Electrochemistry

It is possible from the cells EMF to determine Δ*G*° for a reaction. In regards to electrochemistry and Δ*G*°, 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 Δ*G*°. Quite likely it is historical reasons.

Δ*G*° = -*z·F·E°*

Δ*G*° = -*R·T*·ln(*K*)

Δ

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

Δ*G*° = -*z·F·E°*

In some foreign collections of formulas and educational books, you can encounter this version for the formula:

Δ*G*° = -*n·F·E°*

where they prefer the use of

Considering the way Δ*G* 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 Δ*G*, 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.

Δ*G*° = -*z·F·E°*

to be a general expression for Δ

Δ*G* = -*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

If we take a rechargeable 1.5 V nickel/cadmium cell and try to calculate Δ*G* for this, it looks like this:

For a Ni/Cd cell, the redox reaction is:

Cd(s) + Ni^{2+}(aq) Ni(s) + Cd^{2+}(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) + Ni

or the opposite direction, depending on whether the battery is producing a current or being recharged.

Δ*G* = -*z·F·E*

*G* = -2 · 9.65 · 10^{4} C·mol^{-1} · 1.5 V

*G* = -2.90 · 10^{5} J/mol = -290 kJ/mol

z | = 2 |

F | = 9.65 · 10^{4} C·mol^{-1} |

E | = 1.5 V |

⇕

Δ⇕

ΔHad it been the same cell under standard conditions, it would have looked like this:

Δ*G*° = -*z·F·E*°

*G*° = -2 · 9.65 · 10^{4} C·mol^{-1} · 0.153 V

*G* = -2.95 · 10^{4} J/mol = -29.5 kJ/mol

z | = 2 |

F | = 9.65 · 10^{4} C·mol^{-1} |

E° | = 0.153 V |

⇕

Δ⇕

Δ