Given that the initial rate constant is at an initial temperature of 25 degrees C, what would the rate constant be at a temperature of 130 degrees C for the same reaction described in Part A?
What I need help with is how to set up the equation. I have the Ea, which is 41.4 degrees C, and the activation energy, which is 32.9 kJ/mol.
You have a typo in your post. I don't know what Ea is, either 32.9 or 41.4.
From the data you have and from what I remember about earlier posts I think it is this.
k1 = not given but refers to problem x @ 298.15
k2 = ? @ 403.15
ln(k2/k1) = (Ea/R)(1/298.15 - 1/403.15) and you want to solve for k2.
To determine the rate constant at a different temperature using the Arrhenius equation, you need the activation energy (Ea), the gas constant (R), the initial rate constant (k1) at the initial temperature (T1), and the final temperature (T2).
The Arrhenius equation relates the rate constant (k) to the temperature (T) through the activation energy (Ea):
k = Ae^(-Ea/RT)
Where:
- k is the rate constant
- A is the pre-exponential factor or frequency factor, which represents the fraction of collisions with the correct orientation and enough energy to result in a successful reaction.
- R is the gas constant (8.314 J/mol·K)
- T is the temperature in Kelvin (K)
- Ea is the activation energy
To set up the equation, follow these steps:
Step 1: Convert temperatures to Kelvin.
Convert both the initial temperature (25°C) and the final temperature (130°C) to Kelvin (K) by adding 273.15 to each value:
T1 = 25°C + 273.15 = 298.15 K
T2 = 130°C + 273.15 = 403.15 K
Step 2: Calculate the rate constant at the initial temperature (k1).
Given that the initial rate constant (k1) is provided, you can directly use it.
Step 3: Plug in the values into the Arrhenius equation to calculate the rate constant at the final temperature (k2).
Use the following equation:
k2 = k1 * e^((Ea/R) * (1/T1 - 1/T2))
Where:
- k2 is the rate constant at the final temperature (T2)
- k1 is the initial rate constant at the initial temperature (T1)
- Ea is the activation energy in J/mol
- R is the gas constant (8.314 J/mol·K)
- T1 is the initial temperature in Kelvin (K)
- T2 is the final temperature in Kelvin (K)
For your specific example, plug in the values:
Ea = 32.9 kJ/mol = 32.9 * 10^3 J/mol (convert kJ to J)
R = 8.314 J/mol·K
T1 = 298.15 K (initial temperature)
T2 = 403.15 K (final temperature)
k1 = the given initial rate constant
Substituting the values, the equation becomes:
k2 = k1 * e^((32.9 * 10^3 J/mol / (8.314 J/mol·K)) * (1/298.15 K - 1/403.15 K))
Evaluating this equation will give you the rate constant (k2) at the final temperature (130°C).