Chapter 19, Problem 19.64QP

Interpretation Introduction

Interpretation:

Cell voltage of a given concentration cell has to be calculated.

Concept introduction:

Effect of concentration on cell Emf:

The mathematical relationship between the emf of galvanic cell and the concentration of reactants and products in a redox reaction under nonstandard-state conditions is,

$\begin{array}{l}\text{ΔG}\text{=}{\text{ΔG}}^{\text{0}}\text{+}\text{RTlnQ}\\ {\text{where, ΔG}}^{\text{0}}\text{is}\text{standard}\text{Gibb's}\text{free}\text{energy}\\ \text{ Q}\text{is}\text{reaction}\text{quotient}\text{.}\end{array}$

As known $\Delta {\text{G}}^0\text{=}{\text{-nFE}}_{cell}^0$ and $\Delta \text{G}\text{=}{\text{-nFE}}_{cell}^{}$, above expression can be written as,

$\begin{array}{l}\text{ΔG}\text{=}{\text{ΔG}}^{\text{0}}\text{+}\text{RTlnQ}\\ {\text{-nFE}}_{cell}\text{=}{\text{-nFE}}_{cell}^0\text{+}\text{RTlnQ}\end{array}$

Dividing by –nF, the above equation becomes,

$\begin{array}{l}\frac{{\text{-nFE}}_{cell}}{-nF}\text{=}\frac{{\text{-nFE}}_{cell}^0}{-nF}\text{+}\frac{\text{RTlnQ}}{-nF}\\ \\ {\text{E}}_{cell}\text{=}{\text{E}}_{cell}^0-\frac{\text{RT}}{nF}\text{lnQ}\to \text{Nernst equation}\end{array}$

Nernst equation: The Nernst equation is used to calculate the cell voltage under nonstandard-state conditions.

Concentration cell:

Possibility of constructing a galvanic cell from two half-cells composed of the same material but differing in ion concentration because electrode potential depends on ion concentrations.

Reduction occurs in the more concentrated compartment and oxidation should take place on the more dilute side. As the concentrations of the ions in the two compartments are the same, E becomes zero, and no further change occurs. The standard emf ${\text{E}}_{\text{cell}}^{\text{0}}$ is zero because the same electrode and the same type of ions are involved.

The Nernst equation becomes,

${\text{E}}_{cell}\text{=}0-\frac{\text{RT}}{nF}\text{ln}\frac{{\left[X\right]}_{dil}}{{\left[X\right]}_{conc}}$