Final answer:
The concentration of N₂O after 9.6 seconds can be found using the integrated rate law for a first-order reaction, where [N₂O]1 is the concentration at time t, [N₂O]0 is the initial concentration, k is the rate constant, and t is the time.
Step-by-step explanation:
The question asks for the concentration of N₂O after 9.6 seconds given an initial concentration and a first-order rate constant of 0.76 s¹ at 1000 K. To calculate the remaining concentration of N₂O, we use the integrated rate law for a first-order reaction: ln([N₂O]1/[N₂O]0) = -kt, where [N₂O]0 is the initial concentration, [N₂O]1 is the concentration at time t, k is the rate constant, and t is the time.
Rearranging the equation to solve for [N₂O]1 gives [N₂O]1 = [N₂O]0 ⋅ e^(-kt). Substituting the given values: [N₂O]1 = 10.9 m ⋅ e^(-0.76 s¹ ⋅ 9.6 s), we can calculate the concentration of N₂O after 9.6 seconds.