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
You're on a roll — Step 1: Write the integrated rate law for a first-order reaction. For a first-order reaction, the integrated rate law is given by: [A]_t = -Kt + [A]_0 where [A]_0 is the initial concentration of the reactant, [A]_t is the concentration at time t, and K is the rate constant. This can be rearranged as: (([A]_0)/([A]_t)) = Kt Step 2: Define the half-life (t_1/2). The half-life (t_1/2) is the time required for the concentration of a reactant to decrease to half of its initial value. So, at t = t_1/2, the concentration [A]_t becomes ([A]_0)/(2). Step 3: Substitute the half-life conditions into the integrated rate law. Substitute t = t_1/2 and [A]_t = ([A]_0)/(2) into the integrated rate law: (([A]_0)/([A]_0)2) = K t_1/2 Step 4: Simplify the expression. (2) = K t_1/2 Step 5: Solve for t_1/2. t_1/2 = ((2))/(K) Since (2) ≈ 0.693, the expression can also be written as: t_1/2 = (0.693)/(K) The expression for the half-life period of a first-order reaction is: t_1/2 = ((2))/(K) What's next?