For a particular reaction, the rate constant is 2.32 ✕ 10−3 M/s at 185°C and 3.70 ✕ 10−3 M/s at 235°C. What is the activation energy for this reaction?
_______ kJ/mol
Use the Arrhenius equation. Post your work if you get stuck.
To determine the activation energy for a reaction, we can use the Arrhenius equation. The Arrhenius equation relates the rate constant (k) of a reaction to the temperature (T) and the activation energy (Ea):
k = A * e^(-Ea/RT)
Where:
- k is the rate constant,
- A is the pre-exponential factor (also known as the frequency factor),
- Ea is the activation energy,
- R is the gas constant (8.314 J/(mol·K)),
- T is the absolute temperature.
We can use this equation to set up a system of equations using the given temperature and rate constant values. Rearranging the equation, we have:
ln(k1/k2) = Ea/R * (1/T2 - 1/T1)
Where:
- k1 and k2 are the rate constants at temperatures T1 and T2, respectively.
Using the given values:
- k1 = 2.32 ✕ 10^-3 M/s at 185°C (converted to Kelvin: 185°C + 273.15 = 458.15 K),
- k2 = 3.70 ✕ 10^-3 M/s at 235°C (converted to Kelvin: 235°C + 273.15 = 508.15 K).
Substituting these values into the equation:
ln(2.32 ✕ 10^-3 / 3.70 ✕ 10^-3) = Ea/8.314 * (1/508.15 - 1/458.15)
By substituting these values into a scientific calculator or spreadsheet, we can solve for Ea.
Using ln(2.32 ✕ 10^-3 / 3.70 ✕ 10^-3) ≈ -0.444
-0.444 = Ea/8.314 * (1/508.15 - 1/458.15)
Simplifying the equation:
-0.444 = Ea/8.314 * (0.00196 - 0.00218)
Solving for Ea:
Ea = -0.444 * 8.314 / (0.00196 - 0.00218)
Calculating this expression gives the value of Ea.