Question

What is the activation energy of the following reaction at room temperature?2NO(g) + Cl2(g) → 2NOCl(g)The rate constant of the reaction is 0.00313 L mol^-1 s^-1 at 25°C and increases to 0.05012 L mol^-1 s^-1 at 35°C.

Answer 1

To calculate the activation energy  Ea  of the 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^-1 K^-1 , and T is the temperature in Kelvin.We have two sets of data: k1 = 0.00313 L mol^-1 s^-1 at T1 = 25C  298.15 K  and k2 = 0.05012 L mol^-1 s^-1 at T2 = 35C  308.15 K . We can set up two equations using the Arrhenius equation: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 *  1/T1 - 1/T2  We can rearrange the equation to solve for Ea:Ea = R * ln k1 / k2  /  1/T1 - 1/T2 Plugging in the values:Ea = 8.314 J mol^-1 K^-1 * ln 0.00313 / 0.05012  /  1/298.15 - 1/308.15 Ea  -8.314 * ln 0.0624  /  -0.0034 Ea  68.5 kJ/molThe activation energy of the reaction is approximately 68.5 kJ/mol at room temperature.