Chemistry 4011/8011 Wednesday, September 27 Discussion Question 1. Although gaseous methyl isocyanide (CH3NC) can be stably isolated and bottled at low temperature, at 273 K it isomerizes over the course of hours to acetonitrile (CH3CN), which condenses from the gas as a liquid. The graphs below show how the measured pressure in a sealed container of CH3NC drops with time as the gas is converted to CH3CN liquid. a) Are these graphs consistent with first-order kinetics (in CH3NC)? Can you estimate a rate constant k from these graphs? b) From the integrated rate law for this process and your rate constant k, estimate the half-life t½ for this reaction (where [CH3NC]t /[CH3NC]0 = 0.5). Does this calculated t½ match the data on the graph?1. a) P ∝ [CH3NC], so 00]NCCH[]NCCH[33 ttPP=. If the reaction displayed first-order kinetics, the graph could be fit to kttPP−= e0, or to ln Pt = ln P0 – kt . If you use this second equation, the slope of the graph is equal to k. Here, k ~ 5 × 10-5 /sec. b) 00]NCCH[]NCCH[33ttPP== 0.5 = e-kt. t½ = k).ln( 50 = 14,000 sec.Background Signal in Kinetic DataWhat if the CH3NC was contaminated with 150 torr of air?Background Signal in Kinetic DataFit to[A]0= 150 torrk = 5 × 10-5/secktt−= eYY0Background Signal in Kinetic DataFit toY0= 150 torrk = 5 × 10-5/secFit toktt−= eYY0Y0= 281 torrk = 1.4 × 10-5/secwrong!ktt−= eYY0Fits search for only 2 variables (Y0and k).Background Signal in Kinetic DataY0Y∞(asymptote)We know this, but error in data may make it better to assume we don’t.We don’t know this.Background Signal in Kinetic DataY0Y∞(Yt)t]A[∝t]A[∝kttt−∞∞=−−= eYYYY]A[]A[00()ktt−∞∞−+= eYYYY0Background Signal in Kinetic DataY0Y∞(Yt)kttt−∞∞=−−= eYYYY]A[]A[00()ktt−∞∞−+= eYYYY0Optimize for Y0, Y∞, ksimultaneously.Because function cannot be expressed in terms of y = mx + b, is fit by non-linear
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