if the activation energy for a given compound is found to be 10 kJ/mol, with a frequency factor of 4.0x10^13 s-1, what is the rate constant for this reaction at 398K?
k = Ae(-Ea/RT)
You can read more about it here.
http://en.wikipedia.org/wiki/Arrhenius_equation
I should have written Ea as Ea. Ea is the activation energy.
To find the rate constant for a reaction, you can use the Arrhenius equation. The Arrhenius equation relates the rate constant (k) of a reaction to the activation energy (Ea), the frequency factor (A), and the temperature (T). The equation is given by:
k = A * exp(-Ea / (R * T))
Where:
k = rate constant
A = frequency factor
Ea = activation energy
R = gas constant (8.314 J/(mol K))
T = temperature in Kelvin
Given:
Ea = 10 kJ/mol = 10000 J/mol
A = 4.0×10^13 s^–1
T = 398 K
Now, plug in the given values into the Arrhenius equation and solve for k:
k = A * exp(-Ea / (R * T))
k = (4.0×10^13 s^–1) * exp(-(10000 J/mol) / (8.314 J/(mol K) * 398 K))
Since you have temperature in Kelvin, you can simplify further:
k = (4.0×10^13 s^–1) * exp(-(10000 J/mol) / (3299.672 J/mol))
k ≈ (4.0×10^13 s^–1) * exp(-3.033)
After evaluating the exponential term, you can calculate the approximate value of k.