10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. William H. Green Lecture 4: Reaction Mechanisms and Rate Laws Fundamentals of Chemical Reactions -PSSA (SS, QSSA, PSSH) -long chain approximation -rate-limiting step A+B Stable molecules: neutral, closed shells (-)(e-) (+) nucleus nucleus bond Figure 1. Stable molecules. Pauli Exclusion Principle -You can’t put 2 identical e- in the same exact spot Figure 2. Two electrons in an orbital have opposite spin. Bond Forming H + + 0 e-2 e-empty orbital H H H Figure 3. Bond formation. On the left, an empty orbital receives two electrons from another orbital. On the right, half-filled orbitals on the H atom mix to form a filled bonding orbital with two electrons. Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Boltzmann Distribution −E k T R ( ) ∼ Bp E e Bk = NA E ≫ k T → very unlikelyB E + E > EA B Activation Barrier AB Small fraction will collide correctly and react −E k T a B( ) ∼k T AeA is the prefactor, proportional to the number of ways the molecules get together with sufficient energy to react. Reactive Intermediates -charged acid/base chemistry -empty orbital metal catalyst -single e- orbital free radical Example: RC O OR + H2O ⇌ RC O OH + ROH (endo- thermic) O- k3k2k1 + ROH⇀RC OR → + RO -→OH -+ RC O OR ↽k−1 R OOH R OO-OH (acid) minor (base catalyzed) species minor (SS) species (SS) + H2O ⇌ + OH -ROO-ROOH 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Lecture 4 Prof. William H. Green Page 2 of 4 Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. O- O- O d RC OR  OH ≈ RC OR  ≈ k1 OH -  RC OR  0  OH  k−1 + k2 dt  O- k  RC OR  d [RO -] ≈ 0 RO - ≈ 2  OH  dt k3 [acid]  -rROH = k3 RO [acid]= k2  RC O-OR = k k 1 2 OH -   k−1 + k2 RC O OR OH  k eff Rate Limiting Step -Only 1 rate constant of keff is really relevant -What do you have most of in a reaction mix? This is the material preceding the rate limiting step. RC O OR + H2O ⇌ RC O OH + ROH OH kk1⇀+ R+ H++ RC O OR ↽RC OR 2 → k−1 + ROOH (acid) minor(acid catalyzed) (SS) species (SS) + k3 + R + H O →ROH+H2  OH O  d RC + OR  OH  k1 H+ RC OR  ≈ 0 RC + OR ≈ k−1 + k2 dt  OH   d [R+ ] + k2 RC + OR  dt ≈ 0 R  ≈ k [H O 3 2 ] 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Lecture 4 Prof. William H. Green Page 3 of 4 Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. OH  k k  O  + 1 2 + r = k R [H O ]= k     ROH 3   2 2 RC + OR  = k−1 + k2 H  RC OR  keff Ethylene (in plastics) C H → H +C H 2 6 2 2 4 Ethyl radical C H + Hi → H + C H i 2 6 2 2 5 C H i → C H + Hi 2 5 2 4 −r = k Hi  C H C H 1  [ 2 6 ]2 6 slow iC H inefficient, but important (radical creation) →2CH 2 6 3 CH i + C H → CH + C H i 3 2 6 4 2 5 2C H i → C H + C H (radical destruction) 2 5 2 6 2 4 (disproportionation) C H + C H → 2C H i reverse disproportionation also happens 2 6 2 4 2 5 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Lecture 4 Prof. William H. Green Page 4 of 4 Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month