Final answer:
The activation energy (Ea) is calculated using the rearranged two-point form of the Arrhenius equation by measuring rate constants at two different temperatures and solving for Ea.
Step-by-step explanation:
To calculate the activation energy (Ea) from the Arrhenius equation, one can use the equation in its logarithmic form. The Arrhenius equation is given by k = Ae-Ea/RT, where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. By taking the natural logarithm of both sides of the equation, it becomes ln(k) = ln(A) - Ea/RT. If we measure the rate constant k at two different temperatures, we can rearrange this form into a two-point formula to solve for Ea directly:
ln(k2/k1) = -Ea/R (1/T2 - 1/T1)
Where k1 and k2 are the rate constants at temperatures T1 and T2, respectively. Rearranging for Ea we get:
Ea = -R [ln(k2) - ln(k1)] / (1/T2 - 1/T1)
This allows us to solve for the activation energy without needing the frequency factor A.