electrochemistry-and-the-redox-potential- 1.--nernst
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Electrochemistry and the Redox Potential R. Corn -‐ -‐ Chem M3LC 1. Nernst Equation for reduction-‐oxidation (Redox) reactions For example, consider the reaction: 𝐹𝑒!! + 𝐶𝑒!! → 𝐹𝑒!! + 𝐶𝑒!! ∆𝐺 = −𝑛𝐹𝐸!"## ∆𝐺 = ∆𝐺! + 𝑅𝑇𝑙𝑛𝑄 These two equations are combined to become the Nernst Equation:
𝐸!"## = 𝐸!"##! −𝑅𝑇𝑛𝐹 𝑙𝑛𝑄
where ∆𝐺! = −𝑛𝐹𝐸!"##! The cell potential is related to the ∆G of the reaction. 2. Half Cell Reactions and the Redox Potential The cell potential can be calculated from the difference between two Half Cell Potentials: 𝐹𝑒!! + 𝑒 → 𝐹𝑒!! 𝐶𝑒!! + 𝑒 → 𝐶𝑒!! 𝐸!" = 𝐸!"! − !"
!𝑙𝑛 !"!!
!"!! 𝐸!" = 𝐸!"! − !"
!𝑙𝑛 !!!!
!"!!
𝐸!"## = 𝐸!" − 𝐸!" Half Cells are written as reductions. The E0s are tabulated based on the normal hydrogen electrode (NHE) scale, which defines 𝐸!! as zero:
𝐻! + 𝑒 → !!𝐻!(!) 𝐸! = 𝐸!! +
!"!𝑙𝑛 !!!
!/!
!! 𝐸!! = 0
𝐸!" is called the Half Cell Potential, or the Redox Potential for the Fe2+/ Fe3+ couple. The Redox Potential can be measured in any aqueous system, and sets the
concentration ratios of ALL of the redox species in the solution.
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3. Electrochemical Alpha Fractions
The total concentration of Fe in a solution is given by 𝐶!"!"!: 𝐶!"!"! = 𝐹𝑒!! + 𝐹𝑒!! This concentration is divided into the oxidized and reduced forms. The fraction of
the total Fe in each form is called the alpha fraction:
𝛼!"!! =
!"!!
!!"!"! 𝛼!"!! =
!"!!
!!"!"! 𝛼!"!! + 𝛼!"!! = 1
Using the Fe half cell reaction, we can derive equations for the two alpha fractions
that depend on the value of 𝐸!":
𝛼!"!! = 1+ 𝑒𝑥𝑝𝐹𝑅𝑇 𝐸!" − 𝐸!"!
!!
𝛼!"!! = 1+ 𝑒𝑥𝑝 −𝐹𝑅𝑇 𝐸!" − 𝐸!"!
!!