Table of Contents
Standard Redox Potentials: Definition and Meaning
In earlier chapters, redox reactions were introduced as electron transfer processes and described using oxidation numbers and balanced equations. To compare how “strong” different oxidizing and reducing agents are, chemists use standard redox potentials.
A redox (electrode) potential describes the tendency of a chemical species to be reduced (gain electrons) relative to a reference system. Under standard conditions
- concentration of all dissolved species: $c = 1\,\mathrm{mol\,L^{-1}}$
- pressure of gases: $p = 1\,\mathrm{bar}$
- pure solids and liquids in their standard state
- usually temperature: $T = 25^\circ\mathrm{C} = 298\,\mathrm{K}$
the potential of a half-reaction is called the standard redox potential and is written as $E^\circ$.
Conventionally, all half-reactions are written as reductions, for example:
$$
\ce{Cu^{2+} + 2 e^- -> Cu}
$$
The corresponding standard potential is written as $E^\circ(\ce{Cu^{2+}/Cu})$.
Reference Electrode: Standard Hydrogen Electrode (SHE)
To have a common scale, all half-cell potentials are measured relative to a defined reference: the standard hydrogen electrode (SHE).
- Half-reaction (as reduction):
$$
\ce{2 H^+ + 2 e^- -> H2}
$$ - Under standard conditions ($c(\ce{H^+}) = 1\,\mathrm{mol\,L^{-1}}$, $p(\ce{H2}) = 1\,\mathrm{bar}$, $T = 25^\circ\mathrm{C}$), the potential is defined as
$$
E^\circ(\ce{2 H^+/H2}) = 0.00\,\mathrm{V}
$$
All other $E^\circ$ values are measured against the SHE and placed on a redox series or electrochemical series.
Sign and Magnitude of $E^\circ$
For a half-reaction written as a reduction:
- Large positive $E^\circ$: strong tendency to be reduced
→ strong oxidizing agent in its oxidized form - Large negative $E^\circ$: weak tendency to be reduced (or strong tendency to be oxidized)
→ strong reducing agent in its reduced form
Example values (approximate):
- $\ce{F2 + 2 e^- -> 2 F^-}$, $E^\circ \approx +2.87\,\mathrm{V}$ (very strong oxidizing agent)
- $\ce{Cu^{2+} + 2 e^- -> Cu}$, $E^\circ = +0.34\,\mathrm{V}$
- $\ce{Zn^{2+} + 2 e^- -> Zn}$, $E^\circ = -0.76\,\mathrm{V}$
- $\ce{Na^+ + e^- -> Na}$, very negative $E^\circ$ (strong reducing agent in metallic form)
The more positive the potential of a half-reaction, the more readily it proceeds as written (as a reduction) under standard conditions.
Comparing Redox Couples and Predicting Reaction Direction
For a complete redox reaction, two half-reactions are combined:
- one acts as reduction (gains electrons)
- the other as oxidation (loses electrons, i.e., the reverse of its tabulated reduction)
To predict which direction is favored under standard conditions:
- Write the two possible reduction half-reactions with their $E^\circ$ values.
- The species with the more positive $E^\circ$ will preferentially be reduced.
- The other half-reaction will run in reverse and serve as the oxidation.
Example: Zinc and Copper(II)
Half-reactions (as reductions):
- $\ce{Cu^{2+} + 2 e^- -> Cu}$, $E^\circ = +0.34\,\mathrm{V}$
- $\ce{Zn^{2+} + 2 e^- -> Zn}$, $E^\circ = -0.76\,\mathrm{V}$
Since copper’s $E^\circ$ is more positive, $\ce{Cu^{2+}}$ is reduced, and zinc must be oxidized:
Oxidation (reverse of the tabulated reduction):
$$
\ce{Zn -> Zn^{2+} + 2 e^-}
$$
Overall redox reaction:
$$
\ce{Zn + Cu^{2+} -> Zn^{2+} + Cu}
$$
This prediction matches the observation that zinc metal can displace copper from $\ce{Cu^{2+}}$ solutions.
Calculating Standard Cell Potentials
A complete electrochemical cell consists of two half-cells:
- cathode: site of reduction
- anode: site of oxidation
The standard cell potential $E^\circ_{\text{cell}}$ under standard conditions is:
$$
E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}
$$
Here, $E^\circ_{\text{cathode}}$ and $E^\circ_{\text{anode}}$ are the standard potentials of the half-reactions written as reductions.
Example: Zn–Cu Cell
Cathode (reduction):
$$
\ce{Cu^{2+} + 2 e^- -> Cu}, \quad E^\circ_{\text{cathode}} = +0.34\,\mathrm{V}
$$
Anode (oxidation, but tabulated as reduction):
$$
\ce{Zn^{2+} + 2 e^- -> Zn}, \quad E^\circ_{\text{anode (as red.)}} = -0.76\,\mathrm{V}
$$
Then:
$$
E^\circ_{\text{cell}} = (+0.34\,\mathrm{V}) - (-0.76\,\mathrm{V}) = +1.10\,\mathrm{V}
$$
Notes:
- Do not multiply $E^\circ$ values by stoichiometric factors when balancing electrons. Potential is an intensive quantity.
- A positive $E^\circ_{\text{cell}}$ indicates a reaction that proceeds spontaneously in the written direction under standard conditions.
- A negative $E^\circ_{\text{cell}}$ corresponds to a non-spontaneous direction (the reverse reaction would be spontaneous).
Redox Equilibria and the Nernst Equation
For non-standard conditions, the actual cell potential $E$ differs from $E^\circ$. The relationship between potential, concentrations, and reaction quotient $Q$ is given by the Nernst equation.
For a general redox half-reaction:
$$
\ce{Ox + n e^- <=> Red}
$$
the Nernst equation for the half-cell potential (at $25^\circ\mathrm{C}$) is:
$$
E = E^\circ - \frac{0.059\,\mathrm{V}}{n} \log_{10} \left( \frac{[\ce{Red}]}{[\ce{Ox}]} \right)
$$
More generally (for any temperature):
$$
E = E^\circ - \frac{RT}{nF} \ln \left( \frac{a(\ce{Red})}{a(\ce{Ox})} \right)
$$
with:
- $R$: universal gas constant
- $T$: absolute temperature (K)
- $F$: Faraday constant
- $a(\ce{X})$: activity of species X (approximated as concentration or partial pressure in simple cases)
- $n$: number of electrons transferred in the half-reaction
For a complete cell reaction with $n$ transferred electrons and overall reaction quotient $Q$:
$$
E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.059\,\mathrm{V}}{n} \log_{10} Q
$$
Reaction Quotient $Q$ for Redox Reactions
$Q$ is formed from the activities (or approximate concentrations) of the reaction products divided by the reactants, each raised to the power of their stoichiometric coefficients.
Example for
$$
\ce{Zn + Cu^{2+} <=> Zn^{2+} + Cu}
$$
Solids (Zn, Cu) have activity ≈ 1 and do not appear in $Q$. Thus:
$$
Q = \frac{a(\ce{Zn^{2+}})}{a(\ce{Cu^{2+}})} \approx \frac{[\ce{Zn^{2+}}]}{[\ce{Cu^{2+}}]}
$$
The Nernst equation then links $E_{\text{cell}}$ to the ratio of $\ce{Zn^{2+}}$ and $\ce{Cu^{2+}}$ concentrations.
Connection Between Standard Potentials and Equilibrium Constants
At equilibrium, the net cell reaction no longer proceeds in any direction on the macroscopic scale, and the cell potential is zero:
$$
E_{\text{cell}} = 0
$$
At the same time, the reaction quotient becomes the equilibrium constant $K$.
Inserting $E_{\text{cell}} = 0$ and $Q = K$ into the Nernst equation for the overall cell gives:
$$
0 = E^\circ_{\text{cell}} - \frac{0.059\,\mathrm{V}}{n} \log_{10} K
$$
Rearranged:
$$
E^\circ_{\text{cell}} = \frac{0.059\,\mathrm{V}}{n} \log_{10} K
$$
or equivalently:
$$
\log_{10} K = \frac{n\,E^\circ_{\text{cell}}}{0.059\,\mathrm{V}}
$$
This shows:
- Large positive $E^\circ_{\text{cell}}$ → large $K$
→ equilibrium lies far toward the products of the cell reaction. - $E^\circ_{\text{cell}} \approx 0$ → $K \approx 1$
→ reactants and products have comparable equilibrium activities. - Large negative $E^\circ_{\text{cell}}$ → very small $K$
→ equilibrium lies far toward the reactants.
This provides a quantitative bridge between electrochemical data and the position of chemical equilibrium.
Spontaneity and Direction of Redox Equilibria
Standard redox potentials can be used to judge:
- Which direction a redox equilibrium favors under standard conditions.
- Which redox pairs can react spontaneously with each other.
Procedure:
- Identify the two redox couples.
- Look up their $E^\circ$ (as reductions).
- The couple with the higher $E^\circ$ is reduced; the other is oxidized.
- Compute $E^\circ_{\text{cell}}$ and, if needed, the corresponding equilibrium constant $K$.
If $E^\circ_{\text{cell}} > 0$, the reaction is spontaneous in the direction written (toward products) under standard conditions, and the equilibrium lies on the product side. If $E^\circ_{\text{cell}} < 0$, the equilibrium is shifted toward the reactants; the reverse reaction is spontaneous.
In this way, standard redox potentials serve both as a scale of oxidizing/reducing strength and as a tool for understanding and quantifying redox equilibria.