i seriously do not understand the formula for this problem :(
The reaction for the decomposition of dinitrogen monoxide gas to form an oxygen radical is: N2O(g)==>N2(g)+O(g) . If the activation energy is 250 kJ/mol and the frequency factor is 8.0 x 1011 s-1, what is the rate constant for the first-order reaction at 1000 K?
ln k = ln A - Ea/RT
Plug in the number and calculate k. I believe Ea must be in joules/mole and A is the frequency factor.
Here is some reading material.
http://en.wikipedia.org/wiki/Arrhenius_equation
To solve this problem, we need to use the Arrhenius equation, which relates the rate constant (k) of a chemical reaction to the activation energy (Ea), the temperature (T), and a constant known as the frequency factor (A). The Arrhenius equation is as follows:
k = A * e^(-Ea/RT)
Where:
- k is the rate constant
- A is the frequency factor
- Ea is the activation energy
- R is the gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin (K)
First, we need to convert the activation energy from kJ/mol to J/mol:
Ea = 250 kJ/mol * (1000 J/1 kJ) = 250,000 J/mol
Next, we can substitute the given values into the Arrhenius equation:
k = (8.0 x 10^11 s^-1) * e^(-250,000 J/mol / (8.314 J/(mol·K) * 1000 K))
Now let's solve it step by step:
Step 1: Simplify the units:
k = (8.0 x 10^11) * e^(-250,000 J / (8.314 KJ / mol))
Step 2: Convert kJ to J:
k = (8.0 x 10^11) * e^(-250,000 J / (8.314 KJ / mol * 1000))
Step 3: Simplify the equation within the exponential term:
k = (8.0 x 10^11) * e^(-30,051)
Step 4: Evaluate the exponential term using a calculator:
k ≈ (8.0 x 10^11) * 7.5497 x 10^(-14)
Step 5: Multiply the numbers:
k ≈ 6.03976 x 10^(-2)
So, the rate constant for the first-order reaction at 1000 K is approximately 6.03976 x 10^(-2) s^(-1).