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The Nernst Equation

Key Concepts

  • The Nernst Equation allows us to calculate the voltage produced by any electrochemical cell given Eo values for its electrodes and the concentrations of reactants and products.

  • The general Nernst Equation: E = Eo -(RT/nF)lnQ
          Eo = standard electrochemical cell potential (voltage)
          R = ideal gas constant
          T = temperature
          n = moles of electrons
          F = Faraday constant = 96,485 C mol-1
          Q = mass-action expression (approximated by the equilibrium expression)

  • At 25oC the Nernst Equation is simplified to: E = Eo -(0.0592/n)logQ
          Eo = standard electrochemical cell potential (voltage)
          n = moles of electrons
          Q = mass-action expression (approximated by the equilibrium expression)

  • For a system at equilibrium at 25oC, E = 0 and the Nernst Equation is simplified to:
          Eo = (0.0592/n)logK
          Eo = standard electrochemical cell potential (voltage)
          n = moles of electrons
          K = equilibrium expression

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Example of E Calculation

Calculate the voltage produced by the cell Sn(s)|Sn2+||Ag+|Ag(s) at 25oC given:
[Sn2+] = 0.15 M
[Ag+] = 1.7 M
  1. Write the Nernst Equation for 25oC:
    E = Eo -0.0592/n x logQ

  2. Calculate Eo for the cell:
    anode: Sn(s) Sn2+ + 2e Eo = +0.14V
    cathode: 2x [e- + Ag+ Ag(s)] Eo = +0.80V

    cell: Sn(s) + 2Ag+ Sn2+ + 2Ag(s) Eo = +0.94V

  3. Wite the expression for Q:
    Q = [Sn2+]/[Ag+]2
    (concentrations of solids = 1)

  4. Write the Nernst Equation for this example:
    E = Eo -0.0592/n x log([Sn2+]/[Ag+]2)

  5. Substitute the values:
    Eo = +0.94V
    n = 2 (2 moles of electrons transferred during the redox reaction)
    [Sn2+] = 0.15 M
    [Ag+] = 1.7 M

    E = +0.94 -0.0592/2 x log([0.15]/[1.7]2)

  6. Calculate Q:
    E = +0.94 -0.0592/2 x log[0.0519]

  7. Calculate logQ:
    E = +0.94 -0.0592/2 x -1.285

  8. Calculate E:
    E = +0.94 -0.0592/2 x -1.285
    E = +0.98V
E > Eo, and positive, so the cell reaction has a greater tendency to take place at these concentrations.

Example of K Calculation

Calculate the equilibrium constant, K, for the reaction Sn(s)|Sn2+||Ag+|Ag(s) at 25oC.
  1. Write the Nernst Equation: E = Eo -(0.0592/n)logQ
    At equilibrium Q = K and E = 0

  2. Write the Nernst Equation for the equilibrium expression: Eo = (0.0592/n)logK

  3. Calculate Eo for the equation (as above) = +0.94

  4. Calculate n (moles of electrons transferred) =2

  5. Substitute Eo and n into the equation:
    +0.94 = (0.0592/2)logK

  6. Calculate logK:
    +0.94 = 0.0296logK
    logK = 31.76

  7. Calculate K:
    K = 1031.76 = 5.71 x 1031


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