Chapter 19, Problem 19.103QP

(a)

Interpretation Introduction

Interpretation:

The half-cell reactions and the overall reactions in the given cell has to be calculated.

Concept Introduction:

Nernst equation is one of the important equation in electrochemistry.  In Nernst equation the electrode potential of a cell reaction is related to the standard electrode potential, concentration or activities of the species that is involved in the chemical reaction and temperature.

  ${\text{E}}_{\text{cell}}{\text{=E}}^{\text{°}}{}_{\text{cell}}\text{-}\frac{\text{RT}}{\text{2}\text{.303nF}}\text{log}\frac{\left[\text{Red}\right]}{\left[\text{Oxd}\right]}$

Where,

  ${\text{E}}_{\text{cell}}$ is the potential of the cell at a given temperature

  ${\text{E}}^{\text{°}}{}_{\text{cell}}$ is the standard electrode potential

  $\text{R}$ is the universal gas constant $\text{(R=8}{\text{.314JK}}^{\text{-1}}{\text{mol}}^{\text{-1}})$

  $\text{T}$ is the temperature

   n is the number of electrons involved in a reaction

  $\text{F}$ is the Faraday constant $\text{(F=9}\text{.64853399}\times {\text{10}}^4{\text{Cmol}}^{\text{-1}})$

  $\left[\text{Red}\right]$ is the concentration of the reduced species

  $\left[\text{Oxd}\right]$ is the concentration of the oxidised species

At room temperature $({\text{25}}^{\text{°}}\text{C})$, after substituting the values of all the constants the equation can be written as

  ${\text{E}}_{\text{cell}}{\text{= E}}^{\text{°}}{}_{\text{cell}}\text{-}\frac{0.0591}{\text{n}}\text{log}\frac{\left[\text{Red}\right]}{\left[\text{Oxd}\right]}$

The relation between electrode potential and equilibrium constant: cell potential and equilibrium constant are related by the given equation.

  ${\text{E}}^{°}{}_{\text{cell}}\text{=}\frac{\text{RT}}{\text{nF}}\text{lnK}$

Where,

  ${\text{E}}^{°}{}_{\text{cell}}$ is the standard electrode potential

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

  $\text{K}$ is the formation constant

  $\text{R}$ is the universal gas constant $\text{(R=8}{\text{.314JK}}^{\text{-1}}{\text{mol}}^{\text{-1}})$

  $\text{T}$ is the temperature

  $\text{F}$ is the Faraday constant $\text{(F=9}\text{.64853399}\times {\text{10}}^4{\text{Cmol}}^{\text{-1}})$

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

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

(b)

Interpretation Introduction

Interpretation:

The equilibrium constant for the reaction has to be calculated in accordance with the given conditions.

Concept Introduction:

Nernst equation is one of the important equation in electrochemistry.  In Nernst equation the electrode potential of a cell reaction is related to the standard electrode potential, concentration or activities of the species that is involved in the chemical reaction and temperature.

  ${\text{E}}_{\text{cell}}{\text{=E}}^{\text{°}}{}_{\text{cell}}\text{-}\frac{\text{RT}}{\text{2}\text{.303nF}}\text{log}\frac{\left[\text{Red}\right]}{\left[\text{Oxd}\right]}$

Where,

  ${\text{E}}_{\text{cell}}$ is the potential of the cell at a given temperature

  ${\text{E}}^{\text{°}}{}_{\text{cell}}$ is the standard electrode potential

  $\text{R}$ is the universal gas constant $\text{(R=8}{\text{.314JK}}^{\text{-1}}{\text{mol}}^{\text{-1}})$

  $\text{T}$ is the temperature

  $\text{n}$ is the number of electrons involved in a reaction

  $\text{F}$ is the Faraday constant $\text{(F=9}\text{.64853399}\times {\text{10}}^4{\text{Cmol}}^{\text{-1}})$

  $\left[\text{Red}\right]$ is the concentration of the reduced species

  $\left[\text{Oxd}\right]$ is the concentration of the oxidised species

At room temperature $({\text{25}}^{\text{°}}\text{C})$, after substituting the values of all the constants the equation can be written as

  ${\text{E}}_{\text{cell}}{\text{= E}}^{\text{°}}{}_{\text{cell}}\text{-}\frac{0.0591}{\text{n}}\text{log}\frac{\left[\text{Red}\right]}{\left[\text{Oxd}\right]}$

The relation between electrode potential and equilibrium constant: cell potential and equilibrium constant are related by the given equation.

  ${\text{E}}^{°}{}_{\text{cell}}\text{=}\frac{\text{RT}}{\text{nF}}\text{lnK}$

Where,

  ${\text{E}}^{°}{}_{\text{cell}}$ is the standard electrode potential

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

  $\text{K}$ is the formation constant

  $\text{R}$ is the universal gas constant $\text{(R=8}{\text{.314JK}}^{\text{-1}}{\text{mol}}^{\text{-1}})$

  $\text{T}$ is the temperature

  $\text{F}$ is the Faraday constant $\text{(F=9}\text{.64853399}\times {\text{10}}^4{\text{Cmol}}^{\text{-1}})$

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

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

(c)

Interpretation Introduction

Interpretation:

The cell potential has to be calculated in accordance with the given conditions.

Concept Introduction:

Nernst equation is one of the important equation in electrochemistry.  In Nernst equation the electrode potential of a cell reaction is related to the standard electrode potential, concentration or activities of the species that is involved in the chemical reaction and temperature.

  ${\text{E}}_{\text{cell}}{\text{=E}}^{\text{°}}{}_{\text{cell}}\text{-}\frac{\text{RT}}{\text{2}\text{.303nF}}\text{log}\frac{\left[\text{Red}\right]}{\left[\text{Oxd}\right]}$

Where,

  ${\text{E}}_{\text{cell}}$ is the potential of the cell at a given temperature

  ${\text{E}}^{\text{°}}{}_{\text{cell}}$ is the standard electrode potential

  $\text{R}$ is the universal gas constant $\text{(R=8}{\text{.314JK}}^{\text{-1}}{\text{mol}}^{\text{-1}})$

  $\text{T}$ is the temperature

  $\text{n}$ is the number of electrons involved in a reaction

  F isthe Faraday constant $\text{(F=9}\text{.64853399}\times {\text{10}}^4{\text{Cmol}}^{\text{-1}})$

  $\left[\text{Red}\right]$ is the concentration of the reduced species

  $\left[\text{Oxd}\right]$ is the concentration of the oxidised species

At room temperature $({\text{25}}^{\text{°}}\text{C})$, after substituting the values of all the constants the equation can be written as

  ${\text{E}}_{\text{cell}}{\text{= E}}^{\text{°}}{}_{\text{cell}}\text{-}\frac{0.0591}{\text{n}}\text{log}\frac{\left[\text{Red}\right]}{\left[\text{Oxd}\right]}$

The relation between electrode potential and equilibrium constant: cell potential and equilibrium constant are related by the given equation.

  ${\text{E}}^{°}{}_{\text{cell}}\text{=}\frac{\text{RT}}{\text{nF}}\text{lnK}$

Where,

  ${\text{E}}^{°}{}_{\text{cell}}$ is the standard electrode potential

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

  $\text{K}$ is the formation constant

  $\text{R}$ is the universal gas constant $\text{(R=8}{\text{.314JK}}^{\text{-1}}{\text{mol}}^{\text{-1}})$

  $\text{T}$ is the temperature

  $\text{F}$ is the Faraday constant $\text{(F=9}\text{.64853399}\times {\text{10}}^4{\text{Cmol}}^{\text{-1}})$

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

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