Question

A metal electrode immersed in a solution is used to convert a chemical reaction into an electric current. The electrode potential is measured as the voltage difference between the metal and the solution. The cathodic and anodic Tafel slopes are then calculated in order to determine the rate of the chemical reaction occurring at the electrode. Given a metal electrode immersed in a 0.1 M solution of AgNO3, the cathodic and anodic Tafel slopes are determined to be 120 mV/decade and 110 mV/decade, respectively. Calculate the exchange current density for the reaction occurring at the electrode. If the current density at a potential of -0.5 volts versus the standard hydrogen electrode (SHE) is 50 mA/cm2, what is the current density at a potential of -0.2 volts versus SHE?

Answer 1

To calculate the exchange current density  i0  and the current density at a potential of -0.2 volts versus SHE, we can use the Butler-Volmer equation:i = i0 *  exp  a * F *   /  R * T   - exp  -c * F *   /  R * T   where:i = current density  A/cm i0 = exchange current density  A/cm a = anodic transfer coefficient  dimensionless c = cathodic transfer coefficient  dimensionless F = Faraday's constant  96485 C/mol  = overpotential  V R = gas constant  8.314 J/molK T = temperature  K First, we need to find the anodic and cathodic transfer coefficients  a and c  using the Tafel slopes:Tafel slope  anodic  =  2.303 * R * T  /  a * F Tafel slope  cathodic  =  2.303 * R * T  /  c * F Assuming the temperature is 298 K  25C , we can solve for a and c:a =  2.303 * R * T  /  Tafel slope  anodic  * F a =  2.303 * 8.314 * 298  /  110 * 10^-3  * 96485 a  0.5c =  2.303 * R * T  /  Tafel slope  cathodic  * F c =  2.303 * 8.314 * 298  /  120 * 10^-3  * 96485 c  0.6Now, we can use the Butler-Volmer equation to find the exchange current density  i0 . We are given the current density  i  at a potential of -0.5 volts versus SHE, which is 50 mA/cm or 0.05 A/cm. The overpotential    is -0.5 volts:0.05 = i0 *  exp  0.5 * F * -0.5  /  R * 298   - exp  -0.6 * F * -0.5  /  R * 298   Solving for i0, we get:i0  2.6 * 10^-6  A/cmNow, we can find the current density at a potential of -0.2 volts versus SHE using the Butler-Volmer equation with the calculated i0 and the new overpotential   = -0.2 V :i = 2.6 * 10^-6  *  exp  0.5 * F * -0.2  /  R * 298   - exp  -0.6 * F * -0.2  /  R * 298   i  0.0076 A/cm or 7.6 mA/cmSo, the current density at a potential of -0.2 volts versus SHE is approximately 7.6 mA/cm.