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28 January Material Type: Notes; Professor: Dysleski; Class: General Chemistry II; Subject: Chemistry; University: Colorado State University; Term: Spring 2011;
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28 January For a First-order reaction A → B Rate Law: Rate = k[A] Integrated Rate Law: ln [A]t = -kt + ln [A] 0 Plot of ln [A]t vs. Time results in a linear graph For a Second-order reaction A → B Rate Law: Rate = k [A]^2 Integrated Rate Law: 1/[A]t = kt + 1/[A] 0 Plot of 1/[A]t vs. Time results in a linear graph 2N 2 O 5 (g) → 4NO 2 (g) + O 2 (g) The rate constant, k, for this reaction is 0.00681 s- What is [N 2 O 5 ] at 1.0 hour if [N 2 O 5 ] 0 = 0.200 M? Rate = k [N 2 O 5 ] Ln [N 2 O 5 ] 360 = -(0.00681)(360) + ln[.2] Ln [N 2 O 5 ] 360 = -26. [N 2 O 5 ] 360 = 4.5 x 10-12^ M Answers that wouldn’t make sense here are greater than 2.0 or negative (since it’s a reactant rate, it’s decreasing) What fraction has decomposed by 30 seconds? Ln [N 2 O 5 ] 30 = -(0.00681)(30) + ln [N 2 O 5 ] 0 Ln [N 2 O 5 ] 30 – ln [N 2 O 5 ] 0 = -(0.00681)(30)
Ln ([N 2 O 5 ] 30 / [N 2 O 5 ] 0 ) = -0. ([N 2 O 5 ] 30 / [N 2 O 5 ] 0 ) = 0. 18.5% decomposed Ln [N 2 O 5 ] 0 = 30 (for example) is solved by raising both sides from e. So [N 2 O 5 ] 0 = e^30 How long will it take half to decompose? Ln [N 2 O 5 ]t = -(0.00681)t + ln (N 2 O 5 ) 0 Ln ([N 2 O 5 ]t / [N 2 O 5 ] 0 ) = -(0.00681 s-1)t Ln ½ = -(0.00681 s-1)t T = 101 sec Half-life – the amount of time required for the reactant concentration to reach half of its initial value First-order reactions are the ONLY reactions for which the half-life is independent of concentration (the half-life is the same period each time, first half-life = second half-life = ….)