Calculations on energies
Electrochemistry
Gibbs energy, ΔG°
It is possible from the cells EMF to determine ΔG° for a reaction. In regards to electrochemistry and ΔG°, you have two relevant equations:
Of these we need the formula
In some foreign collections of formulas and educational books, you can encounter this version for the formula:
where they prefer the use of n instead of z. Apparently there is no explanation for the use of n instead of z, when calculating ΔG°. Quite likely it is historical reasons.
ΔG° = -z·F·E°
ΔG° = -R·T·ln(K)
ΔG° = -R·T·ln(K)
| z | = the number of electrons to be transferred |
| F | = Faraday's constant |
| E° | = standard electrode potential for the cell at standard conditions, i.e. E at 1 M and 25 °C |
| R | = the gas constant |
| T | = temperature in degrees Kelvin |
| K | = the equilibrium constant |
Of these we need the formula
ΔG° = -z·F·E°
In some foreign collections of formulas and educational books, you can encounter this version for the formula:
ΔG° = -n·F·E°
where they prefer the use of n instead of z. Apparently there is no explanation for the use of n instead of z, when calculating ΔG°. Quite likely it is historical reasons.
Gibbs energy outside the standard conditions, ΔG
Considering the way ΔG is calculated from chemical potentials (to be shown in details under chemical potentials when I ger around to that), you can extend the expression
to be a general expression for ΔG, i.e. it is also valid outside the standard conditions:
Therefore we can use the formula whether we work under standard conditions or not. You just have to remember to note whether it is under standard conditions or not by marking G and E with a ° under standard conditions.
ΔG° = -z·F·E°
to be a general expression for ΔG, i.e. it is also valid outside the standard conditions:
ΔG = -z·F·E
| z | = the number of electrons to be transferred |
| F | = Faraday's constant |
| E | = the electrode potential for the cell |
Therefore we can use the formula whether we work under standard conditions or not. You just have to remember to note whether it is under standard conditions or not by marking G and E with a ° under standard conditions.
An example
If we take a rechargeable 1.5 V nickel/cadmium cell and try to calculate ΔG for this, it looks like this:
For a Ni/Cd cell, the redox reaction is:
Cd(s) + Ni2+(aq)
Ni(s) + Cd2+(aq)
or the opposite direction, depending on whether the battery is producing a current or being recharged. E° for the Ni/Cd cell, according the the reaction, is 0.153 V (found by looking it up), so we are not working under standard conditions. From the reaction equation we see that z = 2 electrons, so we end up with
Had it been the same cell under standard conditions, it would have looked like this:
For a Ni/Cd cell, the redox reaction is:
Cd(s) + Ni2+(aq)
Ni(s) + Cd2+(aq)or the opposite direction, depending on whether the battery is producing a current or being recharged. E° for the Ni/Cd cell, according the the reaction, is 0.153 V (found by looking it up), so we are not working under standard conditions. From the reaction equation we see that z = 2 electrons, so we end up with
ΔG = -z·F·E
| z | = 2 |
| F | = 9.65 · 104 C·mol-1 |
| E | = 1.5 V |
⇕
ΔG = -2 · 9.65 · 104 C·mol-1 · 1.5 V⇕
ΔG = -2.90 · 105 J/mol = -290 kJ/molHad it been the same cell under standard conditions, it would have looked like this:
ΔG° = -z·F·E°
| z | = 2 |
| F | = 9.65 · 104 C·mol-1 |
| E° | = 0.153 V |
⇕
ΔG° = -2 · 9.65 · 104 C·mol-1 · 0.153 V⇕
ΔG = -2.95 · 104 J/mol = -29.5 kJ/mol