- The balanced chemical equation for the reaction is: \(Cu(s) + 2AgNO_3(aq) \rightarrow Cu(NO_3)_2(aq) + 2Ag(s)\).
- Copper is oxidized: \(Cu(s) \rightarrow Cu^{2+}(aq) + 2e^-\), with its oxidation number increasing from \(0\) to \(+2\).
- Silver is reduced: \(Ag^+(aq) + e^- \rightarrow Ag(s)\), with its oxidation number decreasing from \(+1\) to \(0\).
- Final Answer: The balanced reaction is \(\boxed{Cu(s) + 2AgNO_3(aq) \rightarrow Cu(NO_3)_2(aq) + 2Ag(s)}\).
Explanation
- Formulation and Balancing of the Chemical Equation
When copper metal (Cu) is placed in a silver nitrate (\(AgNO_3\)) solution, a single-displacement reaction occurs. Copper is more reactive than silver and displaces it from the nitrate solution. The chemical equation is represented by the reaction of solid copper with aqueous silver nitrate to produce aqueous copper(II) nitrate and solid silver. Balancing this equation involves ensuring that the number of atoms of each element is the same on both sides of the equation. We start with the skeleton equation:
\[Cu(s) + AgNO_3(aq) \rightarrow Cu(NO_3)_2(aq) + Ag(s)\]
To balance this, we need two moles of silver nitrate for every mole of copper to provide two nitrate ions and two silver ions:
\[Cu(s) + 2AgNO_3(aq) \rightarrow Cu(NO_3)_2(aq) + 2Ag(s)\]
This balanced equation satisfies the law of conservation of mass.
- Identifying and Justifying Oxidation
Oxidation is defined as the loss of electrons, which corresponds to an increase in the oxidation number (O.N.). In this reaction, elemental copper (Cu) starts with an oxidation number of \(0\). In the product, copper is part of the copper(II) nitrate compound, where its oxidation number is \(+2\). Since the oxidation number of copper increases from \(0\) to \(+2\), copper is oxidized. The half-reaction for the oxidation of copper is:
\[Cu(s) \rightarrow Cu^{2+}(aq) + 2e^-\]
The change in oxidation number is \(\Delta O.N. = +2 - 0 = +2\), confirming that two electrons are lost per copper atom.
- Identifying and Justifying Reduction
Reduction is defined as the gain of electrons, which corresponds to a decrease in the oxidation number. In the silver nitrate solution, the silver ion (\(Ag^+\)) has an oxidation number of \(+1\). When it forms solid silver metal (\(Ag\)), its oxidation number becomes \(0\). Since the oxidation number of silver decreases from \(+1\) to \(0\), silver is reduced. The half-reaction for the reduction of silver is:
\[Ag^+(aq) + e^- \rightarrow Ag(s)\]
The change in oxidation number is \(\Delta O.N. = 0 - 1 = -1\), confirming that one electron is gained per silver ion. Since the total charge must be conserved, the two electrons lost by copper are gained by two silver ions (\(2Ag^+ + 2e^- \rightarrow 2Ag\)).
Examples
The chemical process described, where a more reactive metal replaces a less reactive one in solution, is the fundamental principle behind electroplating and the operation of simple electrochemical cells. For example, by controlling these redox reactions, engineers can coat cheaper base metals with thin layers of precious metals like silver or gold to improve corrosion resistance or appearance, a process widely used in jewelry making and electronics manufacturing. Understanding which species are oxidized and reduced allows for precise control over these industrial coating and energy storage processes.