Disproportionation & Electrode Potential

The feasibility of disproportionation is governed by the Standard Electrode Potential ($E^\theta$) of the two relevant half-equations.

Every disproportionation can be broken down into two half-reactions: a reduction half-reaction and an oxidation half-reaction.

The Standard Cell Potential ($E^\theta_{cell}$) is calculated using the formula: $E^\theta_{cell} = E^\theta_{reduction} - E^\theta_{oxidation}$

According to thermodynamic principles, a reaction is feasible if $E^\theta_{cell} > 0$, which corresponds to a negative Gibbs free energy change ($\Delta G^\theta < 0$).

Step 1: Identify Half-Equations: Locate the two half-equations in a standard data table that involve the species in question.

Step 2: Assign Roles: The half-equation with the more positive $E^\theta$ value will proceed as the reduction (forward). The half-equation with the less positive (or more negative) $E^\theta$ value will proceed as the oxidation (reverse).

Step 3: Calculate $E^\theta_{cell}$: Subtract the oxidation potential from the reduction potential.

Step 4: Determine Feasibility: If the resulting value is positive, the species is unstable and will spontaneously disproportionate under standard conditions.

Check the 'Middle' State: Always look for the species that appears on the right-hand side of one half-equation and the left-hand side of another.

Sign Consistency: When calculating $E^\theta_{cell}$, do not change the signs of the values found in the data table; simply use the subtraction formula.

State Symbols: Ensure you check if the reaction is occurring in aqueous solution, as $E^\theta$ values are specific to standard states ($1.00 \text{ mol dm}^{-3}$).

Balancing: Remember that while $E^\theta$ values are not affected by stoichiometric coefficients, the overall equation must be balanced for charge and atoms.

Kinetically Stable vs. Thermodynamically Feasible: A reaction may have a positive $E^\theta_{cell}$ but not occur at a measurable rate due to a high activation energy.

Concentration Effects: Standard potentials only apply at $1.00 \text{ mol dm}^{-3}$. If concentrations change, the actual electrode potential shifts according to Le Chatelier's principle, which might make a 'non-feasible' reaction occur.

Multiplying Potentials: A common error is multiplying the $E^\theta$ value by the number of electrons in the balanced equation. $E^\theta$ is an intensive property and remains constant regardless of stoichiometry.