Domain: Electron-transfer kinetics

A weak-overlap electron-transfer reaction occurs in solution at \( 298\,\mathrm{K} \). The standard free energy for the reaction under the given medium is \( -12.5~\mathrm{kJ/mol} \). The work required to bring the reactants together is \( 4.0~\mathrm{kJ/mol} \), while the work required for the products is \( 1.5~\mathrm{kJ/mol} \). The bimolecular collision frequency in the solution is approximately \( 10^{11}~\mathrm{L\,mol^{-1}\,s^{-1}} \).Calculate the rate constant of this reaction in \( \mathrm{L\,mol^{-1}\,s^{-1}} \).

Grading rubric:
criterion: Correctly converts the standard free energy value (\(\Delta G^\circ\)) to exactly \(-12,500 \text{ J/mol}\).
weight: 20
criterion: Correctly explicitly identifies that the intrinsic electron transfer step is thermodynamically favorable (negative free energy).
weight: 20
criterion: Correctly explicitly states that the reaction is "diffusion-controlled" (or "diffusion-limited") in the text.
weight: 20
criterion: Correctly establishes that the effective activation barrier (\(\Delta G^\ddagger\)) is equal to the work term w_r.
weight: 10
criterion: Correctly explicitly calculates the thermal energy denominator (\(RT\)) as a value between \(2477 \text{ J/mol}\) and \(2478 \text{ J/mol}\). 
weight: 20
criterion: Correctly reports the final rate constant as \(1.99 \times 10^{10} \text{ L mol}^{-1} \text{ s}^{-1}\).
weight: 10

Answer:
1.99 × 10^10 L mol^-1 s^-1