A sample of C60O3 decomposes with an activation energy of 50 kg/mol, an Arrehnius pre-factor of 2e10 s-1 and a k value of .04 s-1. How long does it take for a 25 mg sample at 25 degrees C to produce 10 mg.
Is that C60O<suh>3 or what? And I thought Arrhenius equation had to do with k1 and k2 at T1 and T2 and T1 and T2 are tempeataures, not time.
Yes the compound is C(sub 60)O(sub 3). Sorry, the Arrenhnius stuff was to solve part a to find the k value and I understood that so I just added what I found for k. I thought you are supposed to use the equation, concentration of A equals initial concentration of A times e^(-kt) but I wasn't sure if i could just use the mg as the concentrations or if I had to convert the mg to M.
To solve this problem, we can use the Arrhenius equation, which relates the rate constant (k) to the activation energy (Ea), the Arrhenius pre-factor (A), and the temperature (T):
k = A * e^(-Ea / (R * T))
Where:
- k is the rate constant
- A is the Arrhenius pre-factor
- Ea is the activation energy
- R is the ideal gas constant (8.314 J/mol·K)
- T is the temperature in Kelvin
First, let's convert the given quantities to the appropriate units:
- Activation energy (Ea) = 50 kg/mol = 50,000 g/mol
- Arrhenius pre-factor (A) = 2e10 s^-1
- Temperature (T) = 25 degrees C = 298 K
Next, we need to find the rate constant (k) by rearranging the Arrhenius equation:
k = A * e^(-Ea / (R * T))
Plugging in the values, we get:
k = (2e10 s^-1) * e^(-50,000 g/mol / (8.314 J/mol·K * 298 K))
Calculating this expression will give us the rate constant (k). Once we have the rate constant, we can use it to determine the time required for the sample to produce 10 mg from 25 mg.
Given that the rate constant (k) is 0.04 s^-1, we can use the first-order reaction rate equation:
k = ln(N0/Nt) / t
Where:
- N0 is the initial amount of substance
- Nt is the final amount of substance
- t is the time
We are given N0 = 25 mg and Nt = 10 mg. Plugging these values in, we can rearrange the equation to solve for the time (t):
t = [-ln(Nt/N0)] / k
Calculating this expression will give us the time required for the sample to produce 10 mg from 25 mg at 25 degrees C.