Calculation of Reduction and Oxidation Potential (E° red / E° ox)

Understanding the Calculation of Reduction and Oxidation Potential (E°red / E°ox)

Reduction and oxidation potentials quantify electron transfer tendencies in chemical species. Calculating these potentials is essential for electrochemical analysis.

This article explores detailed formulas, common values, and real-world applications of E°red and E°ox. Expect comprehensive technical insights.

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  • Calculate the standard reduction potential of the Fe3+/Fe2+ couple at 25°C.
  • Determine the oxidation potential of the Cu/Cu2+ redox pair in acidic solution.
  • Compute the cell potential for a galvanic cell combining Zn and Cu electrodes.
  • Evaluate the effect of ion concentration on the reduction potential of the Ag+/Ag couple.

Comprehensive Table of Standard Reduction and Oxidation Potentials

The standard electrode potentials (E°) are measured under standard conditions: 25°C, 1 atm pressure, and 1 M concentration of ions. These values are referenced against the Standard Hydrogen Electrode (SHE), which is assigned a potential of 0.00 V.

Half-ReactionStandard Reduction Potential E°red (V vs SHE)Standard Oxidation Potential E°ox (V vs SHE)Comments
Ag+ + e– → Ag(s)+0.80-0.80Common reference for silver electrodes
Cu2+ + 2e– → Cu(s)+0.34-0.34Widely used in galvanic cells
Fe3+ + e– → Fe2++0.77-0.77Important in redox titrations
Zn2+ + 2e– → Zn(s)-0.76+0.76Common anode material
Cl2(g) + 2e– → 2Cl–+1.36-1.36Strong oxidizing agent
O2(g) + 4H+ + 4e– → 2H2O(l)+1.23-1.23Oxygen reduction in acidic media
H+ + e– → 1/2 H2(g)0.000.00Standard Hydrogen Electrode (SHE)
MnO4– + 8H+ + 5e– → Mn2+ + 4H2O+1.51-1.51Strong oxidizer in acidic solution
NO3– + 4H+ + 3e– → NO + 2H2O+0.96-0.96Nitrogen oxides redox
Cr2O72- + 14H+ + 6e– → 2Cr3+ + 7H2O+1.33-1.33Chromium redox in acidic media

Fundamental Formulas for Calculating Reduction and Oxidation Potentials

The calculation of reduction and oxidation potentials relies on the Nernst equation, which relates the electrode potential to the concentrations (activities) of the chemical species involved.

1. Standard Electrode Potential (E°)

The standard electrode potential is the potential of a half-cell under standard conditions (1 M concentration, 1 atm pressure, 25°C). It is an intrinsic property of the redox couple.

2. Nernst Equation

The Nernst equation allows calculation of the electrode potential (E) under non-standard conditions:

E = E° – (RT / nF) × ln(Q)
  • E: Electrode potential at non-standard conditions (Volts)
  • E°: Standard electrode potential (Volts)
  • R: Universal gas constant = 8.314 J·mol-1·K-1
  • T: Temperature in Kelvin (K)
  • n: Number of electrons transferred in the half-reaction
  • F: Faraday constant = 96485 C·mol-1
  • Q: Reaction quotient, ratio of activities or concentrations of products over reactants

At 25°C (298 K), the equation simplifies to:

E = E° – (0.0257 / n) × ln(Q)

Or using base-10 logarithm:

E = E° – (0.0592 / n) × log10(Q)

3. Reaction Quotient (Q)

The reaction quotient is defined as:

Q = (aRed)coefficients / (aOx)coefficients

Where a represents the activity (or concentration) of the species involved. For example, for the half-reaction:

Ox + n e– → Red

Q = aRed / aOx

4. Relationship Between Reduction and Oxidation Potentials

The oxidation potential is the negative of the reduction potential for the reverse reaction:

E°ox = – E°red

This is because oxidation is the reverse of reduction, and potentials are measured relative to the same reference.

5. Cell Potential (Ecell) Calculation

For a galvanic cell composed of two half-cells, the overall cell potential is:

Ecell = Ecathode – Eanode

Where:

  • Ecathode: Reduction potential of the cathode (where reduction occurs)
  • Eanode: Reduction potential of the anode (where oxidation occurs)

Both potentials are typically taken as standard reduction potentials.

Detailed Explanation of Variables and Typical Values

  • E° (Standard Electrode Potential): Intrinsic property of the redox couple, measured in volts (V). Values range from highly negative (strong reducing agents) to highly positive (strong oxidizing agents).
  • R (Gas Constant): 8.314 J·mol-1·K-1, a universal constant used in thermodynamic calculations.
  • T (Temperature): Absolute temperature in Kelvin. Standard conditions use 298 K (25°C).
  • n (Number of Electrons): Integer representing electrons transferred in the half-reaction, e.g., 1, 2, 3, etc.
  • F (Faraday Constant): 96485 C·mol-1, representing charge per mole of electrons.
  • Q (Reaction Quotient): Dimensionless ratio of activities or concentrations of products to reactants, raised to their stoichiometric coefficients.

Real-World Application Examples

Example 1: Calculating the Reduction Potential of Fe3+/Fe2+ Couple at Non-Standard Conditions

Given the half-reaction:

Fe3+ + e– → Fe2+ E° = +0.77 V

Suppose the concentrations are:

  • [Fe3+] = 0.010 M
  • [Fe2+] = 0.10 M

Calculate the electrode potential at 25°C.

Solution:

First, write the reaction quotient Q:

Q = [Fe2+] / [Fe3+] = 0.10 / 0.010 = 10

Number of electrons transferred, n = 1.

Using the Nernst equation at 25°C:

E = E° – (0.0592 / n) × log10(Q)

Substitute values:

E = 0.77 V – (0.0592 / 1) × log10(10) = 0.77 V – 0.0592 × 1 = 0.7108 V

Interpretation: The electrode potential decreases slightly due to the higher concentration of Fe2+ relative to Fe3+.

Example 2: Calculating the Cell Potential of a Zn-Cu Galvanic Cell

Consider a galvanic cell composed of a zinc electrode and a copper electrode. The half-reactions and standard potentials are:

  • Anode (oxidation): Zn(s) → Zn2+ + 2e– E°ox = +0.76 V (reverse of reduction)
  • Cathode (reduction): Cu2+ + 2e– → Cu(s) E°red = +0.34 V

Calculate the standard cell potential (E°cell).

Solution:

Recall the formula:

E°cell = E°cathode – E°anode

Since the anode potential is given as oxidation potential, convert it to reduction potential by negating:

E°anode = -0.76 V

Calculate:

E°cell = 0.34 V – (-0.76 V) = 1.10 V

Interpretation: The positive cell potential indicates a spontaneous redox reaction, with zinc oxidizing and copper reducing.

Additional Considerations in Calculations

  • Activity vs Concentration: In precise calculations, activities (effective concentrations) should be used instead of molar concentrations, especially in non-ideal solutions.
  • Temperature Dependence: The Nernst equation includes temperature explicitly; deviations from 25°C require recalculating the RT/nF term.
  • pH Effects: For redox reactions involving H+ or OH–, pH significantly affects potentials. The Nernst equation must include these species in Q.
  • Electrode Surface Effects: Real electrodes may have overpotentials or kinetic barriers affecting measured potentials.

References and Further Reading