To calculate the activation energy Ea of a reaction, 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*K , and T is the temperature in Kelvin.Given that the rate constant k increases by a factor of 4 when the temperature is increased from 25C to 50C, we can set up the following equation:k2 / k1 = exp -Ea / R * 1/T1 - 1/T2 where k1 and k2 are the rate constants at temperatures T1 and T2, respectively. Since k2 = 4 * k1, we can rewrite the equation as:4 = exp -Ea / R * 1/T1 - 1/T2 First, we need to convert the temperatures from Celsius to Kelvin:T1 = 25C + 273.15 = 298.15 KT2 = 50C + 273.15 = 323.15 KNow, we can plug the temperatures into the equation:4 = exp -Ea / 8.314 * 1/298.15 - 1/323.15 To solve for Ea, we can take the natural logarithm of both sides:ln 4 = -Ea / 8.314 * 1/298.15 - 1/323.15 Now, we can isolate Ea:Ea = -ln 4 * 8.314 * 1/298.15 - 1/323.15 Ea 19835.6 J/molThe activation energy of the reaction is approximately 19.8 kJ/mol.