The first order rate constant of a unimolecular gas phase reaction A->...
Calculation of Activation Energy for Lindemann Mechanism
Given Data
- Unimolecular gas phase reaction A-> products
- Lindemann mechanism
- First order rate constant k1 = 2.0 s-1 at Pa = 1 atm
- First order rate constant k2 = 4.0 s-1 at Pa = 2 atm
Calculation of Activation Energy
According to the Lindemann mechanism, the rate constant k1 is given by:
k1 = (k1a * PA) / (k1a * PA + k1b)
where k1a and k1b are the rate constants for the activation and deactivation steps, respectively, and PA is the pressure of species A.
Similarly, the rate constant k2 is given by:
k2 = (k2a * PA) / (k2a * PA + k2b)
where k2a and k2b are the rate constants for the activation and deactivation steps, respectively, and PA is the pressure of species A.
Dividing the two equations, we get:
k2/k1 = (k2a * PA + k2b) / (k1a * PA + k1b)
Substituting the given values, we get:
4.0/2.0 = (k2a * 2 atm + k2b) / (k1a * 1 atm + k1b)
Simplifying, we get:
k2a + k2b = 2(k1a + k1b)
Since the overall reaction is unimolecular, the deactivation step is assumed to be negligible. Therefore, k1b is zero.
Substituting this value, we get:
k