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1 he 3 Ktics ad Ractor Dsig Sprg, 00 Washgto Stat Uivrsity Dpartmt of hmical Egrg Richard L. Zollars Exam # You will hav o hour (60 muts) to complt this xam which cosists of four (4) problms. You may us ay boos, ots, tc. that you hav brought with you. Rmmbr that th majority of th pots o ay problm will b giv for clarly dmostratg that you ow how to solv th problm. Thus, it is ot cssary to complt all of th math cssary to rach a fal umrical aswr to rciv most of th pots for ay problm. Ma sur that you hav compltd ach problm to th pot whr oly calculatios rma bfor tag th tim to fish th calculatios o ay problm. Each problm statmt may also cota formatio that is ot cssary for th solutio of th problm.
2 ) (5 pts) You ar opratg a isothrmal STR which th ractio occurs. Th fd to th ractor cosists of oly at a rat of 0 mol/m. Th coctratio th fd stram is mol/litr. t th tmpratur sid th ractor th ractio rat costat is litr/molm. Th ractio is scod ordr. You wat to produc at a rat of 7 mol/m. How larg should th ractor b to accomplish this tas? SOLUTION or a STR opratg at stady-stat th matrial balac is giv by 0 r,,,,,, Thr is o chag th umbr of mols so whthr this is a gas phas of liquid phas ractio w ca assum that thr is o volum chag o ractio. Thus,, v v,,,, rom th stoichiomtry of th ractio This givs,,, 7 mol / m 3 mol / m ( ),, 0 ( 0 mol/ m ), 3 mol / m mol/ litr 0 mol/ m, 0.6 mol / litr, Substitutg all of ths valus ad th giv valu for th rat costat to th matrial balac givs 0 0 mol / m 3 mol / m litr / mol m Solv this for to gt ( 0.6 mol / litr)
3 0 mol / m 3 mol/ m 9. 7 litr litr / mol m ( 0.6 mol/ litr)
4 ) (5 pts) Th gas phas ractio D tas plac sid a isothrmal R. Th ractio rat xprssio for this ractio is r whr th rat costat has a valu of 00 litr/molm at th tmpratur sid th ractor. Th fd to th ractor cosists of mol/m of ad mol/m of. If th ractor oprats at atm ad 00º (R 0.08 litratm/molk) ad has a volum of 400 litr, what is th molar flow rat of lavg th ractor? SOLUTION or a isothrmal R w d oly solv th matrial balac d d r Sc th ractio is gas phas w ca rplac th coctratio trms with mol fractios to gt d d r y y T y y Now us th stoichiomtry to rlat th mol fractios of th molar flow rats Spci Molar low Rat o ( o ) o D o Total o W ar also giv that o o. Thus th mol fractios for ad bcom y y o o o ( ) ( ) o o o o o o Substitutg this to th matrial balac givs
5 d d o o Th variabls ca b sparatd to giv d d o o Th lft had sid of this ca b simplifid th tgratd to giv ( ) 0 l d d o o o o o o o Substitutg th valus w ow givs ( ) ( ) ( ) l 0.08(373) 00(400) l () Solv this quatio for to gt 0.05 mol/m.
6 3) (30 pts) You ar usg a smi-batch ractor (o lt stram, o lt strams) to procss a stram cotag a ractiv compot. Th ractio rat of is first ordr with a rat costat of 0. m -. Th ractio occurs th liquid phas with o chag volum o ractio. Th itial volum of th ractg mixtur th ractor is 00 litr with a coctratio of of 0. mol/litr. t som tim t 0, th ractio is itiatd ad a fd of mols /m is startd. Th coctratio of th fd stram is also 0. mol/litr. ftr 0 muts, what is th coctratio of sid th ractor? SOLUTION Sc o thrmal proprty data is giv w ll assum th ractor is isothrmal. Th matrial balac for a smi-batch ractor with a fd but o flow is d dt, r,,, Th two variabls ( a ad t) ca b sparatd to giv d dt Usg th tgratg factor t givs, t d dt d dt t t ( ) t,, t Itgratg givs t, t or, t To valuat th costat w ow that at tim t 0, o so, o
7 Thus o, rom th data giv o o 0. mol/litr(00 litr) 0 mol. Thus at 0 muts th matrial balac givs,, t o 0.(0) mol To dtrm th coctratio of w will also d th volum th ractor. W ar told that th fd rat is mol/m with a coctratio of 0. mol/litr so v,, 0. 0 litr / m Thus th volum aftr 0 muts is ( 0) litr o vt Th coctratio of th ractor is thus mol / litr 300
8 4) (30 pts) You ar coductg th liquid phas ractio a STR opratg at stady stat. Th ractio is scod ordr with rspct to (r - ) with a rat costat giv by.4 0 xp 7500 T whr th rat costat has uits of litr/molm ad th tmpratur is K. Th stram you ar worg with trs th STR at a molar flow rat of 5 mol/m, a volumtric flow rat of 0 litr/m ad a tmpratur of 0º (93 K). Usg th data blow (if dd) dtrm th siz of th ractor dd to ract 90% of th as wll as th tmpratur sid th ractor. dditioal Data H T p p hx SOLUTION r ( 98K ) 0 cal / mol 5 cal / mol U 300 cal / m 0 o 0,000 cal / mol o o o or this problm w will d to solv both th matrial ad rgy balacs for a STR. Th two quatios ar Matrial alac: Ergy alac:,, r, 0,,, U Tlma Hr, ν i Tlt ( ),, at Tlt i lt Tlt pi dt whr th form of th rgy balac usg th lt molar flow rats has b slctd to simplify th calculatios. W ar giv that 5 mol/m ad that 0.* 0.5 mol/m. Sc th ractio is liquid phas w will assum o volum chag o ractio so 0.* 0.* /v 0.*(5/0) 0.05 mol/litr. W also d to dtrm )Hr (at T). This is giv by
9 H r T ( T ) H ( 98) dt 0000 ( 0 5) r Th rgy balac ow is giv by ν 98 i i p i ( T 98) 850 5T ( 93 T ) ( 850 5T ) 5(0)( T 93) Th lt tmpratur (T) is th oly uow this quatio so solv it to fd T 30.4 K. Now that w ow th tmpratur w ca comput th rat costat T 98 dt xp.4 0 xp 6.40 litr / mol m T 30.4 Substitutg th ow valus to th matrial balac givs Solvg for yilds ( 0.05) ( 0.05) litr 6.40
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