VSPDS-384 [CH3] + CH3 -> CH4 + CH4 The rate constant for this elementary reaction is constant 101.5 mmol^-1 s^-1 at 298 K. The rate constant for this reaction is 1.5 mmol^-1 s^- at 293 K, and 1.5 mmol^-1 s^-1 at 303 K. Determine the Ea and pre-exponential factor for this reaction.
First, determine the activation energy (Ea) for the reaction. Use the Arrhenius equation:
k = A * e^(-Ea / R)
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 K^-1 mmol^-1),
- T is the temperature in Kelvin.
Second, solve for Ea:
ln(k2 / k1) = -(Ea / R) * ((1 / T2) - (1 / T1))
For this example, use the 10.5 mmol^-1 s^-1 rate at 298 K and the 1.5 mmol^-1 s^-1 rate at 293 K:
ln(1.5 / 10.5) = -(Ea / 8.314) * ((1 / 293) - (1 / 298))
Solve for Ea:
Ea = -8.314 * (ln(1.5 / 10.5) / ((1 / 293) - (1 / 298))) = 9835.6 J mol^-1
Next, determine the pre-exponential factor (A):
k = A * e^(-Ea / (R * T))
Make sure the temperature is in Kelvin and solve for A:
A = k / e^(-Ea / (R * T)) = 10.5 / e^(-9835.6 / (8.314 * 298)) = 10197.8 mmol^-1 s^-1
The activation energy and pre-exponential factor for this reaction are 9855.6 J mol^-1 and 10197.8 mmol^-1 s^-1, respectively.
2月 9日 2009年