We've said that the +1 oxidation state is uncommon for indium but is the most stable state for thallium. Verify this statement by calculating E ° and ΔG ° (in kilojoules) for the disproportionation reaction
3 M+1aq2S M3+1aq2 + 2 M1s2 M = In or Tl
Is disproportionation a spontaneous reaction for In+ and/orTl+? Standard reduction potentials for the relevant halfreactions are
In3+1aq2 + 2 e- S In+1aq2 E° = -0.44 V
In+1aq2 + e- S In1s2 E° = -0.14 V
Tl3+1aq2 + 2 e- S Tl+1aq2 E° = +1.25 V
Tl+1aq2 + e- S Tl1s2 E° = -0.34 V

Verified step by step guidance

1. Identify the disproportionation reaction: 3 M^{+1}_{(aq)} \rightarrow M^{3+}_{(aq)} + 2 M_{(s)}.
2. Write the half-reactions for the disproportionation: \text{Oxidation: } M^{+1}_{(aq)} \rightarrow M^{3+}_{(aq)} + 2e^- and \text{Reduction: } M^{+1}_{(aq)} + e^- \rightarrow M_{(s)}.
3. Calculate the standard cell potential (E^\circ_{cell}) for the disproportionation reaction using E^\circ_{cell} = E^\circ_{reduction} - E^\circ_{oxidation}.
4. Use the Nernst equation to calculate \Delta G^\circ: \Delta G^\circ = -nFE^\circ_{cell}, where n is the number of moles of electrons transferred and F is the Faraday constant.
5. Determine if the reaction is spontaneous by checking if \Delta G^\circ is negative. If \Delta G^\circ < 0, the reaction is spontaneous.

Key Concepts

Oxidation States

Oxidation states indicate the degree of oxidation of an atom in a compound, reflecting the number of electrons lost or gained. For indium (In) and thallium (Tl), the +1 oxidation state is less stable for In due to its position in the periodic table, while it is more stable for Tl. Understanding these oxidation states is crucial for predicting the behavior of these elements in redox reactions.

Disproportionation Reaction

A disproportionation reaction is a specific type of redox reaction where a single substance is simultaneously oxidized and reduced, resulting in two different products. In this case, the +1 oxidation state of In or Tl is being analyzed for its stability and tendency to undergo disproportionation. Evaluating the spontaneity of this reaction involves calculating the standard cell potential and Gibbs free energy change.

Standard Reduction Potentials

Standard reduction potentials (E°) quantify the tendency of a chemical species to gain electrons and be reduced. These values are essential for determining the feasibility of redox reactions, including disproportionation. By comparing the E° values for the relevant half-reactions of In and Tl, one can assess whether the overall reaction is spontaneous, which is indicated by a positive cell potential.