### Butler–Volmer equation & Current density

At 298 K the exchange current density (i o ) of an electrode having a surface area of 5 cm 2 , used in an electrodeposition process is 0.79 mA cm –2 . Estimate the applied current through the electrode if the overpotential (η) is 5 mV. Required formula derived from the Butler–Volmer equation is: i = (i o η F) / (R T) where, ‘i’ is the applied current density (mA cm –2 ) i o is exchange current density = 0.79 mA cm –2 η is overpotential = 5 mV F is Faraday = 96485 C mol –1 R is gas constant = 8.314 J K –1 mol –1 T is temperature (in K) = 298 K Current density = Current (mA) / Surface area (cm 2 ) Surface area = 5 cm 2 Substituting these values in the equation, value of the applied current density is: i = (0.79 mA cm –2 × 5 mV × 96485 C mol –1 ) / (8.314 J K –1 mol –1 × 298 K). Since, Joule = Volt × Coulomb or J = V × C. So, i = (0.79 mA cm –2 × 5 mV × 96485 C mol –1 ) / (8.314 V C K –1 mol –1 × 298 K) And, 1 V = 1000 mV