Gibbs Energy & Standard Cell Potential (HL) (DP IB Chemistry) : Revision Note

Gibbs Energy & Standard Cell Potential

• 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