When the corrosion current density of iron is uniformly 1.0 µA/cm² over the whole surface, which value is closest to the rate at which the surface recedes? Assume iron dissolves as Fe²⁺, with a molar mass of 55.85 g/mol, a density of 7.87 g/cm³, a Faraday constant of 96485 C/mol, and one year as 3.15×10⁷ s.

Answer: C. About 12 µm/year

The mass dissolved per unit area per second is iM/(nF) = 1.0×10⁻⁶ × 55.85/(2 × 96485) ≈ 2.9×10⁻¹⁰ g/(cm²·s); dividing by the density of 7.87 g/cm³ gives a recession rate of about 3.7×10⁻¹¹ cm/s. Multiplying by one year gives 3.7×10⁻¹¹ × 3.15×10⁷ ≈ 1.16×10⁻³ cm/year, about 12 µm/year (11.6 µm/year). About 23 µm/year is the mistake of taking n = 1. About 7.7 µm/year calculates with n = 3, as if iron dissolved as Fe³⁺, which does not match the stated conditions. Because current density and corrosion rate are proportional, “1 µA/cm² is about 12 µm/year” for iron is a handy conversion when estimating service life from a corrosion current.