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# Standard Reduction Potentials

## Introduction

Consider again the spontaneous reaction of Zn metal in a solution of Cu2+.
Zn(s) + Cu2+(aq) Zn2+(aq) + Cu(s)

Without doing the experiment, could we have predicted that this reaction would be spontaneous as written?

We can calculate Go, or we can calculate a related quantity, Eo.

First write the half-reactions as reductions:

Cu2+(aq) + 2e- Cu(s)     Eored = +0.340 V
Zn2+(aq) + 2e- Zn(s)     Eored = -0.763 V

Eored are the standard reduction potentials for these two half-reactions, which are taken from tables of data.

The half-reaction with the more positive Eored will occur as written (as a reduction).

So for the Cu2+ and Zn2+ half-reactions, the Cu2+ Eo (+0.340 V) is more positive than the Zn2+ Eo (-0.763 V), so the Cu2+ will be reduced, and Zn metal will be oxidized.

To find the voltage produced by an electrochemical cell we simply sum all of the potentials in the circuit.
Eocell = Eohalf-reactions

For simple cells:
Eocell = Eored + Eoox

The Eo of an oxidation half-reaction is the negative of the Eo of the reduction half-reaction.

For the Cu and Zn example: Eocell = 0.340 V + -(-0.763 V) = 1.103 V

When balancing reactions we sometimes multiply one or both half reactions by a factor so the electrons cancel. The Eo values do NOT get multiplied by these factors.

Eored is the standard reduction potential and is measured relative to:
2H+(aq) + 2e- H2(g)
which is assigned the value Eored = 0.00 V

A positive Eored means that a half-reaction will go in the direction indicated (reduction) when paired with the hydrogen half-reaction:
Cu2+(aq) + 2e- Cu(s)     Eored = +0.340 V
H2(g) 2H+(aq) + 2e-     Eored = 0.00 V

A negative Eored means that a half-reaction will go in the opposite direction indicated (oxidation) when paired with the hydrogen half-reaction:
2H+(aq) + 2e- H2(g)     Eored = 0.00 V
Zn(s) Zn2+(aq) + 2e-     Eored = -0.763 V

In general for any two half-reactions, the half-reaction with the more positive Eored will proceed as a reduction, and the other half-reaction will proceed as an oxidation.

Note that for a reaction to occur the appropriate species must be present. One species must be reduced and another must be oxidized.

The species that is reduced is called an oxidizing agent and the species that is oxidized is called a reducing agent.

## Example

Find a chemical species that will convert Ag+(aq) to Ag(s) without converting Cu+(aq) to Cu(s).

First determine what type of reaction occurs. The conversion of Ag+(aq) to Ag(s) is a reduction (the silver oxidation state goes from +1 to 0).

The half-reaction is:
Ag+(aq) + e- Ag(s)     Eored = 0.799 V

First, do we need a half-reaction with a more positive or more negative Eored value than the silver half reaction? Since converting Ag+(aq) to Ag(s) is a reduction, we want a half-reaction that will go as an oxidation. That means we want a half reaction with a more negative Eored value than the Eored for silver.

Looking in a table of standard reduction potentials, all half reactions with Eored values more negative than 0.799 V will reduce Ag+(aq) to Ag(s).

We don't want to reduce Cu+(aq) to Cu(s). The half-reaction is:
Cu+(aq) + e- Cu(s)     Eored = 0.518 V

So we want a half reaction that has an Eored value less than 0.799 V but not less than or equal to 0.518 V.

Some choices are:
I2 (s) + 2e- I-(aq)     Eored = 0.534 V
Fe3+(aq) + e- Fe2+(aq)     Eored = 0.769 V
Hg22+(aq)(aq) + 2e- 2Hg(l)     Eored = 0.796 V

The Ag+(aq) must react with something that can be oxidized. Species that can be oxidized are on the right side of the equation for reduction half reactions. Our choices are therefore I-(aq), Fe2+(s), and Hg(l).

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