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Prove that for two half reactions having...

Prove that for two half reactions having potentials `E_(1)` and `E_(2)` which are combined to yield a third half reaction, having a potential `E_(3)`,
`E_(3)=(n_(1)E_(1)+n_(2)E_(2))/n_(3)`

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Let `Delta G_(1) , DeltaG_2` and `DeltaG_3` are the free energy changes for the half cell reactions having potentials `E_1 , E_2 ` and `E_3` respectively , then
`Delta G_(3) = Delta G_1 + DeltaG_2`
Since `Delta G = `-nFE
or `- n_3 FE_3 = -n_1 FE_1 - n_2 FE_2`
Dividing both sides by `-n_3 F`
`E_(3) = (n_1 E_1 + n_2 E_2)/(n_(3))`
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