It primarily focuses on redox reactions where electron transfer is fundamental. In electrochemical cells, these reactions allow for the conversion of chemical energy into electrical energy and vice versa.

• **Galvanic Cells**: These use spontaneous redox reactions to generate electricity. A classic example is a battery.
• **Electrolytic Cells**: Here, electricity is used to drive non-spontaneous chemical reactions, such as in electrolysis.

Electrochemistry is integral to many everyday applications, ranging from batteries and fuel cells to metal plating and corrosion prevention.

Oxidation and Reduction Half-Reactions

In any redox reaction, we split the reaction into oxidation and reduction half-reactions to understand the electron transfer process. Each half-reaction shows either the loss or gain of electrons.

• **Oxidation Half-Reaction**: Demonstrates how an element loses electrons. e.g., in the oxidation of copper, \[\text{Cu}^+ \rightarrow \text{Cu}^{2+} + e^- \]
• **Reduction Half-Reaction**: Shows how an element gains electrons. e.g., in the reduction of copper, \[\text{Cu}^+ + e^- \rightarrow \text{Cu(s)} \]

These half-reactions are balanced with respect to mass and charge. Understanding these processes helps students predict the behavior of elements in different redox scenarios and helps formulate balanced redox equations.