To calculate the anodic and cathodic Tafel slopes, we first need to determine the Tafel equation for the given data. The Tafel equation is given by: = b * log10 j/j0 where is the overpotential V , b is the Tafel slope V/decade , j is the current density mA/cm , and j0 is the exchange current density mA/cm .We can determine the Tafel slope by plotting the overpotential against the logarithm of the current density log10 j and calculating the slope of the linear region of the plot. In this case, we can use the data points 0.1, 0.5 , 0.2, 2.0 , and 0.3, 5.0 for the linear region.First, calculate the overpotential for each data point:1 = 0.1 V2 = 0.2 V3 = 0.3 VNext, calculate the logarithm of the current density log10 j for each data point:log10 j1 = log10 0.5 = -0.301log10 j2 = log10 2.0 = 0.301log10 j3 = log10 5.0 = 0.699Now, we can plot the overpotential against the logarithm of the current density log10 j : | log10 j ---|---0.1 | -0.3010.2 | 0.3010.3 | 0.699The slope of the linear region of this plot is the Tafel slope b . We can calculate the slope using the following formula:b = 3 - 1 / log10 j3 - log10 j1 b = 0.3 - 0.1 / 0.699 - -0.301 b = 0.2 / 1.0b = 0.2 V/decadeSince we are given a single set of data points, we cannot differentiate between anodic and cathodic Tafel slopes. Therefore, we will assume that the Tafel slope calculated above represents both the anodic and cathodic Tafel slopes.Now, we can determine the rate constant for the electrochemical reaction using the following equation:k = j0 / n * F * C where k is the rate constant, n is the number of electrons transferred in the reaction assumed to be 2 for copper , F is Faraday's constant 96485 C/mol , and C is the concentration of the copper ions in the solution assumed to be 1 mol/L for simplicity .First, we need to determine the exchange current density j0 using the Tafel equation: = b * log10 j/j0 Rearranging the equation to solve for j0:j0 = j / 10^/b Using the data point 0.1, 0.5 :j0 = 0.5 / 10^0.1/0.2 j0 = 0.5 / 10^0.5j0 = 0.5 / 3.162j0 0.158 mA/cmNow, we can calculate the rate constant k :k = j0 / n * F * C k = 0.158 / 2 * 96485 * 1 k 8.19 x 10^-7 mol/ cms Therefore, the anodic and cathodic Tafel slopes are both 0.2 V/decade, and the rate constant for the electrochemical reaction is approximately 8.19 x 10^-7 mol/ cms .