dm dt = 1 V The number of moles in any volume is M = CV, where C = concentration in M/L V = liters. dcv v
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1 Mg: Pcess Aalyss: Reac ae s defed as whee eac ae elcy lue M les ( ccea) e. dm he ube f les ay lue s M, whee ccea M/L les. he he eac ae beces f a hgeeus eac, ( ) d Usually s csa aqueus eeal pcesses eac, s whch ca be -. Reacs ay ly ccu he suface (heegeeus); he, whee A S suface aea. F a eac: R pp dr p dp d, A S dm Sce hese eacas eac la bass (ccea): les R eed p les P (la bass): ( ) dx, ( ) dp ( ) dr p whee ceffce, whch eas ccea chages ae always:
2 X la ccea. We hae aleady see, whch says he ae f eac s ppal he au f aalable eac (Fs Ode). sle f :, peusly dm, s beces dm. hs s ly f fs de eac ad has us e -. Le L l L S e -. dm l e dm l L L le e epeaue epeaue wll affec. F EES 4 (hecal Pcesses l): whee A csa E aca eegy R gas csa epeaue Kel Ad l( ) l( A) Ae E R E, whch sles: R,
3 whee E E dl( ) ( ) R R E d R d E l( ) R E E l( ) l( ) R R E ( ) l R E R des ay ce ae defed. he, ( ) ' ( ) ( ) e whee has bee defed as.4 f ay applcas bu s suffce hee ae p ha a fs de ay be deeed f a a e epeaue s w ad he he epeaue s specfed. plee M Ms eacs B-Eeal Pcesses ae eesble ad deled as fs de: R P dr Sles RR e Mass Balaces ae equed f ay pcess aalyss as a f(): IN OU hages whee chages ae ypcally gwh, deah, accuula, ec. cpleely ed Flw, c., Flw, c., lue
4 F ay speces wh : IN OU A Decay Reac d d Ne: pleely Med a ccea s sae eeywhee. Us: L h, g L, L, d g L h L h g h g L g h L h g L g L h h g L ( L) ( L) Ne: ge ass us egae e e, ad h - Slg -seady sae: IN OU A Decay Reac d Reaagg ( ) F d dy y K Slu y ye K e Mapula d e e ( ) ( ) 4
5 A : Oupu ccea s fuc f ae csa ad dee e f fs de eac -- l f gwh eac? Ms hae se dea abu g: Mg Mdels: ype () Plug Flw ype () plee M ype () bas ype () ad () Plug Flw: Pcue a lg ppe: Obusly, ey lle ee f ay lecules ecep he dec. Mass Balace: IN - OU Accuula (eglec ulza, gwh, ec.) d Aeage IN OU chage f wh espec ly X he dec α α d α d α α d d α 5
6 f (Dea f al ad fal sae) α d α α bu A, whee d sae scale α α d Ad α α α α α s ly e ly f α α α α whch sply eas plug flw eas hee s NO chage wh e bewee pu ad upu. A spe wuld appea wh e as c. / wh ze g ly asla. plee M: A cpleely ed a eas ha ce a chage (dye) s pu a a, g ccus saaeusly ad he ccea s equal a all ps he a. Oe.M. a: M cpleely ed whee flw M les (ass) lue M a a all ps s ey slu 6
7 Mass Balace, a : IN - OU Accuula d ( ) d, csa - M d (N eac, ly g) l M f.m..: M e (.e.) Pl as f(): M/ M/(.7) e Wha s s pbable f ay lecule f slug M? H.: Whch slce f wuld be lages? Mulple plee M Reacs D f as: 7
8 (a) We wll hadle lues a facs f al (b) I s sla fee-bdy daga Mass Balace : ( ) d As befe: M e M (a ) ( ) d d ( ) d M e Reaagg: d M e F: dy d Py whee P M ad e Slu: y e Pd e Pd 8
9 e M e M e e hs slu beces f.m..: M e! ( ) ().. θ / Wha wuld yeld f esus θ? Resdece e: hape 9 -- begg 9..4 wha wuld cues l le f () / esus θ. We w ca pedc efflue ccea f ehe plug flw cpleely ed dels as a fuc f e. sdeg a eac f M as: Mass Balace: IN - OU Accuula Decay Reac d hs equa was sled f as: e e Leg : e e 9
10 A, f seady sae slu whee d : F as: whch ges fac ulza f,, ad. Decay F Ne: () F cease, us be egae. () Reebe f s egae eas educ f. If s pse eas pduc f. F s ppse fs glace. F plug flw wh eac a seady sae: IN OU Reac (Decay) Accuula Splfes α α α α dd d α α d d d α ( ) α α Neglecg secd de us α d d α
11 d d A d d e L a deee equed f ge % eal: ay ube f as Ne: whch wll sle ehe f s ge. Say w as sees wh dffee lue,, ad wh decay eac: Mass Balace a seady sae: 4 4 Peus equa Plug Flw wh eac s sple fs de slu (deal eae),,, /4 /4 /
12 Mass Balace a seady sae: sdeg w as wh decay eac cludg ecycle wh uequal lues, :, q, q, (/) (/) Mass Balace a seady sae: IN OU q ( q) q q q q whee q ecycle a Mass Balace a seady sae:
13 ( ) ( ) q q q q q q q q q q
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