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Nernst Equation

• The basic Nernst Equation is written as -
  
  
  
  E = E^o - (RT/nF)lnQ
  
  
  
  and expresses the electrical potential of a electrochemical cell at non-standard state conditions and at any time during the electrochemical cell's reaction.
  
  
• The Nernst equation is derived from thermodynamic considerations.
  
  
• The reactants' free energies are expressed as electrical potentials.
  
  
• The term E^o is the standard electric potential of the reference electrode
  
  
• The term lnQ represents the natural logarithm (ln) of the reaction quotient (Q) of the species involved.
  
  lnQ can be expressed as a logarithm to the base 10 by -
  
  2.303 log₁₀Q.
  
  and log₁₀Q, for pH measurements, can be expresses in terms of the hydrogen ion activity by -
  
  -log₁₀a_H+ which is the pH of a solution.
  
  
  Hence the equation becomes -
  
  
  

  				R * T
  E	=	Eo	+	----------- * 2.303 pH
  				n * F

  
  
  
  
• The constants of the Nernst equation -
  
  R is the universal gas constant -
  
  R = 8.3145 J/mol.K (Joule per mol and per Kelvin)
  
  
  n is the number of moles of electrons transferred in the balanced equation or the charge/valency of the ion. Which in the case of the hydrogen ion -
  
  n = 1
  
  
  F is the Faraday constant which is the electrical charge in coulombs (C) for every mole (mol) of reactant involved in the electrochemical cell -
  
  F = 96485.309 C/mol
  
  
  
• At a temperature (T) of 298.15 ^oK (25^o C) the Nernst equation can be rewritten as -
  
  
  

  				8.3145 J/mol.K * 298.15 K
  E	=	Eo	+	--------------------------------------- * 2.303 pH
  				96485.309 C/mol

  
  
  
  

  E

  =

  Eo

  +

  0.059 V pH

  (1 J/C = 1 Volt (V))

  
  
  
  That is a change of 56 mV per pH unit.