Question

Why do you NOT scale the standard cell potential when you scale reactions by a constant?

Answer 1

`E_(cell)^@` scales with the mols of electrons, as well as the mols of reactants... But they cancel out.

`DeltaG_(rxn)` is related to `RTlnQ`, and we know already that `Q -> Q^c` if the reaction is scaled, so `DeltaG_(rxn)` is scaled by `c` since `RTlnQ^c = cRTlnQ`.

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In the Nernst equation we have

`E_(cell) = E_(cell)^@ - (RT)/(nF) lnQ`,

and the units work out as

`(("V" cdot "C/mol reactant" cdot "K")("K"))/(("mol e"^(-)"/mol reactant")("C/mol e"^(-)))`

to give units of `"V"`. It must, or else `E_(cell)^@` can't add to `-(RT)/(nF)lnQ`...

If you scale the reaction by a factor of `c`, you raise `Q` to the `c` and multiply the number of electrons `n` by `c`.

For some general redox reaction, we would get something like:

`M^(+)(aq) + A(s) rightleftharpoons A^(+)(aq) + M(s)`

`" "" "" "darr`

`cM^(+)(aq) + cA(s) rightleftharpoons cA^(+)(aq) + cM(s)`

The charge contribution on each side clearly changes. Thus, you would get that the number of electrons changes as `n -> cn` and `Q -> Q^c`. As a result:

`-(RT)/(nF) lnQ -> [-(RT)/(cnF) lnQ^c = -(RT)/(cancel(c)nF)cdotcancel(c)lnQ]`

`= -(RT)/(nF) lnQ`

which is the same expression as before. If we do not affect `-(RT)/(nF) lnQ`, then by inference, `E_(cell)` and `E_(cell)^@` do not change due to scaling the reaction by a constant.