Question

Calculate the activation energy required for a chemical reaction to occur, given that the rate constant at 298 K is 4.70 x 10^-3 s^-1 and the rate constant at 313 K is 1.20 x 10^-2 s^-1. (Assume the Arrhenius equation applies.)

Answer 1

To calculate the activation energy  Ea  for the reaction, we will 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.We have two sets of data: k1 = 4.70 x 10^-3 s^-1 at T1 = 298 K and k2 = 1.20 x 10^-2 s^-1 at T2 = 313 K. We can set up two equations:k1 = A * exp -Ea / R * T1 k2 = A * exp -Ea / R * T2 Now, we can divide the first equation by the second equation to eliminate the pre-exponential factor  A :k1 / k2 = exp -Ea / R * T1  / exp -Ea / R * T2 Simplifying the equation: k1 / k2  = exp Ea / R *  1/T2 - 1/T1  Now, we can solve for Ea:Ea = R * ln k1 / k2  /  1/T2 - 1/T1 Plugging in the values:Ea = 8.314 J/mol*K * ln  4.70 x 10^-3 s^-1  /  1.20 x 10^-2 s^-1   /  1/313 K - 1/298 K Ea  8.314 * ln 0.3917  / 0.000107Ea  -18.58 / 0.000107Ea  -173,551 J/molThe activation energy for the reaction is approximately 173.6 kJ/mol.