To calculate the activation energy Ea for the electrochemical reaction between zinc and copper ions, we can use the Arrhenius equation:k = A * exp -Ea / R * T where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant 8.314 J mol^-1 K^-1 , and T is the temperature in Kelvin.We have two sets of data: k1 = 1.5 x 10^-4 mol L^-1 s^-1 at T1 = 25C 298.15 K and k2 = 6.2 x 10^-3 mol L^-1 s^-1 at T2 = 40C 313.15 K .First, we can divide the two Arrhenius equations to eliminate the pre-exponential factor A:k2 / k1 = exp -Ea / R * T2 / exp -Ea / R * T1 Now, we can simplify the equation: k2 / k1 = exp Ea / R * T1 - Ea / R * T2 Taking the natural logarithm of both sides:ln k2 / k1 = Ea / R * 1 / T1 - 1 / T2 Now, we can solve for Ea:Ea = R * ln k2 / k1 / 1 / T1 - 1 / T2 Plugging in the values:Ea = 8.314 * ln 6.2 x 10^-3 / 1.5 x 10^-4 / 1 / 298.15 - 1 / 313.15 Ea 8.314 * ln 41.333 / -0.000051 Ea 62.84 kJ/molThe activation energy for the electrochemical reaction occurring between zinc and copper ions is approximately 62.84 kJ/mol.