The activation energy for a reaction is 37.6 kJ/mole. The rate constant for the reaction is 5.4 x 10-3 s-1 at 45 oC, Calculate the rate constant at 145 oC.
Don't you use the Arrhenius equation?
To calculate the rate constant at 145°C, we can use the Arrhenius equation. The Arrhenius equation describes the temperature dependence of the rate constant for a chemical reaction.
The Arrhenius equation is given as:
k = A * e^(-Ea/RT)
Where:
- k is the rate constant
- A is the pre-exponential factor or frequency factor (a constant specific to each reaction)
- Ea is the activation energy
- R is the gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin
To solve this problem, we need to convert both temperatures to Kelvin.
Given information:
- Activation energy (Ea) = 37.6 kJ/mol
- Rate constant (k) = 5.4 x 10^(-3) s^(-1) (at 45°C)
Step 1: Convert temperatures to Kelvin
To convert temperatures from Celsius to Kelvin, use the equation:
T(K) = T(°C) + 273.15
So, for 45°C:
T1 = 45 + 273.15 = 318.15 K
And for 145°C:
T2 = 145 + 273.15 = 418.15 K
Step 2: Calculate the rate constant at 145°C
Now, we can use the Arrhenius equation to find the rate constant (k2) at 145°C:
k2 = A * e^(-Ea/RT2)
Substituting the given values:
k2 = A * e^(-Ea/(R * T2))
Step 3: Solve for k2 using the given values:
k2 = (5.4 x 10^(-3) s^(-1)) * e^(-((37.6 kJ/mol) * 1000)/(8.314 J/(mol·K) * 418.15 K))
Note: We multiplied the activation energy by 1000 to convert kJ to J.
Now, calculate the value using a calculator or software:
k2 ≈ 2.865 x 10^(-2) s^(-1)
Therefore, the rate constant at 145°C is approximately 2.865 x 10^(-2) s^(-1).