The Arrhenius equation is given by:k = Ae^-Ea/RT 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/molK , and T is the temperature in Kelvin.We are given two sets of data: k1 = 0.005 s^-1 at T1 = 25C 298.15 K and k2 = 0.01 s^-1 at T2 = 35C 308.15 K . We can set up two equations using the Arrhenius equation:k1 = Ae^-Ea/RT1 k2 = Ae^-Ea/RT2 Now, we can divide the first equation by the second equation to eliminate the pre-exponential factor A:k1/k2 = e^-Ea/RT1 / e^-Ea/RT2 Take the natural logarithm of both sides:ln k1/k2 = ln e^-Ea/RT1 / e^-Ea/RT2 Using the property of logarithms, we can simplify the equation:ln k1/k2 = -Ea/RT1 - -Ea/RT2 Now, we can plug in the given values for k1, k2, T1, and T2:ln 0.005/0.01 = -Ea/ 8.314*298.15 - -Ea/ 8.314*308.15 Solve for Ea:ln 1/2 = Ea/ 8.314*308.15 - Ea/ 8.314*298.15 Ea = ln 1/2 * 8.314 * 298.15 * 308.15 / 308.15 - 298.15 Ea 5233.6 J/molThe activation energy for the first-order reaction is approximately 5233.6 J/mol.