ERT 316: REACTION ENGINEERING CHAPTER 3 RATE LAWS & STOICHIOMETRY

Transcription

1 ER 316: REIO EGIEERIG HER 3 RE LWS & SOIHIOMERY 1

2 OULIE R 1: Rte Lws Reltive Rtes of Retion Retion Orer & Rte Lw Retion Rte onstnt, k R 2: Stoihiometry th System Stoihiometri le low System Stoihiometri le lultion for onentrtion in terms of onversion

3 1. RELIE RES O REIO r r r r Retion Stoihiometry EMLE 2O O O r O 2 r O 2 O r 2 2 If O 2 forme t 4 mol/m 3 /s (r O2 = 4 mol/m 3 /s), wht is the rte of formtion of O?

4 1. RELIE RES O REIO 2O O O r O 2 r O 2 O If O 2 forme t 4 mol/m 3 /s (r O2 = 4 mol/m 3 /s), wht is the rte of formtion of O? r 2 2 r O r O2 2 2 r O 2 4mol / m 2 3 / s r O 2 4mol / m 2 3 / s 4mol / m 3 / s

5 1. RELIE RES O REIO EERISE he Retion: 23 5 is rrie out in retor. If t prtiulr point, the rte of ispperne of is 1 mol/m 3 /s, wht re the rtes of n?

6 1. RELIE RES O REIO 23 5 he reltive rtes re r 2 r 3 r 5 Given, the rte of ispperne of, -r, is 1mol/m 3 /s hus, solving the rtes of & ; r = -1 mol/m 3 /s r r 2 3 r 3 1mol / m 3 / mol / m / s s r r r 1mol / m / mol / m / s s

7 2. REIO ORER & RE LW Rte lw is kineti expression tht gives the reltionship etween retion rte, -r, n onentrtion. he retion rte (rte of ispperne) epens on temperture n omposition. It n e written s the prout of retion rte onstnt, k n funtion of onentrtions (tivities) of the retnts involve in the retion: r k fn,...

8 2. REIO ORER & RE LW Rte lw is kineti expression tht gives the reltionship etween retion rte, -r, n onentrtion. or retion in whih the stoihiometri oeffiient is 1 for LL speies: 1OH 1Hl 1l 1H O 2 we shll elete the susript on the speifi retion rte, (e.g.; in k ) to let k koh khl kl kh2o

9 2.1 OWER LW MOELS & ELEMERY RE LWS ower Lw Moel: r k he rxn is α orer wrt retnt he rxn is β orer wrt retnt he overll orer of the retion, n; n

10 2.1 OWER LW MOELS & ELEMERY RE LWS he unit of the speifi retion, k, will vry with the orer of retion. routs Zero orer (n=) irst orer (n=1) Seon orer (n=2) hir orer (n=3) k onentrtion ime r k r k 1n 3 k mol / m s 1 k s 2 r k 3 k m / mol s r k k m 3 / mol s

11 2.1 OWER LW MOELS & ELEMERY RE LWS Elementry retion: hemil retion in whih one or more of the hemil speies ret iretly to form prouts in single retion step n with single trnsition stte. routs Unimoleulr retion routs imoleulr retion Elementry rte lw: he rxn is si to follow the elementry rte lw if the stoihiometi oeffiients re IEIL to the retion orer of eh speies. 2O O O r k O 2 2 O 2 O O 2 2

12 EMLES O REIO RE LWS

13 EMLES O REIO RE LWS

14 EMLES O REIO RE LWS

15 2.2 O-ELEMERY RE LWS on-elementry rte lws: retions tht o not follow simple rte lws (power rte lws). Exmple 1: Homogeneous Rxn O l 2 Ol 2 he kineti rte lw is: Gs phse synthesis of phosgene r k O O 3 2 l 2 Rxn orer: first orer wrt to O, three-hlves orer wrt l 2, five-hlves orer overll.

16 2.2 O-ELEMERY RE LWS Exmple 2: Heterogeneous Rxn 6H5H3 H2 6H6 H 4 t he rte of ispperne of toluene per mss of tlyst is : r ' 1 H 2 K k where K & K is the sorption onstnts. H t 2 K M Gs-soli tlyze rxn: Hyroemethyltion of toluene () In terms of prtil pressure rther thn onentrtions follows Lngmuir- Hinshelwoo kinetis

17 2.3 REERSILE REIOS or reversile rxn, ll rte lws must reue to the thermoynmi reltionship relting the reting speies onentrtions t equilirium. K e e e e hermoynmi Equilirium Reltionship

18 2.3 REERSILE REIOS EMLE: omintion rxn of 2 mol of enzene to form 1 mol H 2 n 1 mol iphenyl. symolilly; 2 H H H 6 r k 6 k k - k 2, forwr H 2 k - he rte of ispperne of enzene; OR 2 r k 2, forwr he reverse rxn tween iphenyl & hyrogen; k - 12H1 H2 26H 6 he rte of formtion of enzene (in reverse iretion); r k, reverse H 2

19 2.3 REERSILE REIOS he net rte of formtion of enzene is; Multiplying oth sies y -1, we otin the rte lw of ispperne of enzene, -r reverse forwr net r r r r,,, 2 2 H k k 2 2 H k k r 2 2 H k k k

20 2.3 REERSILE REIOS Repling the rtio of the reverse & forwr rte lw onstnt y equilirium onstnts; where K k k 2 2 H k k k r H K k r 2 2 onentrtion equilirium onstnt

21 3. HE REIO RE OS k e E / R rrhenius eqution = preexponentil ftor or frequeny ftor E= tivtion energy, J/mol or l/mol R=gs onstnt = J/mol-K = l/mol-k = solute temperture, K E R e / -no of ollision -proility tht the ollision will result in retion

22 3. HE REIO RE OS k e E / R tivtion energy is mesure of the minimum energy tht the reting moleules must hve in orer for the retion to our (energy require to reh trnsition stte). rnsition stte Energy rier k - no of ollision tht result in rxn -totl no of ollision Retnts routs E e / R proility tht - the ollision will result in rxn

23 3. HE REIO RE OS k e E / R king nturl logrithm; ln E 1 k ln R E, k, -r = he lrger the tivtion energy, the more temperture sensitive k n thus the retion rte.

24 4. H SYSEMS SOIHIOMERI LE urpose of eveloping stoihiometri tle: o etermine the no of moles of eh speies remining t onversion of.

25 4. H SYSEMS SOIHIOMERI LE omponents of stoihiometri tle: refers to moles of speies rete or forme Speies I Initilly (mol) hnge (mol) Remining (mol) otls

26 4. H SYSEMS SOIHIOMERI LE Rell from hpter 2: + + moles of rete torizing; 1 moles of remining in the retor t onversion of

27 4. H SYSEMS SOIHIOMERI LE Moles rete, Moles rete Moles rete Moles rete Moles forme, Moles forme,

28 4. H SYSEMS SOIHIOMERI LE moles remining in the system, moles of initilly in the system moles of rete moles of forme moles of forme

29 4. H SYSEMS SOIHIOMERI LE Speies Initilly (mol) hnge (mol) I - otls I Remining (mol) I I 1

30 4. H SYSEMS SOIHIOMERI LE otl no of moles per mole of rete n e lulte s: 1 where hnge in the totl numer of moles per mole of rete 1

31 4. H SYSEMS SOIHIOMERI LE r k 2 3 r k r k n we express onentrtion of eh speies?? Speies Initilly hnge Remining onentrtion I otls

32 onentrtion of eh speies in terms of onversion n e expresse s: 4. H SYSEMS SOIHIOMERI LE 1 / Remining (mol) / / Rell from stoihiometri tle

33 / / 4. H SYSEMS SOIHIOMERI LE / / / / / /

34 / / 4. H SYSEMS SOIHIOMERI LE / / i i i i y y

35 4. H SYSEMS SOIHIOMERI LE Speies Initilly hnge Remining onentrtion I - I I I 1 / / / IO i i i i y y

36 4. H SYSEMS SOIHIOMERI LE Speies Initilly hnge Remining onentrtion I - I I I 1 / / / IO

37 4. H SYSEMS SOIHIOMERI LE EMLE Given the sponifition for the formtion of sop from queous usti so & glyeryl sterte is: q 17H35OO H H 35 OO 3 H 5 3 3OH OH 3 Letting the onversion of soium hyroxie, set up stoihiometri tle expressing the onentrtion of eh speies in terms of its initil onentrtion n the onversion.

38 4. H SYSEMS SOIHIOMERI LE OH H OO H H OO H q OH We know tht this is liqui-phse retion. herefore, = / EMLE

39 4. H SYSEMS SOIHIOMERI LE Speies Initilly hnge Remining onentrtion I - otl I I I IO 3 1 EMLE

40 5. LOW SYSEMS SOIHIOMERI LE urpose of eveloping stoihiometri tle: o etermine the effluent flow rte of eh speies t onversion of.

41 5. LOW SYSEMS SOIHIOMERI LE omponents of stoihiometri tle: Speies I ee rte to retor (mol/time) hnge within the retor (mol/time) Effluent rte from retor (mol/time) otls

42 5. LOW SYSEMS SOIHIOMERI LE Speies ee rte to retor (mol/time) hnge within the retor (mol/time) Effluent rte from retor (mol/time) onentrtion (mol/l) I - otls i I I I 1 / / / I I

43 QUIZ 3 Given liqui phse retion: he initil onentrtion of n re 1.8 kmol/m 3 n 6.6 kmol/m 3 respetively. onstrut stoihiometri tle for flow system onsiering s the sis of lultion.

44 SWER OR QUIZ Given: O 1.8kmol / m 6.6kmol / m 3 3 O kmol/ m kmol/ m i 3 3 i i y y i Sine & re prouts. rom stoihiometry, we know tht, i i

45 SWER OR QUIZ 5 Speies ee rte to retor (mol/time) hnge within the retor (mol/time) Effluent rte from retor (mol/time) otls

46 SWER OR QUIZ 5 Sustituting the numeril vlues; Speies ee rte to retor (mol/time) hnge within the retor (mol/time) Effluent rte from retor (mol/time) otls

47 1. or liqui phse: th System: 6. OERIO I ERMS O OERSIO 1 / / / / / / / / /

48 1. or liqui phse: low System - 6. OERIO I ERMS O OERSIO 1 / / / / / / / / /

49 6. OERIO I ERMS O OERSIO 2. or gs phse: th System ee to sustitute from gs lw eqution rom eqution of stte; t ny time t, Z R (1) = temperture, K = totl pressure, tm (1 tm= 11.3 k) Z= ompressiility ftor R= gs onstnt =.826 m 3 -tm/mol-k t initil onition (t=) Z R (2)

50 6. OERIO I ERMS O OERSIO 2. or gs phse: th System Z R (1) Z R (2) iviing (1) y (2); Z Z (3) Rell from stoihiometri tle (4) iviing (4) y ; 1 1y

51 2. or gs phse: th System pplies for oth th n flow systems 6. OERIO I ERMS O OERSIO y y t omplete onversion (for irreversile rxn): =1, = f Rerrnging; f Will e sustitute in (3)

52 2. or gs phse: th System Sustituting the expression for / in (3), 6. OERIO I ERMS O OERSIO Z Z (3) Z Z 1 If the ompressiility ftor re not hnge signifintly uring rxn, Z Z 1 (5)

53 6. OERIO I ERMS O OERSIO 2. or gs phse: low System rom gs lw, t ny point in the retor, ZR t the entrne of retor; j (3) Z R iviing (1) y (2) j ee to sustitute υ from gs lw eqution (1) (2)

54 2. or gs phse: low System Sustituting for ; 6. OERIO I ERMS O OERSIO Rell from stoihiometri tle 1 1 y 1 (4)

55 2. or gs phse: low System Sustituting υ & j ; 1 6. OERIO I ERMS O OERSIO (4) j j ee to sustitute υ from gs lw eqution 1 x v j j j v j j j j (5) x v j j 1 Stoihiometri oeffiient (/, /, -/, -)

56 1 2. or gs phse: low System onentrtion for eh speies: 6. OERIO I ERMS O OERSIO / / / 1 / x 1 / x 1 / x 1 1 x I I I I 1 x I

57 SUMMRY Reltive rte of retion: r r r ower Lw Moel: r r k

58 SUMMRY Elementry rte lw: he rxn tht in whih its stoihiometi oeffiients re IEIL to the retion orer of eh speies. on-elementry rte lws: he retions tht o not follow simple rte lws (power rte lws) in whih its stoihiometi oeffiients re O IEIL to the retion orer of eh speies. Reversile retion: ll rte lws must reue to the thermoynmi reltionship relting the reting speies onentrtions t equilirium.

59 SUMMRY Retion Rte onstnt, k k e E / R E, k, -r he lrger the tivtion energy, the more sensitive k is, (towrs the hnge in temperture)

60 SUMMRY Stoihiometri le for th Systems Speies Initilly hnge Remining I I - I I

61 SUMMRY Stoihiometri le for low Systems Speies ee rte to retor (mol/time) hnge within the retor (mol/time) Effluent rte from retor (mol/time) I - otls I i I I

62 SUMMRY Expression of n υ in lulting the onentrtion of eh speies: th systems Liqui phse: Gs phse: 1 low systems Liqui phse: Gs phse: 1

63 EERISE Given gs phse retion: onstrut stoihiometri tle for flow system onsiering s the sis of lultion with equimolr fee of 5% n 5%. erive the onentrtion for eh speies (for n isotherml gs phse retion, with no pressure rop).

64 1 1 2 rom stoihiometry tle Spe ies ee rte to retor (mol/time) hnge within the retor (mol/time) 2 2 Effluent rte from retor (mol/time) R y R