A first order chemical reaction has a rate constant of 8.7×103 s-1 at 30 °C and a rate constant of 5.8×104 s-1 at 64 °C.
Calculate the activation energy, Ea, for the reaction.
I keep getting 5.25e-6 kJ/mol but apparently that's not the correct answer.
ln(5.8e4/8.7e3)=-ea/8.315e-3(1/337-1/303)
I get 47,369 J using your numbers.
To calculate the activation energy (Ea) for the reaction, we can use the Arrhenius equation and the given rate constants at different temperatures.
The Arrhenius equation is given by: k = A * e^(-Ea/RT)
Where:
k is the rate constant
A is the pre-exponential factor or frequency factor
Ea is the activation energy
R is the gas constant (8.315 J/(mol*K))
T is the temperature in Kelvin
We can rearrange the equation to solve for Ea:
Ea = -R * ln(k/A) / (1/T)
Given:
k1 (rate constant) = 8.7 * 10^3 s^-1 at 30°C (303 K)
k2 (rate constant) = 5.8 * 10^4 s^-1 at 64°C (337 K)
Let's calculate Ea:
Ea = -8.315 J/(mol*K) * ln(5.8 * 10^4 s^-1 / 8.7 * 10^3 s^-1) / (1/337 K - 1/303 K)
Ea ≈ 49.37 kJ/mol
So, the correct answer for the activation energy (Ea) is approximately 49.37 kJ/mol, not 5.25e-6 kJ/mol.
Make sure to double-check the calculations and be careful with units when performing these calculations.