Unit 3: KineticsHalf-LifeUnit 3Episode 13In Our Last EpisodeRate laws: Rate laws relate the concentrations of the reactants to thereaction rate at any given moment in time.rate = k[A]x[B]yIntegrated rate laws: Integrated rate laws allow us to predict how long a reaction will take, or how much of the reactant remains after a certain amount of time.[A] = [A]0– kt ln[A] = ln[A]0– kt 1/[A] = 1/[A]0– ktHalf-life (t½)How much time it takes for one half of [A]0to react away.After 1 half-life [A] = ½[A]0After 2 half lives [A] = 14[A]0After 3 half-lives [A] = 18[A]0The amount of reactant remaining after n half-lives is[A] = (½)n[A]0QuestionWhat percentage of reactant will remain after five half-lives have passed?Half-life (t½)At t½, [A] = ½[A]0We can substitute ½[A]0into the integrated rate laws and derive an equation to calculate the half-life for each order of reaction.Half-life EquationZeroZero Order Half-lifechem.libretexts.orgFirst Order Half-lifechem.libretexts.orgSecond Order Half-lifechem.libretexts.orgFormula Summary0thOrder 1stOrder 2ndOrderRate Law rate = k rate = k[A] rate = k[A]2Integrated Rate LawHalf Life EquationQuestionCompounds A and B react to form C and D in a reaction that was found to be second order overall and second order in A. The rate constant k at 30ᵒC is 0.622 M–1min–1. What is the half-life of A when 0.0410 M A is mixed with excess
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