Question #44785

A localized pitting corrosion cell on an iron surface at $298 \text{ K}$ features a micro-capillary pit of cross-sectional area $A = 1.0 \times 10^{-4} \text{ cm}^2$. The pit is covered by a porous \ce{Fe2O3} film of thickness $l = 2.0 \times 10^{-4} \text{ cm}$. The bulk resistivity of solid \ce{Fe2O3} is $\rho = 6.0 \times 10^6 \ \Omega \cdot \text{cm}$, and the standard cell potential for the overall corrosion reaction is $E^\circ_{cell} = 1.20 \text{ V}$. Due to the porous, non-ohmic nature of the micro-capillary oxide layer, the corrosion kinetics are governed by activation polarization rather than macroscopic bulk resistance. The measured charge-transfer (polarization) resistance of the pit is $R_p = 2.6 \times 10^4 \ \Omega$, and the Stern-Geary constant for the system is $B = 0.026 \text{ V}$. Calculate the true corrosion current ($I_{corr}$) and the theoretical ohmic current ($I_{ohmic}$) that would be erroneously predicted if the oxide layer were treated as a simple bulk ohmic resistor.