Nernst Equation

The Nernst equation is used to calculate the voltage of an electrochemical cell or to find the concentration of one of the components of the cell. 

For the reaction

aA + bB → cC + dD

Reaction Quotient

And ΔG = ΔG° + 2.303 RTlogQ

ΔG° = - nFE°_cell

ΔG = - nFE_cell

E_cell = E°_cell - (2.303RT/nF) logQ

Note:

⇒ n is the number of Moles of electrons exchanged

⇒ F is the Faraday constant (96,500 C/mol), and

⇒ E is potential difference.

For example: [Daniel-cell]

Zn(s) + Cu²⁺_(aq) → Cu_(s) + Zn²⁺_(aq)

E_cell = E°_cell - (0.0591/2) log [Zn²⁺]/ [Cu²⁺]

Nernst equation can be used to determine electrode potential of a half cell

a. Zn|Zn²⁺_(aq)

Zn_(s) → Zn²⁺_(aq) + 2e¯, Q = [Zn²⁺]

E_Zn|Zn²⁺ = E°_Zn|Zn²⁺ - (0.0591/2) log [Zn²⁺]

b. Cu²⁺_(aq)|Cu

Cu²⁺_(aq) + 2e¯ → Cu_(s), Q = 1/ [Cu²⁺]

E_Cu²⁺|Cu = E°_Cu²⁺|Cu - (0.0591/2) log 1/ [Cu²⁺]

At equilibrium Q = K_eq and E_cell = 0, E°_cell = (0.0591/η) logK_eq