Feasibility and the Nernst equation
Feasibility and the Nernst equation
- A positive cell potential means a reaction is feasible.
- Cell potential links to free energy.
- Non-standard concentrations are handled by the Nernst equation.
Feasibility and redox equations
- A reaction is feasible when $E^{\ominus}_{\text{cell}}$ is positive.
- To build the full equation: take the two half-equations, reverse the one that is oxidised, and add them so the electrons cancel.
- Link to free energy: $\Delta G^{\ominus} = -n E^{\ominus}_{\text{cell}} F$ (n = moles of electrons).
Practice
A redox reaction is feasible when the cell potential is:
A positive E°cell means the reaction can happen (analogous to a negative ΔG).
Practice
The link between cell potential and free energy is:
ΔG° = −nE°cellF; a positive E°cell gives a negative ΔG° (feasible).
Practice
To build the overall redox equation from two half-equations, you:
One half-equation runs in reverse (oxidation); adding them so electrons cancel gives the full equation.
The Nernst equation
If concentrations aren't standard, $E$ changes:
$$E = E^{\ominus} + \frac{0.059}{z} \log \frac{[\text{oxidised}]}{[\text{reduced}]}$$
- $z$ = number of electrons in the half-equation.
- Raising the oxidised species' concentration makes $E$ more positive.
Practice
According to the Nernst equation, increasing the concentration of the oxidised species makes E:
The log term rises, so E becomes more positive when the oxidised species is more concentrated.
You've got it
Key idea
- a reaction is feasible when $E^{\ominus}_{\text{cell}} > 0$
- build the equation: reverse the oxidised half-equation and add so electrons cancel
- $\Delta G^{\ominus} = -n E^{\ominus}_{\text{cell}} F$
- Nernst: $E = E^{\ominus} + \dfrac{0.059}{z}\log\dfrac{[\text{oxidised}]}{[\text{reduced}]}$ — more oxidised species → more positive $E$