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# Chem Reaction Engr CHE 4210

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This 62 page Class Notes was uploaded by Kaela Funk on Wednesday October 21, 2015. The Class Notes belongs to CHE 4210 at Tennessee Tech University taught by Holly Stretz in Fall. Since its upload, it has received 44 views. For similar materials see /class/225686/che-4210-tennessee-tech-university in Chemical Engineering at Tennessee Tech University.

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Date Created: 10/21/15

Topic 3 Chemical Equilibria Reactions proceed until they reach equilibrium composition 30 we need to understand equilibrium K depends on T but not P Use van t Hoff equation to approximate K fT Equilibrium composition depends on T P and initial conditions nK vs 1T slope can tell you if a reaction is exothermic or not Multiple reaction equilibria involves simultaneous solution of equilibrium composition ratios Equilibria for heterogeneous reactions in multiple phases may be simplified if Henry s Law applies What is the origin of the equilibrium constant Given dG SdT VdP 2 Mn J We wish to see the result when we reach equilibrium defined as dG d 0 i Gibbs energy versus reaction extent at constant T and P DUIIAZJHOIDIAZf7IAZ0 mums 19 u11y 9 7739 quotIlenuelod 4o peelsu steJ Amuse esn quotugly 19 s 9 eaugs Ozf AZ d l f 973 AZ d pue iluelsuoa 1V P AZJPAJPSDP sqqm 01H emulsan 511901 2 up quelxe 40 pp eq Rearranging AGO RT1nHaJVJ 0 Leads to familiar V expressions for K K Haj J K e AGO RT So K is a strong function of the system temperature and defines a relationship for the final composition of the reaction mixture It is not a function of the system pressure Equilibrium composition is a function of the pressure 5 Example Calculation of equilibrium composition isobutane 1butene 223trimethy1pentane 1BP Determine the equilibrium composition for this system at a pressure of 25 atm and temperature of 400 K Assume the gases are ideal and this reaction is the only one that occurs The standard Gibbs energy change for this reaction at 400 K is 372 kcalmol Calc equilibrium K aP composmon aIaB P J a 2 02yjP f Also know that mole fractions sum to one 2 1 J39 Notice that this is not enough to solve the problem3 unknowns and 2 equations One more piece of information is needed initial conditions Start with closed vessel equimolar mix of isobutane butene 72127210 6 71327230 6 nPZnPO Convert this to mole fractions Which may be scaled if we define a dimensionless reaction extent y10 Mao g ypo39i39g39 y11 Cf YB1 Cf Yp 11g Insert into the expression for K yPo 6391 39 yBo 539y10 539P Solve when yP0O yBOyIO12 520KP 5391 KP14KP 0 Solve the quadratic y 00573yB 00573yp 0885 K The equilibrium at 400 K favors the trimethylpentane product Temperature dependence of standard Gibbs energy and K Partial derivatives applied to the Gibbs equation gives us for standard state BAGO ASO W P nj We also have AGO AH TAS Solving for A80 and dividing by RT we arrive at 1 BAGquot AGO AH E M RT2 10 The LHS may be rewritten as AGO 8 RT AH0 aT RT2 which can be expressed in terms of K 8ln K AHO 8T RT2 This is the Van t Hoff equation After integrating if the standard heat capacity change is zero and AH0 is constant 11 Notice that the H0 may be a strong function of temperature but if ACP O then AHO is still fairly independent of temperature and one may use the integrated form of van t Hoff to determine an equilibrium constant at one temperature from a K given at a different temperature To check this assumption InK AHZZVJHJ 1T ACP AAABTACT2 ADT3 Not linear then ern IS not cons ant Notice that van t Hoff can be plotted as a linear relationship and the slope can tell us if the reaction is exothermic or not AH0 AH0 P RTz 81TP R 9 8T an an 1T 1T Exo if T increases K decreases Endo if T increases K increases 13 Equilibrium composition for multiple reac ons For ith reaction o Initial conditions n n10 21051 Equilibrium constant VI Kl Ha J Free energy of system must still be minimized to LGva 0 achieve equilibrium 895 J J composition 14 Example equilibrium composition for multiple reactions We now have two simultaneous reactions in a closed reactor at 400 K isobutanc 1butcnc 223trimcthylpentane IBP isobutanc 1butcnc 224trimethylpentane IBP AGO 449 kcalmol for P formation 15 n1 n10 1 2 n3 nBO l 2 nP 2 mm 61 my 2 mp 62 Convert to mole fractions where iiin nT nTO 1 2 y10 139 239 y30g139 239 y YB 1 139 239 1g139g239 yPO 139 yp0 239 Fm yP 1 39 5239 Two equilibria K yP K2 1 hhp th Two equations for two unknown extents PK1y10 391 2y30 391 392ypo V11 1 3920 PK2y10 391 2y30 1 392yp0 V21 V1 V2 0 Use starter guess from earlier example and yl0yBOO5 yP0yPOO as initial conditions to numerically solve both equations simultaneously 5 0133 5 0351 M 0031 yB 0031 yP 0258 yp 0680 Note that 2nol reaction causes the 223 isomer fraction to be reduced reducing the octane content of the product mix We would choose a catalyst to selectively produce the 223 isomer17 Alternative approachcan minimize the Gibbs energy of the system by solving an opt39mization problem see handout How do we set up initial conditions when coefficients gt 1 See Davis review 19 Example equilbrium composition for heterogeneous reactions Consider the liquidphase reaction 6 AU BU 9 CU Occurring in a 3phase system vgir gecfhases are In Intimate ABQ gas PhasCe Nonideal mixture ofA and o O O Phase II Pure liquid B 0 gja Phase III Ideal gas mixture ofA o 039 o 39 o B and C o B 20 Activity coefficients given by Margules 111 7A XCZ AAC 2ACA AAC xA 1 7C XAZ AC1 2AAC ACA xc Also given AAC14 ACA2O PA O65 atm PB O5O atm PC O5O atm 21 1 Plot the partial pressures of A and C vs xA for a vapor phase that is in equilibrium with only the AC liquid phase Compute the Henry s law constants for A and C from the Margules equation Equate fugacities at liquid PA ff ff 2 fALxAyA gas interface L Fugacity of pure liquid A at fA P system temperature is simply the vapor pressure PAO The PA Pix1n Margules equation can be used to compute 39y A P Q Vx SZ 0390 2390 7390 9390 8390 O39L Patm P P P P P 7 O N h 05 co 0 IIIIIIIIIIIIIIIIII 39U 10 gt I g U U O IIIIIIIIIIIII IIIIIII P P P P P 7 O N h 05 co 0 39Bugxgw map wOJ uonegAep eAmsod e squqxe wasRs qu 19L eloN 2 Use Henry s law to calculate the composition of all three phases for K47 What is the equilibrium pressure Assume xA is small because C is large and Henry s law is valid There are six unknowns XA XC yA yB yC system pressure Equate the fugacities of each component at gas liquid interface Mole fractions sum to one in each of the gas and A C liquid phases oChemical equilibrium provides the sixth equation 24 Start with aC K equilibrium In IquId aAaB Assume Henry s law AA fAL kAxA for component A aL fa o A A Assume fugaCIty of pure A is PAO If xC is near unity we 51L 2 x may assume C C Component B is in a all 1 pure liquid phase 25 Topic 2 Stoichiometry Elementary versus global rxn Decomposition of dinitrogen pentoxide 091911 an important reservoir of nitrogen in Antarctic stratosphere 1 2 N205 3 2 N204 02 2 N205 6 No2 NO3 3 N02 NO3NOZ 02 No 4 N02 N03 N205 5 NO N205 3 N02 1Ogg RA J Chem Phys 15 337 1947 2 N205 2N204 02 2 1 M Biodiesel combustion kinetics 9A B 1 o C H C6004 OH CCvacrc High T 39 3 02 Low T E 9 2 9 L D GeeCiro CCQCOC G F CH3 Q0 4 O Cc jer Detailed Chemical Kinetic RIechanisms CH 6 g H for Combustion of Oxygenated Fuels c c c lt C C 0 02 QH 1 x 1 1 Q C D E MF1539uer 39 WJ P112 H J C39uu39zurquot and C K Westbrook O QH 5 39 O 3 e C K H 8 qCQCOC g 0 gogc Oa 00 o CZH4 L C 0 H OH OH OH Branching B B BD combustion kinetics simple 1ABC 2 Ck zEF 3 CDk 3G 4 GLH 5H KLB 6 HDk 61 71JB 8J MB 3 AC2DH EFKLZBM Measures of reaction progress Extentofreaction i i i i i i MM moles Rate of reaction moles volsec Rate law and rate constant Elementaryr3 k3CNOZCN03 GI b I O a I 2k2k3C39N205 k2 k3 Reaction order may not have a definite meaning for a global reaction Both extent and rate of a reaction change during course of a reaction batch reactor h n39lr wx nrenhall 39 quot quot quot 39 Jialibmedia 5 portfoliotextimagesCH13FG1306J PG Production rates for each species are coupled to reaction rates through stoichiometry 2 N205 6 2 N204 02 V 1A 1 0 law of mass action for single rxn VUAj 0 Z M 0 for set of reactions V is coef cient reactants are neg products pos j is jth component i is ith rxn N 20 5 N20 4 0 221000 2 0 NO 2 No NO What is the stoichiometric matrix for the reaction set on slide 1 gtu 73 I g 273 E73 N07 7 9 VOZN gOZN IIN Do we have more info than we need in the matrix Determine the rank of the matrix Try to get 1 along diagonal Rank a matrix in Matlab transposing a matrix M files How many of these reactions are linearly independent by inspection Ans 4 10 How is production rate related to reactor design Mole balance Quick overview of the design equationsdN F F dV J 0 I J J J V State Of ow Rate of flow Rate of generation Rate of accumulation S 6668 mo of of Species j by of speciesj within the t 39 J 39 speciesj out chemical reaction system 9 of the molestime molestime system I System molestime molestime Cautionwe are assuming constant volume for these derivations 11 Batch reactor Neither inflow nor outflow while reaction is in progress Fj0Fj0 If reaction is well mixed no variation in rate throughout reactor volume so we can take rj out of the integral Putting this in integral form allows us to determine the time to reduce the initial number of moles of a reactant A to a final state dN JVUrJdV J V dt dNJ 7 Vijer t NAG dNA 1 N ViArAV 12 Topic 1 Introduction Team Activity Organize into teams of 34 Characterize your assigned reactor in bWNT 901 terms of Mixing InputsOutputs Shape Draw a cartoon diagram the simplest you can of your reactor elements Share your cartoon on the board5 min What is it that engineers would need to predict about a reactor Consider that you are trying to convince management to build a reactor to change the current design or inputs What basic principles would you then need to mathematically model the performance of a reactor Team 1 Catalytic converter CATALYTIC CONVERTER httpwwwaa1carcomIibraryconvertergif 2 Team 2 Formation of smog in the LA basin southportjplnasagov Team 3 Chemical Vapor Deposition Reactor forming computer chip films yst r r httpwwwsvmi korea comimagesphotosservices 21109 httpwww personalpsu edupce3Re search20TopicsfiesCVDI Nitra tesjpg 4 Team 4 Emulsion polymerization reactor enwikipediaorg ACRYLHJFG Team 5 Haber process for nitrogen fixation to fertilizer Pump iozi e3 ibchemcom Team 6 Fermentation reactor www biocriceedu Team 7 Cellular mitochondria as a reactor 110681JF6 nup 39 quot iquotCaI In 9 39 39 inn Characterizing chemical reactors Idealized reactor designs deviations Mixing patterns Interfaces homogenous and heterogeneous Arrangement series versus parallel Scale microfluidics to petroleum cracking Phase plasma gas liquid solid Reaction kinetics Selectivity Control of heat Temperature simulation for a See virtual demo of CSTR at Batch reactor used in adhesive virtualcvutczvirtual experimentscstr resin formulation Fluent Plug flow reactors are assumed to have good radial mixing but will have gradients along the length of the tube What overlying physics governs reactions and flow dynamics happening in these reactors 8C A V o N A R A at BSL 2nd ed p 583 11 Equation of continuity for species A in molar quantities What are the simplifying design assumptions for each of these ideal reactors Batch CSTR PFR 12 CSTR O Plug Flow Reactor 21lt A v u Io Types of chemical reactions Reaction order Zero first second Reversible irreversible Nonstoichiometric versus stoichiometric 14 Descriptions of chemical reactions kinetics Intermediates Transition state Extent of reactionkeeps track of number of times a reaction event ie productive collision occurs moles A5 739 At39V Reaction rate r o If fonvard event occurs more often than the reverse then Ag is positive If reverse event occurs more often than the fonvard then Ag is negative If the system is at equilibrium then Ag is zero Selectivity 15 Topic 4 Batch Reactor Assumptions wellmixed Composition and temperature are not functions of position only of time Independent variable Generally liquid phase density won t change much as T changes so we assume the volume is constant Advantages Disadvantages Design equation for batch reactor d E JdeVzQOCjO Q1C JRjdV t V V Start with material balance No flow in or out of reactor Constant volume Rate of production can be expressed in terms of species concentration Example production rate for single reac on ZA B Liquid phase reaction no volume change so concentration is natural unit for the mole balance Note that the rate constant k has a strong temperature dependence k k e EaRT Rate constant is quite 0 sensitive to a temperature d1n k Ea change This is the Arrhenius relationship d lT R Mini L How k changes With k1 R T2 T1 temperature NOT related to van t Hoff Ea is always positive Ink 1T Calculated variable 9 conversion Dependent variable is really moles but concentration is often a convenient unit Remember you can only do this if the reactor volume is constant h If molar denSIty changes V go back to the design R0 equation and use moles CA Example problem A 236C CA0 2 molliter CBO 5 molliter k 02 litermolhr Units of k tells you the order of the reaction 1St order time391 2nd ordervomo1 time1 How does concentration of B change with concentration of A Look for linear combinations that 0 then argument will be a constant Constant can toe 2CA CB 2CAO CBO evaluated at Initial conditions Takes care of limiting reagent Check this process get expression for CC CB 2CAOCBO2CA CB2CA1 Now solve for tbatch Substitute new relation for CB in design equation for species A A 7 rd CA dCA Separate va OI Ci kCA12CA and integrat CRC for sol p 39 this integral abxab x provide hanl Solution to tbatch 1 1 2 C tbatch 1n CA A0 k CA 1 2CA0 1 12CA0 e CA0 CA 2 01 f time kinetic order magnitude of k initial conditions What is time for 95 conversion CACA01XACAO1O95 solve for thatch f change Bo what happens to conversion

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