The standard cell potential`(E_("cell")^(@))` is the potential difference between standard electrode potentials of cathode and anode .
`(E_("cell")^(@))=E_(underset("(LHE)")("cathode"))^(@)-E_(underset("(THE)")("anode"))^(@)`
Since , the standard potential , when the substances taking part in the electrode reactions are in their standard electrode potentials are constant at constant temperature and independent of the concentrations or the amount of the substance . Hence `E_("cell")^(@)`
is independent of the amount of the substance , therefore `E^(@)` represents an intensive property .
The standard free change `DeltaG^(@)` for the cell reaction is given by :
`delta G^(@) - nFE_("cell")^(@)`
where n is number of electrons transfered and F is faraday .
` :. E_("cell")^(@)= (-DeltaG^(@))/(nF)`
Gibbs free energy is a thermodynamic function, hence an extensive property and depends upon the amount of the substance .
If the stochimetric equation for all overall cell reaction is multiplied by 2 or 3 then the value of n will be 2 or 3 and the values of standard free energy change will be ` 2 DeltaG^(@) or 3DeltaG^(@) `. Then
` E_("cell") ^(@) = (-2 DeltaG^(@))/(2F) = (-3DeltaG^(@))/(3F)`
` = (DeltaG^(@))/F = "constant"`
Hence , `E^(@)._("cell")` becomes independent of the amount of the substance hence , it is an intensive property.
