   # The following standard reduction potentials have been determined for the aqueous chemistry of indium: a. What is the equilibrium constant for the disproportionation reaction, where a species is both oxidized and reduced, shown below? 3 In + ( a q ) → 2 In ( s ) + In 3 + ( a q ) b. What is Δ G f ∘ for In + (aq) if Δ G f ∘ = −97.9 kJ/mol for In 3+ ( aq )? ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 17, Problem 155IP
Textbook Problem
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## The following standard reduction potentials have been determined for the aqueous chemistry of indium: a. What is the equilibrium constant for the disproportionation reaction, where a species is both oxidized and reduced, shown below? 3 In + ( a q ) → 2 In ( s ) + In 3 + ( a q ) b. What is Δ G f ∘ for In+(aq) if Δ G f ∘ = −97.9 kJ/mol for In3+(aq)?

(a)

Interpretation Introduction

Interpretation: The equilibrium constant for the given disproportionation reaction and the standard Gibbs free energy of formation ΔGfο are to be calculated.

Concept introduction: Equilibrium constant is defined as the ratio of the concentration of products and the concentration of the reactants and Gibbs free energy is a thermodynamic quantity that is used to calculate the maximum work of reversible reaction performed by a system. It is equal to the difference between the enthalpy and the product of entropy at absolute temperature.

To determine: The equilibrium constant for the given disproportionation reaction.

### Explanation of Solution

Explanation

The equilibrium constant for the given disproportionation reaction is K=5.77×1010_ .

Given

The half cell reactions for the cell are,

In3+(aq)+2eIn+(aq)                      E1ο=0.444 V (1)

In+(aq)+eIn(s)                           E2ο=0.126 V (2)

Where,

• E1ο is the standard electrode potential of equation (1).
• E2ο is the standard electrode potential of equation (2).

The balanced cell reaction obtained by reversing reaction (1) and then multiplying reaction (1) by 3 and reaction (2) by 2 is,

3In3+(aq)+3e3In+(aq)                      E2ο=0.126 V (3)

2In+(aq)2In(s)+2e                         E1ο=0.444 V (4)

The overall cell reaction is,

3In+(aq)+e2In(s)+In3+(aq) (5)

The standard electrode potential of equation (5) is calculated by the formula,

Ecellο=E2οE1ο

Where,

• Ecellο is the standard electrode potential of equation (3).

Substitute the values of E1ο and E2ο in the above formula

(b)

Interpretation Introduction

Interpretation: The equilibrium constant for the given disproportionation reaction and the standard Gibbs free energy of formation ΔGfο are to be calculated.

Concept introduction: Equilibrium constant is defined as the ratio of the concentration of products and the concentration of the reactants and Gibbs free energy is a thermodynamic quantity that is used to calculate the maximum work of reversible reaction performed by a system. It is equal to the difference between the enthalpy and the product of entropy at absolute temperature.

To determine: The standard Gibbs free energy of formation ΔGfο for the given disproportionation reaction.

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