Chapter 18, Problem 18.89QP

Interpretation Introduction

Interpretation:

The equilibrium constant for the given reaction has to be calculated.

Concept Introduction:

Free energy (Gibbs free energy) is the term that is used to explain the total energy content in a thermodynamic system that can be converted into work.  The free energy is represented by the letter $\text{G}$.  All spontaneous process is associated with the decrease of free energy in the system.  The standard free energy change ${\text{(ΔG}}^{\text{°}}{}_{\text{rxn}})$ is the difference in free energy of the reactants and products in their standard state.

${\text{ΔG}}^{\text{°}}{}_{\text{rxn}}\text{=}\sum {\text{nΔG}}_{\text{f}}{}^{\text{°}}\text{(Products)-}\sum {\text{nΔG}}_{\text{f}}{}^{\text{°}}\text{(Reactants)}$

Where,

$\text{n}$ is the number of moles

The standard electrode potential of a cell ${\text{(E}}^{°}{}_{\text{cell}})$ is the difference in electrode potential of the cathode and anode.

${\text{E}}^{\text{°}}{}_{\text{cell}}={\text{E}}^{\text{°}}{}_{\text{cathode}}-{\text{E}}^{\text{°}}{}_{\text{anode}}$

The relation between Gibbs free energy and cell potential: The amount of energy in a system that can be converted into useful energy is defined as free energy in thermodynamics.

Free energy and the cell potential is related by the given equation.

$\text{ΔG=-nFE}$

Where,

$\text{ΔG}$ is the change in free energy

$\text{n}$ is the number of electrons transferred

$\text{F}$ is the Faraday constant $\text{(F}={\text{96500Cmol}}^{\text{-1}})$

$\text{E}$ is the cell potential

The relation between Gibbs free energy and equilibrium constant: Free energy and equilibrium constant are related by the given equation.

$\text{ΔG=-RTlnK}$

Where,

$\text{ΔG}$ is the change in free energy

$\text{R}$ is the universal gas constant $\text{(R=0}{\text{.0821LatmK}}^{\text{-1}}{\text{mol}}^{\text{-1}})$

$\text{T}$ is the temperature

$K$ is the equilibrium constant