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Considering a sparingly soluble salt $M_xN_y$ of the metal $M$, in which the corresponding reaction is $M_xN_y$ = $xM^{y+}$ + $yN^{x-}$, the standard electrode potential is given by $E^{o}_{M_xN_y/M/N^{x-}}$ = $E^{o}_{M^{y+}/M}$ + $\frac{RT}{xy\times 96485}$ $\ln{K_\text{sp}}$.

This derivation is done by writing $E_{M_xN_y/M/N^{x-}}$ = $E_{M^{y+}/M}$, i.e. equating the electrode potentials (not the standard) of $M_xN_y/M$ and $M^{y+}/M$. I do not understand the reason behind doing so. Why are they equal at this instant?

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