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)#

1 Answer
Truong-Son N.
Dec 16, 2016

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")#

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