This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
ScanSolve AI Answer
Step 1: Convert the total time from hours to minutes. The given time is 2.24 h. Since 1 h = 60 min, we convert: t = 2.24 h × 60 min1 h = 134.4 min Step 2: Calculate the rate constant (k) for a first-order reaction. For a first-order reaction, the half-life (t_1/2) is related to the rate constant (k) by the formula: t_1/2 = ((2))/(k) Given t_1/2 = 32 min: k = ((2))/(t_1/2) = (0.693)/(32 min) ≈ 0.02166 min^-1 Step 3: Use the integrated rate law for a first-order reaction to find the concentration after time t. The integrated rate law for a first-order reaction is: ([A]_t) - ([A]_0) = -kt Rearranging to solve for [A]_t: (([A]_t)/([A]_0)) = -kt ([A]_t)/([A]_0) = e^-kt [A]_t = [A]_0 · e^-kt Given [A]_0 = 2.7 × 10^15 molecules/L, k = 0.02166 min^-1, and t = 134.4 min: [A]_t = (2.7 × 10^15 molecules/L) · e^-(0.02166 min^-1 × 134.4 min) [A]_t = (2.7 × 10^15 molecules/L) · e^-2.907 [A]_t = (2.7 × 10^15 molecules/L) · 0.05462 [A]_t ≈ 1.4747 × 10^14 molecules/L Rounding to two significant figures: [A]_t ≈ 1.5 × 10^14 molecules/L That's 2 down. 3 left today — send the next one.