# 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: $2 {H}_{2} O \left(l\right) + 2 {e}^{-} \to {H}_{2} \left(g\right) + 2 O {H}^{-} \left(a q\right)$ 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. ${M}^{3 +} \left(a q\right) + 3 {e}^{-} \to M \left(s\right)$

Dec 16, 2016

Write out a number line. The original ${E}_{\text{red}}^{\circ}$ was $- \text{0.8277 V}$, when in reference to the Standard Hydrogen Electrode, which is normally the one at $\text{0.0000 V}$.

If we offset this reduction of water in base forward by $+ \text{0.8277 V}$, we offset the Standard Hydrogen Electrode forward by that much, as well as every remaining reduction potential.

Normal Reduction Potentials (V)

$\text{ "" "-0.8277" "stackrel("(SHE)")(0.0000)" "" } 1.34$
$\left\langle- - - | - - - | - - - | -\right\rangle$

New Reduction Potential Scale (V)

" "" "" "0.0000" "stackrel("(SHE)")(0.8277)" "" "???
$\left\langle- - - | - - - | - - - | -\right\rangle$

Thus, $\textcolor{b l u e}{{E}_{\text{red,new"^@) = "1.34 V" + "0.8277 V" = color(blue)("2.17 V}}}$