GATE 2020 MT – Question 53
Iron corrodes in fresh water with dissolved oxygen 15 mM. Find anodic current density at overpotential 120 mV, in A/cm² to 3 decimals. Anodic Tafel slope = 0.06 V; oxygen diffusivity $2.42\times10^{-5}$ cm²/s; diffusion-layer thickness 0.06 cm.
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Correct answer: 0.190 to 0.238
Explanation
In the intended oxygen-diffusion-limited corrosion model, $i_{corr}=4FDC/\delta$, using four electrons per oxygen molecule. Convert 15 mM to $15\times10^{-6}$ mol/cm³. With F ≈ 96500 C/mol, $i_{corr}=0.0023353$ A/cm². A 0.120 V anodic shift at a 0.060 V/decade slope multiplies current by $10^{0.120/0.060}=100$. Thus $i_a=0.23353\approx0.234$ A/cm². This derivation assumes the overpotential is measured from the corrosion state and oxygen reduction is transport limited; without that reference an exchange-current datum would be needed.