Question

If given the following what would the reduction potential be on the new scale in which the reaction of water in base has an `E^o"_(red) = 0.000 V`?

Suppose there were a new scale for expressing electrode potentials in which the standard potential for the reduction of water in base:

`2H_2O(l) + 2e^(-) -> H_2(g) + 2OH^(-)(aq)`

is assigned an `E^o"_(red)` value of 0.000 V. In current standard reduction tables, the following reaction has a standard reduction potential of 1.34 V.

`M^(3+)(aq) + 3e^(-) -> M(s)`

Answer 1

Write out a number line. The original `E_"red"^@` was `-"0.8277 V"`, when in reference to the Standard Hydrogen Electrode, which is normally the one at `"0.0000 V"`.

If we offset this reduction of water in base forward by `+"0.8277 V"`, we offset the Standard Hydrogen Electrode forward by that much, as well as every remaining reduction potential.

Normal Reduction Potentials (V)

`" "" "-0.8277" "stackrel("(SHE)")(0.0000)" "" "1.34`
`<< --- | --- | --- | - >>`

New Reduction Potential Scale (V)

`" "" "" "0.0000" "stackrel("(SHE)")(0.8277)" "" "???`
`<< --- | --- | --- | - >>`

Thus, `color(blue)(E_"red,new"^@) = "1.34 V" + "0.8277 V" = color(blue)("2.17 V")`