To calculate the rate constant k for the polymerization of styrene, we can use the rate law equation for a first-order reaction:rate = k [styrene]where rate is the rate of polymerization, k is the rate constant, and [styrene] is the initial concentration of styrene.We are given the rate of polymerization 2.21 x 10^-3 mol L^-1 s^-1 and the initial concentration of styrene 0.02 mol L^-1 . Plugging these values into the rate law equation, we can solve for k:2.21 x 10^-3 mol L^-1 s^-1 = k 0.02 mol L^-1 k = 2.21 x 10^-3 mol L^-1 s^-1 / 0.02 mol L^-1 k = 1.105 x 10^-1 s^-1Now that we have the rate constant k at 60C, we can calculate the activation energy Ea using 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 are given the activation energy Ea = 101 kJ mol^-1 = 101,000 J mol^-1 and the temperature 60C = 333.15 K . We can rearrange the Arrhenius equation to solve for A:A = k / exp -Ea / R * T Plugging in the values for k, Ea, R, and T:A = 1.105 x 10^-1 s^-1 / exp -101,000 J mol^-1 / 8.314 J mol^-1 K^-1 * 333.15 K A 1.105 x 10^-1 s^-1 / exp -36.53 A 1.105 x 10^-1 s^-1 / 1.33 x 10^-16A 8.31 x 10^14 s^-1Now we have the pre-exponential factor A and the activation energy Ea . The rate constant k for the polymerization of styrene at 60C is 1.105 x 10^-1 s^-1, and the activation energy is 101 kJ mol^-1.