Closed reactor, const. VCatalysis Conservation Laws10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. William H. Green Lecture 2: The Reaction Rate & Reaction Mechanisms The lecture covers: Definitions in terms of reacting compounds and reaction extent, rate laws, Arrhenius equation, elementary, reversible, non-elementary, catalytic reactions. From previous lecture: ,AAo A A A AdNFFGG rdVdt=−+ =∫ Example: CBA 2→+ *Reactions are reversible (often will neglect reverse) AoAAoNNXN−=A AoAAoFFXF−=A 2CCAoFXF= FAo FBo C,A,B A,B Figure 1. A reactor with reactants A and B constantly flowing in and product C and unused reactants A and B flowing out. [][][][][]literssecmoles A flowing insecmoles A flowing outsec1Ao in oinput oAooutputoutoutputininFAFAAvXAv=====−utvAvv= Closed reactor, const. V Detailed balance- all steps in equilibrium, total system [][][][][][]2AeqdArkABdtCKAB==−= when [][][]2eqCABK= the rxn. stops -> rA=0 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].[][][]2, , forward-reverse in one expressionsame!forAreveq eqkCrkAB kKK⎛⎞⎜⎟=− − =⎜⎟⎝⎠ Catalysis [][][](),may be includedi.e. when B is very smallcatalystAforward catrk AfB= Rate limiting step determines the kinetics (slow step). The kinetics are insensitive to [B] because B is not part of this slow step. [][][][][][][][]2,,2,catalystA reverse A forwardeqA net cateqCrrKABCrk AKAB=⎛⎞⎜⎟=− −⎜⎟⎝⎠ 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Lecture 2 Prof. William H. Green Page 2 of 3 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]. Stoichiometric coefficient ,,GRT o oeq f products f reactantsKe GG GΔΔΔ Δ−==− ABC→+ eqK[][][][]molesliterBCA== CK[][][]Partial PressuresIdeal Gas:BCeqooABCppKPpPARTnPpV nRTVRT===⇒= Po is the standard state pressure (1 atm), this makes the units cancel. Using partial pressures is accurate within 10%, more error with liquids. ,,A A initial A i iNNνξ=+∑ Standard state Extent of rxn. ,,1rxnNC C initial C i iiNNνξ==+∑ column columnvector vectormatrix vectoroNNνξ=+i Do columns span space? Often no, limits on what is achievable. 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Lecture 2 Prof. William H. Green Page 3 of 3 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]. () ()dNFNdt= Figure 2. A plot of the reaction trajectory. ξ is the extent of reaction. Conservation Laws Conserve atoms 42 24 22CH O C H 2H O+→ + constant molesconst.AA BB CCCN CN CN++= 4244242,,:1 2:4 4 2CH C H C initialCH C H H O H initialCN N NHN N N N×+× =×+× + = ξ=ΝNCΑοξ t=10 t=0.01 ξ1=0 NBNAReaction trajectory- Plot state of