Gibbs Energy & Standard Cell Potential (HL) (HL IB Chemistry)

• Previously we have seen the concept and term free energy, ΔG^θ
  • Free energy is a measure of the available energy to do useful work and takes into account the entropy change, ΔS^θ, as well as the enthalpy change of a reaction, ΔH^θ
• For reactions to be spontaneous, the free energy change must be negative
• We have also seen that to calculate a cell potential using standard electrode potentials we use the expression:

EMF = E_RHS – E_LHS

• This is not an arbitrary arrangement of the terms
• The convention of placing the half cell with the greatest negative potential on the left of the cell diagram ensures that you will always get a positive reading on the voltmeter, corresponding to the spontaneous reaction
  • If you have done an experiment on measuring electrode potentials, you have probably been told to 'swap the terminals if you don't get a positive reading on the voltmeter'

• In electrochemical cells, a spontaneous reaction occurs when the combination of half cells produces a positive voltage through the voltmeter, i.e. the more negative electrode pushes electrons onto the more positive electrode
• It doesn't really matter if you are using a digital multimeter as a voltmeter as you will still get a reading (with the wrong sign), but analogue voltmeters will only work if the terminals are correctly connected to the positive and negative half cells
• This should give you an insight into why the following statements are true:

If ΔE^θ is positive, the reaction is spontaneous as written

If ΔE^θ is negative, the forward reaction is non-spontaneous but the reverse reaction will be spontaneous

• You should now be able to see that there is a link between  ΔG^θ and E^θ
• This relationship is the equation:

ΔG^θ = -nFE^θ

• • Where:
    • n = number of electrons transferred
    • F = the Faraday constant, 96 500 C mol^-1

• When a reaction has reached equilibrium, there is no free energy change so ΔG^θ  is zero and it follows that E^θ must also be zero
• This is effectively what happens when the reactants in a voltaic cell have been exhausted and there is no longer any push of electrons from one half-cell to the other

• The three conditions of free energy and electrode potential are summarised below

Summary table of the conditions of free energy and electrode potential

Free energy change	Standard electrode potential	Reaction
ΔGθ = -ve	Eθ = +ve	The reaction is spontaneous
ΔGθ = +ve	Eθ = -ve	This reaction is non-spontaneous
ΔGθ = 0	Eθ = 0	The reaction is at equilibrium