Chapter 19, Problem 19.25QP

Interpretation Introduction

Interpretation: The spontaneous reaction occurs among the given ions at standard state conditions should be determined. Also the values of ${\text{ΔG}}^0$ and ${\text{K}}_{\text{c}}$ in the reaction should be calculated.

Concept introduction:

• The substance that easily be reduced in a reaction is represented as an oxidizing agent. For metal cations, a good oxidizing agent can be determined by the standard reduction potential values.
• Half-cell: In the electrochemical cell, both oxidation and reduction occurs. Oxidation occurs at the anode and reduction occurs at the cathode
• Standard electrode potential of cell is defined as the difference of reduction potential at cathode to the reduction potential at anode.
• For the cathode and anode reactions, the values are taken from the standard reduction potential table. The standard cell potential is calculated by taking the difference between the standard reduction potential values of the cathode and anode.

${\text{E}}_{\text{cell}}^{\text{0}}={\text{E}}_{\text{cathode}}^{\text{0}}-{\text{E}}_{\text{anode}}^{\text{0}}$

• $\begin{array}{c}{\text{ΔG}}^0\text{=}-{\text{nFE}}_{\text{cell}}^{\text{0}}\\ {\text{ΔG}}^0=\text{Standard}\text{free}\text{energy change}\\ {\text{E}}_{\text{cell}}^{\text{0}}\text{=}\text{Standard}\text{electrochemical}\text{cell}\text{potential}\\ \text{F}\text{=}\text{Faraday}\text{constant}\\ \text{n}\text{=}\text{number}\text{of}\text{electrons}\text{passed}\text{from}\text{anode}\text{to}\text{cathode}\end{array}$
• $\begin{array}{c}\text{log}\text{K}\text{=}\frac{{\text{nE}}_{\text{cell}}^{\text{0}}}{\text{0}\text{.0592}\text{V}}\\ \text{K}\text{=}\text{equilibrium}\text{constant}\end{array}$

To determine: The spontaneous reaction occur among the given ions at standard state conditions and the values ${\text{ΔG}}^0$ and ${\text{K}}_{\text{c}}$ of the reaction.