What is Nernst equation?

1 Answer
Truong-Son N.
Apr 10, 2018

The Nernst equation describes the change in the cell potential at nonstandard conditions.

And it is:

#E_(cell) = E_(cell)^@ - (RT)/(nF)lnQ#

where:

  • #E_(cell)# is the cell potential in #"V"# at nonstandard conditions.
  • #E_(cell)^@# is the standard cell potential in #"V"#, i.e. at #25^@ "C"# and #"1 bar"#.
  • #R = "8.314472 V"cdot"C/mol"cdot"K"# is the universal gas constant.
  • #T# is the temperature in #"K"#.
  • #n# is the mols of electrons per atom, i.e. #"mol e"^(-)"/mol atom"#.
  • #F = "96485 C/mol e"^(-)# is the Faraday constant.
  • #Q# is the usual reaction quotient (i.e. the "not-yet-equilibrium" constant).

This can be derived by knowing how #DeltaG# relates to #E#.

#DeltaG = -nFE_(cell)#
#DeltaG^@ = -nFE_(cell)^@#

From this, and knowing that #DeltaG = DeltaG^@ + RTlnQ#,

#-nFE_(cell) = -nFE_(cell)^@ + RTlnQ#

Dividing through by #-nF#,

#barul|stackrel(" ")(" "E_(cell) = E_(cell)^@ - (RT)/(nF)lnQ" ")|#

And just like #DeltaG = 0# at equilibrium, #E_(cell) = 0# at equilibrium, so that

#E_(cell)^@ = (RT)/(nF)lnK#

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