Which expression gives the diffusion-limited current for a planar electrode with semi-infinite diffusion, assuming surface concentration is zero?

• A. i_lim = δ / (n F A D C_bulk)
• B. i_lim = n F A D C_bulk / δ
• C. i_lim = n F A / (D δ) C_bulk
• D. i_lim = (D C_bulk) / (n F A δ)

Answer: (B)

The main idea is diffusion-limited current for a planar electrode under semi-infinite diffusion, obtained from Fick’s law. With the surface concentration at the electrode set to zero, the entire bulk concentration C_bulk is available to diffuse across a thin layer of thickness δ. The concentration gradient is ΔC/δ = C_bulk/δ, so the diffusion flux toward the electrode is J = D ΔC/δ = D C_bulk/δ. The total current is then i_lim = n F A J = n F A D C_bulk / δ. This shows why the expression with D, A, and C_bulk in the numerator and δ in the denominator is the correct one.

The other forms misplace factors or invert the dependence on D or δ, leading to incorrect units or scaling.