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Unformatted text preview: INTEGRATED RATE LAW So far we have used differential rate laws e.g., for aA → products rate =  ∆ [A]/ ∆ t = k[A] x (a differential eqn) Integration gives [A] as a function of t (more useful) 1 st order reaction (x = 1): ln([A] /[A]) = 2.303 log ([A] /[A]) = kt or [A] = [A] ekt 2 nd order reaction (x = 2): 1/[A] = kt + 1/[A] GRAPHICAL ANALYSIS 1 st order : ln[A] = kt + ln[A] Plotting ln[A] vs. t ⇒ straight line slope = k intercept = ln[A] CH 3 N ≡ C: → CH 3 C ≡ N: 1 st order reaction A [ ] = [ A ] t = e − kt n [A] = n[A] − k t Integrated first order rate law: concentration as a function of time Half lives Half life ≡ time it takes for rxn to go halfway to completion e.g. A → products t 1/2 is where [A] = 1/2[A] For 1 st order rxns: ln([A] /[A]) = ln(2) = kt 1/2 t 1/2 = ln2/k = .693/k Note for a 1 st order reaction t 1/2 doesn’t depend on concentration E.g. nuclear decays: 14 C → 14 N + e t 1/2 = 5730 years (carbon dating) HALF LIFE CONTD....
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This note was uploaded on 10/04/2011 for the course CHEM 437623 taught by Professor Sherylrummel during the Spring '10 term at Pennsylvania State University, University Park.
 Spring '10
 SHERYLRUMMEL

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