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At equimolar concentration of Fe^(2+) an...

At equimolar concentration of `Fe^(2+) and Fe^(3+)` what must `[Ag^(+)]` be so that the voltage of the galvanic cell made from `Ag^(+)//Ag and Fe^(3+)//Fe^(2+)` electrodes equals zero? The reaction is `Fe^(2+) + Ag^(+) hArr Fe^(3+) + Ag`. Determine the equilibrium constant at `25^(@)C` for the reaction. Given `E_(Ag^(+)//Ag)^(@)= 0.799V and E_(Fe//Fe^(2+))^(@)= 0.771V`

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The correct Answer is:
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`E_("cell")^(@) = E_(Fe^(2+)//Fe^(3+))^(@) + E_(Ag^(+)//Ag)^(@)= -0.771 + 0.799= 0.028V`
At equilibrium, `E_("cell") =0`, so `0 = E_("cell")^(@) = (0.0591)/(1) "log" ([Fe^(3+)])/([Fe^(3+)][Ag^(+)])`
`E_("cell")^(@)= 0.0591 "log" (1)/([Ag^(+)]) rArr [Ag^(+)] = 0.34M` Now, log `K= (nE^(@))/(0.0591) rArr K= 3.0`
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