Question

A chemistry student is required to determine the cathodic and anodic Tafel slopes for a reaction occurring at an electrode surface. The current density at the cathodic surface is known to be 1.8 mA/cm² and the current density at the anodic surface is known to be 1.2 mA/cm². The current potential relationship is given by the Tafel equation:log (i) = log (i0) + β_c * (E-E_c) for cathodic reactionlog (i) = log (i0) + β_a * (E-E_a) for anodic reactionWhere i is the current density, i0 is the exchange current density, β_c and β_a are the cathodic and anodic Tafel slopes respectively, E is the elect

Answer 1

First, we need to convert the given current densities to A/cm:Cathodic current density: 1.8 mA/cm = 0.0018 A/cmAnodic current density: 1.2 mA/cm = 0.0012 A/cmNow, we can use the Tafel equations to solve for the cathodic and anodic Tafel slopes  _c and _a .For the cathodic reaction:log 0.0018  = log 5.6  10^-6  + _c *  E - E_c For the anodic reaction:log 0.0012  = log 5.6  10^-6  + _a *  E - E_a We have two equations with two unknowns  _c and _a . However, we cannot solve for the Tafel slopes directly since we do not know the values of E, E_c, and E_a. To eliminate these unknowns, we can subtract the anodic equation from the cathodic equation:log 0.0018  - log 0.0012  = _c *  E - E_c  - _a *  E - E_a Now, we can use the properties of logarithms to simplify the equation:log 0.0018/0.0012  = _c *  E - E_c  - _a *  E - E_a log 1.5   0.1761 = _c *  E - E_c  - _a *  E - E_a Since we cannot solve for _c and _a directly, we can only express their relationship in terms of the overpotentials  E - E_c  and  E - E_a :0.1761 = _c *  E - E_c  - _a *  E - E_a This equation shows the relationship between the cathodic and anodic Tafel slopes and the overpotentials. To determine the exact values of _c and _a, additional information about the electrode potential  E  and the overpotentials  E_c and E_a  would be required.