(Solved): An iron-carbon alloy initially containing \( 0.280 \) wt\% C is exposed to an oxygen-rich and virtu ...

An iron-carbon alloy initially containing \( 0.280 \) wt\% C is exposed to an oxygen-rich and virtually carbon-free atmosphere at \( 1050^{\circ} \mathrm{C} \). Under these circumstances the carbon diffuses from the alloy and reacts at the surface with the oxygen in the atmosphere; that is, the carbon concentration at the surface position is maintained essentially at \( 0.0 \mathrm{wt} \mathrm{C} \). At what position will the carbon concentration be \( 0.210 \) wt\% after a \( 9 \mathrm{~h} \) treatment? The value of \( \mathrm{D} \) at \( 1050^{\circ} \mathrm{C} \) is \( 6.5 \times 10^{-10} \mathrm{~m}^{2} / \mathrm{s} \).