Sapling HW Week 9/10 #11

[Adam_Ventura_1H]

I am having difficulty with the second part of this question. I was able to find the half-life in hours, but I am not sure what equation I would need to use to find the concentration after a certain amount of hours.

Question: Dinitrogen pentoxide, N2O5, decomposes by first‑order kinetics with a rate constant of 3.7×10−5 s−1 at 298 K. (I found the half life to be equal to 5.20 hours)
If [N2O5]0=0.0741 mol⋅L−1, what will be the concentration of N2O5 after 3.2 h?

[Sandy Lin 1L]

To calculate the concentration you would use the 1st order integrated rate law which will be ln[N2O5] = -kt + ln[initial N2O5]. The rate constant, k is already given to you so is the initial concentration of N2O5. The time is given in hours so just make sure to convert 3.2 h into seconds.

[Scot Widjaja Dis 1J]

Using the first order equation, [N2O5] = [N2O5]0e^(-Rt), plug in the values on the right side of the equation to solve for the final concentration of N2O5. We know the rate of the constant since that was given. We also know the initial concentration since that's also given. And for time, we need to convert 3.2 hours to seconds by multiplying it by 3600. Then solve for the final concentration.