Chapter 18.4, Problem 2RCF

Interpretation Introduction

Interpretation:

The Gibb’s free energy for following cell reaction has to be calculated.

Concept introduction:

Standard reduction potential: The voltage associated with a reduction reaction at an electrode when all solutes are 1M and all gases are at 1 atm. The hydrogen electrode is called the standard hydrogen electrode (SHE).

Standard emf: ${\text{E}}_{cell}^0$ is composed of a contribution from the anode and a contribution from the cathode is given by,

$E_{cell}^o=E_{cathode}^o-E_{anode}^o$

Where both $E_{cathode}^o$ and $E_{anode}^o$ are the standard reduction potentials of the electrodes.

Thermodynamics of redox reactions:

The change in free-energy represents the maximum amount of useful work that can be obtained in a reaction: $\Delta {\text{G}}^0\text{=}{\text{-nFE}}_{cell}^0$

Relation between ${\text{E}}_{cell}^0$ and equilibrium constant (K) of a redox reaction:

$\begin{array}{l}{\text{E}}_{\text{cell}}^{\text{0}}\text{=}\frac{\text{RT}}{\text{nF}}\text{lnK}\\ \text{where}\text{R}\text{is}\text{gas}\text{constant}\left(\text{8}\text{.314}\text{J/K}\text{.mol}\right)\\ \text{T}\text{is}\text{Temperature}\text{in}\text{Kelvin}\\ \text{n}\text{is}\text{no}\text{.of}\text{electrons}\text{transferred}\text{in}\text{redox}\text{reaction}\\ \text{F}\text{is}\text{Faraday}\text{constant}\left(\text{96500}\text{J/V}\text{.mol}\right)\\ \text{K}\text{is}\text{equilibrium}\text{constant}\\ \end{array}$

Relation between $\Delta {\text{G}}^0$ and K:$\Delta {\text{G}}^0\text{=}\text{-}RT\ln K$