   Chapter 18, Problem 76E

Chapter
Section
Textbook Problem

# Calculate ΔG° and K at 25°C for the reactions in Exercises 38 and 42.

(a)

Interpretation Introduction

Interpretation: The standard Gibbs free energy (ΔGο) and the value of equilibrium constant (K) for the given reactions are to be calculated at 25 οC .

Concept introduction: 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. Equilibrium constant is defined as the ratio of the concentration of products and the concentration of the reactants.

To determine: The standard Gibbs free energy (ΔGο) and the value of equilibrium constant (K) for the given reaction at 25 οC .

Explanation

Explanation

Given

The half cell reactions for the cell are,

Anode: Fe2+(aq)Fe3+(aq)+e               Eanodeο=0.77V (1)

Cathode: 4IO3(aq)+12H+(aq)+10eI2(aq)+6H2O(l)   Ecathodeο=1.20 V (2)

Where,

• Eanodeο is the standard electrode potential of equation (1).
• Ecathodeο is the standard electrode potential of equation (2).

The overall cell reaction is,

10Fe+2(aq)+ 4IO3(aq)+12H+(aq)10Fe3+(aq)+I2(aq)+6H2O(l) (3)

The standard electrode potential of equation (3) is calculated by the formula,

Ecellο=EcathodeοEanodeο

Where,

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

Substitute the values of Ecathodeο and Eanodeο in the above formula.

Ecellο=1.20 V0.77 V=0.43 V

The standard cell potential of the given cell is 0.43 V .

The reaction between ΔGrxnο and Ecellο is given as,

ΔGcellο=nFEcellο

Where,

• n is the number of electrons involved in the cell reaction.
• F is the faradays constant (96500 C)

(b)

Interpretation Introduction

Interpretation: The standard Gibbs free energy (ΔGο) and the value of equilibrium constant (K) for the given reactions are to be calculated at 25 οC .

Concept introduction: 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. Equilibrium constant is defined as the ratio of the concentration of products and the concentration of the reactants.

To determine: The standard Gibbs free energy (ΔGο) and the value of equilibrium constant (K) for the given reaction at 25 οC .

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