Chapter 6, Problem 6C.3BE

(i)

Interpretation Introduction

Interpretation: The Nernst equation for the reaction has to be written.

Concept introduction: The Nernst equation gives the relationship between the standard electrode potential and the electrode potential for a given cell at given concentrations and temperature.  The formula for Nernst equation is,

    $E_{\text{cell}}=E_{\text{cell}}^{\text{ο}}-\frac{RT}{nF}\ln \text{Q}$

Where,

• $n$ is the number of electrons
• $T$ is the temperature
• $\text{Q}$ is the reaction quotient
• $F$ is the Faraday constant.
• $E_{\text{cell}}^{\text{ο}}$ is the standard cell potential.
• $E$ is the cell potential at given conditions.

(ii)

Interpretation Introduction

Interpretation: The value of ${\Delta }_{\text{r}}G$ for the cell reaction has to be calculated.

Concept introduction: The Gibbs free energy is related to the electrode potential of the cell by the expression,

    ${\Delta }_{\text{r}}G=-nF{E}_{\text{cell}}$

Where,

• $n$ is the number of electrons.
• $F$ is the Faraday’s constant.
• $E_{\text{cell}}$ is the standard cell potential.

(iii)

Interpretation Introduction

Interpretation: The value of $E_{\text{cell}}^{\text{ο}}$ has to be calculated.

Concept introduction: To determine the activity coefficient of an ion in a dilute solution of known ionic strength, the Debye-Hückel limiting law is used.  The expression for the Debye-Hückel limiting law is,

    $\log {\gamma }_{\pm }=-A\left|z_{+}{z}_{-}\right|I^{1/2}$

The value of $A$ is $0.509$.

Where,

• $I$ is the ionic strength.
• $z_{+}$ and $z_{-}$ are the charges for the cation and anion, respectively.
• $A$ is the constant.
• ${\gamma }_{\pm }$ is the mean ionic coefficient.