Question

Calculate the anodic Tafel slope (in mV/decade) for the corrosion of iron in a solution containing 0.1 M HCl, given that the corrosion current density is 2.5 mA/cm2 and the exchange current density is 0.25 mA/cm2. Assume T = 25°C and the activation energy of the reaction is 40 kJ/mol.

Answer 1

To calculate the anodic Tafel slope, we can use the Tafel equation: = b * log10 i / i0 where  is the overpotential, b is the Tafel slope, i is the corrosion current density, and i0 is the exchange current density.First, we need to find the overpotential   . We can use the Butler-Volmer equation to do this:i = i0 *  exp  * F /  RT   - exp - * F /  RT   where i is the corrosion current density  2.5 mA/cm , i0 is the exchange current density  0.25 mA/cm , F is the Faraday constant  96485 C/mol , R is the gas constant  8.314 J/molK , and T is the temperature  25C = 298.15 K .Rearranging the equation to solve for : =  RT / F  * ln i / i0 Plugging in the values: =  8.314 J/molK * 298.15 K  /  96485 C/mol  * ln 2.5 mA/cm / 0.25 mA/cm  = 0.0257 V * ln 10  = 0.0257 V * 2.303 = 0.0592 VNow we can use the Tafel equation to find the anodic Tafel slope  b :0.0592 V = b * log10 2.5 mA/cm / 0.25 mA/cm b = 0.0592 V / log10 10 b = 0.0592 VThe anodic Tafel slope  b  is 59.2 mV/decade.