Private: Chapter Seventeen
Potential, Free Energy, and Equilibrium (17.4)
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Learning Objectives
By the end of this section, you will be able to:
- Explain the relations between potential, free energy change, and equilibrium constants
- Perform calculations involving the relations between cell potentials, free energy changes, and equilibrium
- Use the Nernst equation to determine cell potentials under nonstandard conditions
So far in this chapter, the relationship between the cell potential and reaction spontaneity has been described, suggesting a link to the free energy change for the reaction (see chapter on thermodynamics). The interpretation of potentials as measures of oxidant strength was presented, bringing to mind similar measures of acid-base strength as reflected in equilibrium constants (see the chapter on acid-base equilibria). This section provides a summary of the relationships between potential and the related thermodynamic properties ΔG and K.
E° and ΔG°
The standard free energy change of a process, ΔG°, was defined in a previous chapter as the maximum work that could be performed by a system, wmax. In the case of a redox reaction taking place within a galvanic cell under standard state conditions, essentially all the work is associated with transferring the electrons from reductant-to-oxidant, welec:
ΔG° = wmax = welec
The work associated with transferring electrons is determined by the total amount of charge (coulombs) transferred and the cell potential:
ΔG° = welec = −nFE °cell
ΔG° = −nFE °cell
where n is the number of moles of electrons transferred, F is Faraday’s constant, and E°cell is the standard cell potential. The relation between free energy change and standard cell potential confirms the sign conventions and spontaneity criteria previously discussed for both of these properties: spontaneous redox reactions exhibit positive potentials and negative free energy changes.
E° and K
Combining a previously derived relation between ΔG° and K (see the chapter on thermodynamics) and the equation above relating ΔG° and E°cell yields the following:
ΔG° = −RT ln K = −nFE °
[latex]E^{°}_{cell} = (\frac{RT}{nF})ln K[/latex]
This equation indicates redox reactions with large (positive) standard cell potentials will proceed far towards completion, reaching equilibrium when the majority of reactant has been converted to product. A summary of the relations between E°, ΔG° and K is depicted in Figure 17.7, and a table correlating reaction spontaneity to values of these properties is provided in Table 17.2.
Figure 17.7 Graphic depicting the relation between three important thermodynamic properties.
|
K |
ΔG° |
E°cell |
|
|
> 1 |
< 0 |
> 0 |
Reaction is spontaneous under standard conditions Products more abundant at equilibrium |
|
< 1 |
> 0 |
< 0 |
Reaction is non-spontaneous under standard conditions Reactants more abundant at equilibrium |
|
= 1 |
= 0 |
= 0 |
Reaction is at equilibrium under standard conditions Reactants and product