L2 - Nernst Equation

objectives

Understandings

• When Eº is positive, ΔGº is negative indicative of a spontaneous process.
• When Eº is negative, ΔGº is positive indicative of a non-spontaneous process. When Eº is 0, then ΔGº is 0.
• ΔG = -nFE^o

Applications and Skills

• Determination of standard free-energy changes (∆Go) using standard electrode potentials.

Linking Electrochemistry to Gibbs Free Energy

• We will now extend electrochemistry by determining the relationship between Ecell∘and the thermodynamics quantities such as ΔG° (Gibbs free energy) and K (the equilibrium constant).
• In galvanic cells, chemical energy is converted into electrical energy, which can do work.
• The electrical work is the product of the charge transferred multiplied by the potential difference (voltage):

• The charge on 1 mole of electrons is given by Faraday’s constant (F)

• In this equation, n is the number of moles of electrons for the balanced oxidation-reduction reaction.
• The measured cell potential is the maximum potential the cell can produce and is related to the electrical work (wele) by

• The negative sign for the work indicates that the electrical work is done by the system (the galvanic cell) on the surroundings.
• In Thermodynamics The free energy was defined as the energy that was available to do work.
• In particular, the change in free energy was defined in terms of the maximum work (wmax), which, for electrochemical systems, is wele.

• We can verify the signs are correct when we realize that n and F are positive constants and that galvanic cells, which have positive cell potentials, involve spontaneous reactions.
• Thus, spontaneous reactions, which have ΔG < 0, must have Ecell > 0. If all the reactants and products are in their standard states, this becomes: