Final answer:
To find the time required for the total pressure in a system containing N2O5 to rise to a certain value, we can use the first-order rate equation and rearrange it to solve for time. The length of time required for the total pressure to rise to 0.145 atm is approximately 40.9 seconds, and the length of time required for the total pressure to rise to 0.200 atm is approximately 57.8 seconds. After 100 seconds of reaction, the total pressure is approximately 0.006734 atm.
Step-by-step explanation:
In order to answer these questions, we need to use the first-order rate equation:
ln[N2O5] = -kt + ln[N2O5]0
Where [N2O5] is the concentration of N2O5 at time t, k is the rate constant, and [N2O5]0 is the initial concentration of N2O5.
a. Time required for the total pressure to rise to 0.145 atm:
To find the time required, we can rearrange the rate equation to solve for t:
t = (ln([N2O5]0) - ln([N2O5])) / k
Plugging in the values, we get:
t = (ln(0.1) - ln(0.145)) / 7.48 * 10-3
t ≈ 40.9 seconds
b. Time required for the total pressure to rise to 0.200 atm:
Using the same formula as above, we can find the time required:
t = (ln(0.1) - ln(0.2)) / 7.48 * 10-3
t ≈ 57.8 seconds
c. Total pressure after 100 seconds of reaction:
Again using the rate equation, we can find the concentration of N2O5 after 100 seconds:
[N2O5] = [N2O5]0 * e-kt
Plugging in the values, we get:
[N2O5] = 0.1 * e-7.48 * 10-3 * 100
[N2O5] ≈ 0.006734 atm