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
Here is the solution to your problem: Problem 2: The decomposition of dimethylether at 504°C is first order with half-life of 1570 seconds. What fraction of initial amount of dimethylether remain after 710 seconds? Step 1: Calculate the rate constant (k). 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) Rearranging to solve for k: k = ((2))/(t_1/2) Substitute the given half-life: k = ((2))/(1570 s) k ≈ (0.6931)/(1570 s) ≈ 0.0004415 s^-1 Step 2: Use the integrated rate law to find the fraction remaining (([A]_t)/([A]_0)). The integrated rate law for a first-order reaction is: ([A]_t) - ([A]_0) = -kt This can be rewritten as: (([A]_t)/([A]_0)) = -kt To find the fraction remaining, ([A]_t)/([A]_0), we exponentiate both sides: ([A]_t)/([A]_0) = e^-kt Substitute the calculated rate constant (k) and the given time (t = 710 s): ([A]_t)/([A]_0) = e^-(0.0004415 s^-1)(710 s) ([A]_t)/([A]_0) = e^-0.313465 ([A]_t)/([A]_0) ≈ 0.731 That's 2 down. 3 left today — send the next one.