1. A] Define Single Electrode Potential. Derive Nernst equation for single electrode potential.
Answer:
SINGLE ELECTRODE POTENTIAL: “Single electrode potential is defined as the potential generated when the metal is dipped in the solution consisting of its own ions, at the interphase between solution and metal”
NERNST EQUATION:
Nernst equation is a thermodynamic equation which relates the cell potential with concentrations Mn+ using standard free energy equation.
The decrease in free energy change (-∆G) is given by the maximum amount of work done by an electrochemical cell.−∆𝐺=𝑊𝑚𝑎𝑥−−−→1
The maximum work done by the electrochemical cell depends on, Number of coulombs that flow and the energy available per coulomb.
𝑊𝑚𝑎𝑥=𝑁𝑜 𝑜𝑓 𝑐𝑜𝑙𝑜𝑚𝑏𝑠 𝑋 𝐸𝑛𝑒𝑟𝑔𝑦 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑝𝑒𝑟 𝐶𝑜𝑢𝑙𝑜𝑚𝑏
The number of coulombs that flow is equal to the number of moles of electrons (n) and the faraday(F).
∴𝑁𝑜 𝑜𝑓 𝑐𝑜𝑢𝑙𝑜𝑚𝑏𝑠 = 𝑛𝐹
Energy available per coulomb is the emf of the cell E. The maximum work done for an electrochemical cell is given by
𝑊𝑚𝑎𝑥=𝑛𝐹𝑋𝐸——-2
Substituting equation 2, in 1 we have,
∆𝑮=−𝒏𝑭𝑬−−−→3
When the concentrations of all species is unity at 250C the standard free energy change ∆𝐺0 is given as
∆𝑮𝟎=−𝒏𝑭𝑬𝟎−−−→4
Where E0 is the standard electrode potential
“Standard electrode potential is the potential when a metal is dipped in 1M solution of its ions or when an inert electrode is in contact with a gas at temperature at 298K”
Consider a red-ox reaction involved in an electrochemical cell,
The equilibrium constant Kc is given by change in free energy by the equation,
∆𝐺=∆𝐺0+𝑅𝑇𝑙𝑛𝐾𝑐 𝑤ℎ𝑒𝑟𝑒 𝐾𝑐=[𝑀][𝑀𝑛+]
Therefore, the above equation becomes,
Substituting equations 3 and 4 in equation 5 we have,
−𝑛𝐹𝐸 = −𝑛𝐹𝐸0 + 𝑅𝑇𝑙𝑛[𝑀] − 𝑅𝑇𝑙𝑛[𝑀𝑛+]
Dividing throughout by –nF, and under standard conditions M=1. Hence the above equation becomes,
Nernst equation at 298K and converting natural log to the base 10 is,
