Tutorial Chemical Reaction Engineering:

Transcription

1 Dipl.-Ing. ndreas Jöre Tutorial hemical Reaction Engineering: 6. Kinetics II Institute of Process Engineering, G25-27, 26-May-5

2 Tas 6.: yrene polymerization in an isothermal batch reactor T cool M T cool TIR t / h c / mol/l c / mol/l c / mol/l, T383 K, T393 K, T403 K c (t = 0) = 5 mol/l V R = const r c n Rate law: Determine inetic parameters using the differential and integral method Determine activation energy and collision factor RE: Kinetics II 26-May-5 2

3 Differential Method First step: reactor model! Mass balance General form of a balance equation: ccumulation = (Input - Output) ± Source/Sin For a batch system: dc dt c n Differential method: Linearize mass balance! Use logarithm dc n c ln ln ln dt ST Linear function with slope n and intersection ln() Linear regression will lead to inetic parameters! RE: Kinetics II 26-May-5 3

4 Differential Method pproximation of the derivative with finite differences and using an averaged styrene concentration dc c c, j c c, j, j 2 n c, j, j, j ln ln ln ln ln dt t t j j j t j c c c ln t 403 K n 383 K.5 n n l mol s 393 K 393 K n n l mol s 383 K 403 K n n l mol s ln c RE: Kinetics II 26-May-5 4

5 Integral Method lternative: Solve mass balance ODE to get an explicit expression for c as a function of time t (remember tutorial 5!) dc c c,0 dt n c n n cˆ dcˆ dtˆ n n,0 t0 c c t c t n t c t n n,0 Perform linear regression c c,0 T For n =.5 Linearization c c 2 t,0 383 K 393 K l mol s l mol s t 403 K l mol s RE: Kinetics II 26-May-5 5

6 Temperature dependence of rate constants: rrhenius equation ctivation energy G E RT exp T Reactand E ollision factor Linearization of the rrhenius equation: Product ξ ln ln E R T Perform linear regression to obtain the activation energy (slope) and collision factor (intersetction) RE: Kinetics II 26-May-5 6

7 rrhenius plot: ln E.73 0 l mol s 04.5 J/mol T RE: Kinetics II 26-May-5 7

8 Non-idealities far away from infinite dilution: onsideration of activities instead of concentrations? Eyring-Theory! * + P Fast quasi-equilibrium between reactants and activated complex! Rate approach for product formation: mol r c * and r ls o a * * c * c ci K with ai i a a c c c c c K c K c o o c * c c * * K o c * n r c c c c n o G Reactand E P Product g E -models, NRTL, UNIF, UNIQU, P(P)-SFT In general: difficult! ξ RE: Kinetics II 26-May-5 8

9 Summary Tas 6.: alance equation and inetic approach is needed Two methods: Differential method and Integral method Differential method is easy to apply Linearization yields good approximations of the reaction order and rate constants Integral method yields better rate constants but the reactor model has to be integrated sometimes not possible or difficult RE: Kinetics II 26-May-5 9

10 Tas 6.2: Langmuir isotherm, Specific surface Homogeneous systems Now: Heterogeneous systems M TIR T cool T cool RE: Kinetics II 26-May-5 0

11 Now: Phenomena on surfaces that lead to chemical reactions Important: dsorption haracterization of material properties and mathematical description! + atalyst * * Tas 6.2: Langmuir isotherm, Specific surface of microporous coal N 2 PIR oal mass m =.37 g Temperature T = 77 K p N n / bar / mmol 2 2 N,ads RE: Kinetics II 26-May-5

12 an measurements be described with the Langmuir-isotherm? Physical adsorption van-der-waals forces / interactions pv nrt p Without adsorbent With adsorbent n ads n Isotherm: Plot of adsorbed amount of substance vs. pressure n ads n mono monolayer capillary condenstion ssumptions for Langmuir isotherm: Only monolayers No interactions between adsorbed molecules No interactions between adsorption sides Energetically equivalent adsorption sides Uniform surface p RE: Kinetics II 26-May-5 2

13 Definition: Surface coverage n n ads mono 0 We consider adsorption and desorption as equilibrium reaction N 2 r r N 2 * Surface balance: N 2 free Rate approach: Power law r r p N2 free r r pn2 free N2 N2 pn 2 N 2 N : b 2 RE: Kinetics II 26-May-5 3

14 Langmuir-isotherm continued: b p N N N N b p b p b p N N N N N N N N N b p n N 2 b p n N N N,ads N N mono 2 2 Θ Langmuir-Isotherm p Linearization yields: n n n b p N,ads mono mono N N Perform linear regression to obtain the quantities of interest! RE: Kinetics II 26-May-5 4

15 Linear regression of the Langmuir-isotherm to experimental data n N,ads 2 n mono b N mmol 0.99 bar p N 2 The good fit indicates that the measurements can be described with a Langmuir-isotherm! RE: Kinetics II 26-May-5 5

16 oal sample characteristics: Specific monolayer capacity: n mono mmol/g m Sample surface: S nmonon N 653. m 2 2 o / molecule vogadro constant mol 23 rea corresponds to 3 tennis courts! Specific coal surface: ˆ S S 476 m m g 2 RE: Kinetics II 26-May-5 6

17 Tas 6.3: Heterogeneous atalysis Langmuir-Hinshelwood-mechanism (two reactants adsorbed) + atalyst +[*] r r * +[*] r r * r *+* * + r * r * * Rate approach for Langmuir-Hinshelwood inetics: RE: Kinetics II 26-May-5 7

18 Tas 6.3: Heterogeneous atalysis Eley-Rideal-mechanism (one reactant adsorbed, one gas-phase) + atalyst r +[*] * r r *+ * * + r * Rate approach for Eley-Rideal inetics: r p RE: Kinetics II 26-May-5 8

19 omparison of the two mechanisms for + : Perform experiment (eep p const and increase p ) chec which mechanism fits best! rate p = const st order for 0 zeroth order for Eley-Rideal Langmuir-Hinshelwood negative order for 0 p This tutorial: Langmuir-Hinshelwood approach! onsidering Langmuir-adsorption Reaction driving force: Surface concentration! Site balance: free r RE: Kinetics II 26-May-5 9

20 Derivation of the rate expression as a function of the partial pressures r p p : p free r p : p r pfree with b p r free with b p 0 bp b p b p RE: Kinetics II 26-May-5 20

21 Derivation of the rate expression as a function of the partial pressures bp b p b p r * * bb pp pp b p b p + b p b p RE: Kinetics II 26-May-5 2

22 If additional adsorption of occures: r p free r r p free r r pfree r free p p p bp + b p b p b p bp + b p b p b p bp i i Multi-Langmuir equation: i + bp j j j r * * bb pp pp b p b p b p + b p b p b p RE: Kinetics II 26-May-5 22