Question #44779

A sample of iron undergoes corrosion in a stagnant, aerated aqueous solution at $298 \text{ K}$ under a constant $O_2(g)$ pressure of $1 \text{ bar}$. Under these stagnant conditions, the overall rate of corrosion is strictly controlled by the mass transport (diffusion) of dissolved oxygen to the metal surface.

Given the following thermodynamic and kinetic parameters: $\bullet$ Activation energy for the electrochemical reduction of $O_2$ at the iron surface: $E_{act} = 50.0 \text{ kJ mol}^{-1}$ $\bullet$ Activation energy for the diffusion of $O_2$ in water: $E_{diff} = 18.0 \text{ kJ mol}^{-1}$ $\bullet$ Standard enthalpy of dissolution of $O_2(g)$ in water: $\Delta H^\circ_{sol} = -14.0 \text{ kJ mol}^{-1}$

Assuming the thickness of the diffusion layer remains constant, what is the apparent activation energy ($E_{app}$) for the overall corrosion rate?