2_kinetics_2 - Rate Law as a func-on of -me We are studying...

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Rate Law as a func-on of -me This is a differential equation. Integration gives [A] as a function of t 1 st order reaction (x = 1): 1 Chem 112 Integrate to get: We are studying a chemical reaction e.g., for aA products We measure the rate as a function of concentration (the rate law) rate = "# A [ ] # t = k A [ ] x rate = !" A [ ] " t = k A [ ] MJ Bojan

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n [A] = n[A] 0 k t Integrated first order rate law: concentration as a function of time 2 Chem 112 A [ ] = [ A ] t = 0 e " kt Plot the experimental results for the following Frst order reac-on: CH 3 ί N C : CH 3 ί C N : MJ Bojan
FYI: deriva-on of integrated ±rst order rate law If Δ [A] d[A] as Δ t 0 then Differential first order rate law Rearrange Integrate: at t = 0, [A] = [A] 0 Integrated first order rate law: concentration as a function of time 3 Chem 112 rate = "# A [ ] # t = k A [ ] " A [ ] A [ ] = # k " t d A [ ] A [ ] = " kdt d A [ ] A [ ] A [ ] 0 A [ ] " = # k dt 0 t " ln A [ ] # ln A [ ] 0 = ln A [ ] A [ ] 0 = # kt MJ Bojan

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INTEGRATED RATE LAW 2nd order reac-on 2 nd order reaction (x = 2): differential rate law Integrate to get: rate = "# A [ ] # t = k A [ ] 2 1 A [ ] = k t + 1 A [ ] 0 MJ Bojan Chem 112 4
FYI: deriva-on of integrated second order rate law If Δ [A] d[A] as Δ t 0 then Differential second order rate law Rearrange Integrate: at t = 0, [A] = [A] 0 Integrated 2 nd order rate law: concentration as a function of time 5 Chem 112 rate = "# A [ ] # t = k A [ ] 2 " A [ ] A [ ] 2 = # k " t d A [ ] A [ ] 2 = " kdt " d A [ ] A [ ] 2 A [ ] 0 A [ ] # = k dt 0 t # 1 A [ ] " 1 A [ ] 0 = kt MJ Bojan

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Example Take data Calculate these Time(s) [NO 2 ]M ln [NO 2 ] 1/[NO 2 ] 0.0 0.01000 4.610 100 50.0 0.00787 4.845 127 100.0 0.00649 5.038 154 200.0 0.00481 5.337 208 300.0 0.00380 5.573 263 6 Chem 112 Reaction: NO 2 (g) NO + ½ O 2 Measure [NO 2 ] as a function of time. Is reaction first or second order? (How do you know?) MJ Bojan
Example Con-nued Is reaction first or second order?

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This note was uploaded on 01/18/2012 for the course CHEM 112 taught by Professor Vandersluys,lorschmid,kylem during the Summer '07 term at Pennsylvania State University, University Park.

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2_kinetics_2 - Rate Law as a func-on of -me We are studying...

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