Day12 - CE 561 Lecture Notes Fall 2009 Day 12 Unimolecular...

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CE 561 Lecture Notes Fall 2009 p. 1 of 11 Day 12: Unimolecular Reactions and Pressure Dependent Rate Parameters A unimolecular reaction is an elementary reaction that nominally involves only one reactant. This could be an isomerization, such as CH 3 NC CH 3 CN In this case, the reaction is also unimolecular in the reverse direction. A unimolecular decomposition is a reaction such as CH 3 CH 2 Cl C 2 H 4 + HCl, or C 2 H 6 2 CH 3 . In these cases, the reverse reaction is bimolecular. These reactions, in the gas phase, have rates that depend not only on the concentration of the reactant, but also on the total concentration of all species (or, equivalently, the total pressure). The first qualitatively correct explanation for the pressure dependence of these reactions was presented by Lindemann in 1922. He correctly reasoned that only molecules with total energies greater than some critical energy were capable of reacting, and that the molecules must obtain this energy through collisions with other molecules. He wrote the overall reaction process as A + M A* + M with rate constant k 1 A* + M A + M with rate constant k -1 A* Products with rate constant k 2 where A is the reactant, and A* is a reactant molecule with sufficient energy to react. M is any molecule. It is assumed that A is energized and de-energized by a single collision. This is known as the strong collision assumption . If we apply the pseudo-steady-state approximation to A* in this mechanism we obtain: 112 [ ]* 0 [ ][ ] [ *][ ] [ *] dA k A MkA Mk A dt = = −− so the concentration of A* is 1 12 [ ][ ] [ *] [] kAM A kM k = + The reaction rate (the production rate of products) is 2 [ ][ ] [Products] [ ] [ *] kk A M d kA dt dt k M k = −= = + and the effective unimolecular rate constant is given by uni kk M k = + . At high pressures ([M] ) this becomes k uni = k 1 k 2 / k -1 ( k ), and the effective rate constant is independent of pressure. At low pressures ([M] 0) this becomes k uni = k 1 [M] ( k o ), and the effective rate constant is directly proportional to pressure. This low-pressure limit is called the
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CE 561 Lecture Notes Fall 2009 p. 2 of 11 bimolecular limit, since the reaction behaves as a second order (bimolecular reaction). k 1 can be identified as the bimolecular rate constant. It is reasonable to assume that every collision of A* leads to de-energization, and therefore k -1 can be equated to the gas-kinetic collision rate constant. However, only a small fraction of the collisions of A lead to energization (creation of A*) so k 1 is not simply a collisional rate constant. For this simple theory, called the Lindemann-Hinshelwood or Lindemann-Christiansen theory, a log-log plot of the unimolecular rate constant ( k uni ) looks like: The pressure range where the rate goes from the high pressure regime (rate independent of pressure) to the low-pressure regime (rate proportional to total pressure) is known as the falloff regime . The pressure range over which this happens is frequently identified by stating the pressure ( p 1/2 ) at which the observed rate constant ( k uni ) is one-half of the high pressure rate constant ( k
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Day12 - CE 561 Lecture Notes Fall 2009 Day 12 Unimolecular...

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