Question

A reaction is followed and found to have a rate constant of 3.36 x 10⁴ m⁻¹s⁻¹ at 344 k and a rate constant of 7.69 m⁻¹s⁻¹ at 219 k. Determine the activation energy for this reaction.

Answer 1

The activation energy for the reaction can be determined using a derived form of the Arrhenius equation given two sets of rate constants and temperatures. Substituting the provided values and solving the equation results in an activation energy of approximately 87.1 kJ/mol.

Step-by-step explanation:

To determine the activation energy for a reaction, the Arrhenius equation is typically used which is formulated as: 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, and T is the temperature.

However, in this context, we are provided with two sets of rate constants (k) and temperatures (T). Therefore, we resort to a derived form of the Arrhenius equation: ln(k2/k1) = -Ea/R * (1/T2 - 1/T1).

Inputting the known values: ln(7.69/33600) = -Ea/8.314 *(1/219 - 1/344). Solving for Ea yields an activation energy approximately equal to 87,095 J/mol. Remember to convert the energy into kJ/mol if necessary, which will be approximately 87.1 kJ/mol.

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