To calculate the cathodic Tafel slope, we can use the Tafel equation: = b * log10 i / i0 where is the overpotential, b is the Tafel slope, i is the current density, and i0 is the exchange current density.First, we need to convert the given current density from mA/cm to A/cm:50 mA/cm = 0.05 A/cmNow, we can rearrange the Tafel equation to solve for the Tafel slope b :b = / log10 i / i0 We need to find the overpotential to calculate the Tafel slope. The overpotential can be determined using the Nernst equation: = -RT/nF * ln [Zn]/[Zn] where R is the gas constant 8.314 J/molK , T is the temperature in Kelvin 25C = 298.15 K , n is the number of electrons transferred 2 for the Zn/Zn redox couple , F is the Faraday constant 96485 C/mol , and [Zn] and [Zn] are the concentrations of Zn ions and Zn in the solution, respectively.Since the concentration of Zn ions is given as 0.1 M, and the concentration of Zn in the solution is negligible, we can simplify the equation: = -RT/nF * ln 0.1 -8.314 * 298.15 / 2 * 96485 * ln 0.1 -0.135 VNow, we can plug the values of , i, and i0 into the rearranged Tafel equation:b = -0.135 / log10 0.05 / 1.2 x 10^-6 b 0.135 / log10 41666.67 b 0.135 / 4.619b 0.0292 V/decadeThe cathodic Tafel slope for the zinc electrode in the given conditions is approximately 0.0292 V/decade.