Question #44778

A transition metal $M$ (Atomic weight = $50 \text{ g/mol}$, $\rho_M = 5.0 \text{ g/cm}^3$) has standard reduction potentials $E^\circ(M^{2+}/M) = -0.20 \text{ V}$ and $E^\circ(MO_3/M) = -1.50 \text{ V}$ at $298 \text{ K}$. Despite the highly negative reduction potential (indicating a strong thermodynamic driving force for oxidation to $MO_3$), $M$ exhibits exceptional corrosion resistance in strongly oxidizing environments due to the formation of a kinetic barrier (passivation). The metal is anodized at a constant current density of $10 \text{ mA/cm}^2$ to artificially grow this protective $MO_3$ layer (Molar mass = $98 \text{ g/mol}$, $\rho_{ox} = 7.0 \text{ g/cm}^3$). Assuming $100\%$ current efficiency and $F = 96500 \text{ C/mol}$, calculate the Pilling-Bedworth Ratio (PBR) of the oxide and the time ($t$) required to grow a layer of thickness $1.4 \,\mu\text{m}$.