An iron$-$carbon alloy initially containing $0\mathrm{.}219$ wt$\%$ C is exposed to an oxygen$-$rich and virtually carbon$-$free atmosphere at $1160\backslash$deg 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 $0\mathrm{.}0$ wt$\%$ C$.$ At what position will the carbon concentration be $0\mathrm{.}164$ wt$\%$ after a $9$ h treatment? The value of D at $1160\backslash$deg C is $4\mathrm{.}3\backslash$times $10-11$ m$2/$s$.$