Question

In acidic solution, silver(II) oxide first dissolves to produce \(A g^{2+}(a q) .\) This is followed by the oxidation of \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) to \(\mathrm{O}_{2}(\mathrm{g})\) and the reduction of \(\mathrm{Ag}^{2+}\) to \(\mathrm{Ag}^{+}\) (a) Write equations for the dissolution and oxidationreduction reactions. (b) Show that the oxidation-reduction reaction is indeed spontaneous.

Short answer

The dissolution reaction can be written as \(AgO_{(s)} + 2H^{+}_{(aq)} \to Ag^{2+}_{(aq)} + H_2O_{(l)}\). The redox reaction is represented as \(4Ag^{2+}_{(aq)} + 2H_{2}O_{(l)} \to 4Ag^{+}_{(aq)} + O_{2(g)} + 4H^{+}_{(aq)}\). The redox reaction is spontaneous as there's a flow of electrons, leading to decrease in oxidation state (-1) in the reduction half and increase in oxidation state (+1) in the oxidation half.

Step-by-step solution

Dissolution Reaction

Silver(II) oxide (\(AgO\)), in acidic solution, will first dissolve to produce silver(II) ions (\(Ag^{2+}\)) in aqueous solution. Writing this dissolution reaction in terms of an equation: \(AgO_{(s)} + 2H^{+}_{(aq)} \to Ag^{2+}_{(aq)} + H_2O_{(l)}\)

Oxidation-Reduction Reaction

In this reaction, water is oxidized to oxygen gas, and \(Ag^{2+}\) ions are reduced to \(Ag^{+}\) ions. These are represented by the following half-reactions: Oxidation: \(2H_{2}O_{(l)} \to O_{2(g)} + 4H^{+}_{(aq)} + 4e^{-}\) Reduction: \(Ag^{2+}_{(aq)} + e^{-} \to Ag^{+}_{(aq)}\) To balance the electrons in the half-reactions, the reduction reaction is multiplied by 4 and then they are added: \(4Ag^{2+}_{(aq)} + 4e^{-} \to 4Ag^{+}_{(aq)}\) \(2H_{2}O_{(l)} \to O_{2(g)} + 4H^{+}_{(aq)} + 4e^{-}\) _______________ \(4Ag^{2+}_{(aq)} + 2H_{2}O_{(l)} \to 4Ag^{+}_{(aq)} + O_{2(g)} + 4H^{+}_{(aq)}\)

Spontaneity of the Reaction

The spontaneity of a chemical reaction can be determined by the change in oxidation states. In the reduction half-reaction, \(Ag^{2+}\) ions are reduced to \(Ag^{+}\) ions, meaning they gained electrons (reduction leads to decrease in oxidation state, \(-1\)). In the oxidation half-reaction, water loses electrons to form oxygen gas, meaning it is being oxidized (oxidation leads to increase in oxidation state, \(+1\)). The combined reaction is therefore spontaneous because reduction and oxidation occur simultaneously, leading to the flow of electrons and creating a redox reaction.

Key concepts

Chemical Spontaneity

Understanding the spontaneous nature of a reaction is essential in chemical processes. Chemical spontaneity refers to the inherent tendency of a chemical reaction to occur without being driven by an external force. The spontaneity of a reaction is commonly assessed using Gibbs free energy, with a negative Gibbs free energy indicating a spontaneous process.

For redox reactions, spontaneity can often be inferred by looking at the oxidation states of the reactants and products. If a reaction involves a transfer of electrons from a reducing agent (oxidation) to an oxidizing agent (reduction), and the resulting electron flow is energetically favorable, the reaction is considered spontaneous. This is typically observed when the oxidation states of the reactants decrease in the reduction reaction and increase in the oxidation reaction, with no outside energy input required.

Dissolution Reaction

A dissolution reaction is the process by which a solute dissolves in a solvent to form a homogeneous mixture or a solution. In the context of redox reactions, dissolution is crucial as it often precedes the redox process and makes the reactants accessible in the aqueous phase.

For example, the dissolution of silver(II) oxide in an acidic solution can be represented by the equation: \(AgO_{(s)} + 2H^{+}_{(aq)} \to Ag^{2+}_{(aq)} + H_2O_{(l)}\). Here, the solid silver oxide reacts with the hydrogen ions from the acid, leading to the formation of soluble silver ions and water. This initial step is important as it sets the stage for subsequent redox transformations.

Balancing Redox Equations

Balancing redox equations is critical to correctly represent the conservation of mass and charge during a reaction. In a redox process, electrons are transferred, and this transfer must be accounted for in each half-reaction.

In the provided exercise, the half-reactions for the oxidation of water and the reduction of silver ions were first written separately. Ensuring that the number of electrons lost in the oxidation half-reaction equals the number gained in the reduction half-reaction is key to balancing. If these do not match, as in the exercise, the reduction half-reaction is multiplied accordingly. The balanced overall chemical equation then combines the half-reactions, thoroughly representing the redox process that occurs.

Half-Reactions

Half-reactions are the separate consideration of the oxidation and reduction processes that occur in a redox reaction. Each half-reaction displays the change in oxidation state for the species involved and the corresponding electrons gained or lost.

In the context of oxidation, water is transformed into oxygen gas, represented by the equation: \(2H_{2}O_{(l)} \to O_{2(g)} + 4H^{+}_{(aq)} + 4e^{-}\). Conversely, the reduction half-reaction shows the reduction of silver(II) to silver(I): \(Ag^{2+}_{(aq)} + e^{-} \to Ag^{+}_{(aq)}\). These half-reactions are essential in determining how the overall redox reaction is balanced and are crucial for understanding the movement of electrons that characterize redox processes.