# What is the difference between #E# and #E^@# in electrochemistry?

##### 1 Answer

Well, the mathematical difference is

We define **standard conditions** to be

Many chemical functions, particularly in thermodynamics and electrochemistry, are *temperature-dependent*. Thus, we must be able to account for that...

We recall that for the Gibbs' free energy:

#DeltaG = DeltaG^@ + RTlnQ# (if you do not recall this equation, look here for a derivation.)

and:

#DeltaG^@ = -nFE^@# (which I will not derive as it is a simple unit conversion.)

The first equation uses

Hence:

#-nFE = -nFE^@ + RTlnQ#

Dividing by

#bb(E = E^@ - (RT)/(nF)lnQ)# which is the purest version of the

Nernst equation(before any simplifications), where:

#n# is the number of electrons transferred in the redox reaction#F = "96485 C/mol e"^(-)# is the Faraday constant.#R# and#T# are known from the ideal gas law.#Q# is the reaction quotient, i.e. not-yet-equilibrium constant.#E# is the "electromotive force" for the cell process.#E^@# is, of course,#E# at standard conditions.

Likewise,

#E = E^@ - cancel((("8.314472 J/mol"cdot"K")("298.15 K"))/(nF)ln(1))^(0)#

#=> E = E^@#

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