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Obtain a relation between standard cell ...

Obtain a relation between standard cell potential ( or standard emf) and equilibrium constant of the cell reaction.

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For any galvanic cell, the overall cell reaction at equilibrium can be represented as,
Reactants `hArr` Products.
[For example for Daniell cell, `Zn_((S) +Cu_((aq))^(2)) hArr Zn_((aq))^(2+) +Cu_((s))`]
The equilibrium constant is related to the standard free energy change `DeltaG^(@)` as , follows.
`DeltaG^(@) = - RT` in K
If `E_("cell")^(0)` is the standard cell potential (or emf) of the galvanic cell, then
`DeltaG^(@) = - nFE_("cell)^(@)`
By comparing above equations,
`DeltaG^(@) = - nFE_("cell")^(@) = - RT In k`
`therefore E_("cell")^(@) = (RT)/(nF)` In K
OR `E_("cell")^(0) = (2.303 RT)/(nF) log_(10)` K
At `25^(@)C`
`(2.303 xx RT)/(F) = (2.303 xx 8314 xx 298)/(96500) = 0.0592`
`therefore E_("cell")^(0) = (0.0592)/(n) log_(10)K`
This is a relation between equilibrium constant and `E_("cell")^(0)`
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