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CHE 304 (Spring 2007) __________________ LAST NAME, FIRST Quiz #1 Note: Your answers must be correct to 3 significant figures and have the appropriate units. I . Fo rt h eg a sp ha s er e a c t i o n

2 A+B C+3 D

Th er e a c t i o ni sr e v e r s i b l ea tc o n s t a n tt e mpe r a t u r ea n dpr e s s u r e .Th ef e e di st womo l e so fApe r o n emo l eo fB. 1 .Wr i t et h ec o nc e n t r a t i o no fAi nt e r mo fCA0a n dX.

_ _ _ __ _ _ _ _ _ __ _ _

C (1  X ) CA = A0 (1  X / 3) 2 .Wr i t et h ec o nc e n t r a t i o no fCi nt e r mo fCA0a n dX.

__ _ _ _ _ _ __ _ _ _ _ _

C ( X) CC = A0 2(1  X / 3) II The irreversible elementary reaction 2A  B takes place in the gas phase in an isothermal tubular reactor. Th ef e e di st womo l e so fAp e ro n emo l eo fC,a ni n e r t . The entering temperature and pressure are 427oC and 10 atm, respectively. Gas constant R = 0.082 atmL/moloK. 3. Determine the concentration of A at the entrance to the reactor.

____________

. 1 1 6mo l / L CA0 =0

4. If CA0 = 1.0 mol/L, the concentration of A at 90% conversion of A is

____________

CA =0 . 14 3mo l / L

III. (5) Hydrogen gas is fed to a burner, where it is combusted with 300% excess air (21% O 2). Moles of nitrogen required for each mole of hydrogen is ______________ H2 + 0.5O2  H2O Moles of nitrogen = 7.52 moles

IV. The chemical species A is known to decompose according to

A(g) = B(g) + C(g) A rigid container is filled with pure gaseous A at 300 oK and 760 mmHg and then heated. Assume ideal-gas behavior and chemical equilibrium. (6) If the pressure was observed to be 1610 mmHg at 510oK, the mole fraction of A is yA = 0.605 (7) If the fractional conversion of A is 0.50 at 650oK, determine the pressure of the reactor. P = 2470 mmHg V. (8) Th ei r r e v e r s i b l efir s to r d e rr e a c t i o nA Bi sc a r r i e do u ti nat u b u l a rr e a c t o ri nwh i c ht h e v o l u me t r i cflo wr a t eQi sc o n s t a n t .De t e r mi n et h er e a c t o rv o l u mene c e s s a r yt or e d u c et h ee x i t i n g c o n c e n t r a t i o nt o5 %o ft h ee nt e r i n gc o n c e n t r a t i o nwh e nt h ev o l u me t r i cflo wr a t ei s3 0l i t e r s / mi n 1 a n dt h es p e c i ficr a t ec on s t a nt ,k , i s0 . 2 0m-i n . V = 449 liters

VI. The exothermic reaction AB +C was carried out adiabatically and the following data are given:

The entering molar flow rate of A was 400 mol/min. 9) The volume of a CSTR required for 20% conversion is

____________

V =4.8 L

10) The volume of a PFR required for 20% conversion is V = 6.4 L

____________

CHE 304 (Spring 2007) __________________ LAST NAME, FIRST Quiz #2 Note: Your answers must be correct to 3 significant figures and have the appropriate units. I. The gas phase reaction

A + 4B  2C

which is first-order in A and first-order in B is to be carried out isothermally in a plug flow reactor. The entering volumetric flow rate is 4.0 L/min, and the feed is equimolar in A and B. The entering temperature and pressure are 527oC and 8 atm, respectively. You can neglect pressure drop in the reactor. The specific reaction rate at this temperature is 5 L/mol min and the activation energy is 12,000 cal/mol. Gas constant R = 0.082 atmL/moloK = 1.987 cal/moloK 1) Determine the volumetric flow rate when the conversion of A is 25%.

____________

Q = 2.5 L/min 2) Determine the concentration of A at the entrance to the reactor.

____________

CA0 =0 . 0 6 1mo l / L 3) Write the concentration of A in terms of CA0, and X. CA =

____________

C A0 (1  X ) (1  1.5X )

II. For a gas phase reaction where  rA = kCACB What is the effect on the reaction rate of increasing the reaction pressure by 10% while maintaining constant temperature? The reactio rate increase by: A. 10%

B. 100%

C. 121%

D. None of the above

I I I .Dibutyl phthalate (DBP), a plasticizer, is to be produced by reaction of n-butanol phthalate (MBP). The liquid reaction follows an elementary rate law and is catalyzed by H2SO4. MBP + n-butanol  DBP + H2O A stream containing MBP and butanol is to be mixed with the H 2SO4 catalyst immediately before the stream enters the reactor. The concentration of MBP in the stream entering the reactor is 0.4 lbmol/ft3 and the molar feed rate of butanol is five times that of MBP. The specific reaction rate at 100oF is 1.2 ft3/lbmolhr. There is a 1000-gallon CSTR and associated peripheral equipment available for use on this project for 30 day a year (operating 24 h/day). 5) Determine the flow rate in lbmol/hr of DBP leaving the available CSTR to produce 6 million lb/year of DBP (Mw = 278) ____________ 30 lbmol/hr 6) Determine the exit conversion in the available 1000-gal reactor if the DBP flow rate is 20 lbmol/hr (1 ft3 = 7.48 gal.) X = 0.814 7) If the MBP feed rate is 60 lbmol/hr and the exit conversion in the CSTR is 0.4, what conversion would be achieved if a second 1000-gal CSTR were placed in series with the first CSTR? X = 0.786 3A  B

IV) For the reaction

The reaction is irreversible at constant temperature and pressure with pure gas A fed to the reactor. Write the concentration of A in terms of CA0, and X. 1 X CA = CA01 2 X / 3

V) For the reaction

2A  B

The reaction is reversible, non-isothermal with pure gas A fed to the reactor. Write the concentration of A in terms of CA0, T0, T, P0, P, and X. 1  X  P   T0     P CA = CA01 0.5X  0   T 

VI) Ca l c u l a t et h epa r t i a lp r e s s u r eo fmon a t o mi ch y d r o g e ng a sa t1 0 0 0oKa n d1a t mp r e s s u r e . Fo r½H2( g ) H( g ) o =1 2 0 , 0 0 0J / mo l ,g a sc o n s t a n tR=8 , 3 1 4J / mo l oK  G1000 K

t m . 3 91 0-7a PH =5

_ _ _ _ _ _ __ _ _ _ _ _ __

CHE 304 (Winer 2007) __________________ LAST NAME, FIRST Quiz #3 Note: Your answers must be correct to 3 significant figures and have the appropriate units. I. We have a mixture with 2 moles of CH 4 for every mole of O2 at 10 atm. Estimate the adiabatic reactor temperature if all of the available O2 react to form CO2 and H2O. The feed is at 300oC (HRx =  152 kcal/mol, Cp = 7 cal/moloK.). T = 3919oC = 4192oK 2A+B C+3 D

I I .F o rt h eg a sp ha s er e a c t i o n

Th er e a c t i o ni sr e v e r s i b l ea tc o n s t a n tt e mpe r a t u r ea n dpr e s s u r e .Thef e e di st womo l e so fAp e r o n emo l eo fB. n dX. 2 .Wr i t et h ec o nc e n t r a t i o no fAi nt e r mo fCA0a

_ _ _ _ _ __ _ _ _ _ _ _ _

(1 X ) CA =CA01 X / 3 n dX. 3 .Wr i t et h ec o nc e n t r a t i o no fCi nt e r mo fCA0a

__ _ _ _ _ _ __ _ _ _ _ _

X 2 1  X / 3

CC =CA0

III. Dibutyl phthalate (DBP), a plasticizer, is to be produced by reaction of n-butanol phthalate (MBP). The liquid reaction follows an elementary rate law and is catalyzed by H2SO4. MBP + n-butanol  DBP + H2O A stream containing MBP and butanol is to be mixed with the H 2SO4 catalyst immediately before the stream enters the reactor. The concentration of MBP in the stream entering the reactor is 0.2 lbmol/ft3 and the molar feed rate of butanol is five times that of MBP. The specific reaction rate at 100oF is 1.5 ft3/lbmolhr. There is a 500 ft3 CSTR and associated peripheral equipment available for use on this project for 30 day a year (operating 24 h/day). 4) Determine the exit conversion in the available 500 ft 3 reactor if the DBP flow rate is 40 lbmol/hr (1 ft3 = 7.48 gal.) X = 0.691

5) If the MBP feed rate is 60 lbmol/hr and the exit conversion in the CSTR is 0.4, what conversion would be achieved if a second 500 ft3 CSTR were placed in series with the first CSTR? X = 0.806

6) What CSTR volume would be necessary to achieve a conversion of 95% for a molar feed rate of MBP of 60 lbmol/hr? V = 4691 ft3 II. A solute diffuses through a membrane that separates two compartments A and B that have different initial concentrations. The solute concentrations in the two compartments as a function of time, CA and CB are shown below. The volumes of the two compartments are VA and VB. (A) VA > VB

(B) Solute diffuses from compartment B to A.

a . Aa n dBa r et r u e b.Onl yAi st r ue c .On l yBi st r u e

d.Aa n dBa r ef a l s e

10

C

A

5

C

B

0

t

I V.Fo rt h er e a c t i o n A( g )+2 B( g ) C( g )+D( g , l ) Th ef e e dc o n t a i n so n l yAa n dBi ns t o i c h i o me t r i ca mo u nt s .Th et o t a lp r e s s u r ei s1 0 1 . 3k Paa n d s p e c i e sD h a sav a p o rp r e s s u r eo f3 0 . 39kPaa tt h ei s o t h e r ma lr e a c t i o nt e mp e r a t u r eo f30 0oK. Ca l c u l a t et h ec o n v e r s i o na twh i c hc o n d e n s a t i onb e g i n s . X=0 . 9/ 1. 3=0 . 6 9 2 V.Th eg a s p h a s er e a c t i o nA( g) 3 B( g )ob e y sz e r o t h o r d e rki n e t i c swi t hr=0 . 2 5mo l e s / l i t e r h r St a r t i n gwi t hp u r eAa t1a t m, c a l c u l a t et h e a t2 0 0oC.Ga sc o n s t a n tR=0 . 0 82La t m/ mo l oK. t i mef o r9 5 %o ft h eAt ob er e a c t e da wa yi n 9 )ac o n s t a n t v o l u meb a t c hr e a c t o r

_ _ _ _ _ __ _ _ _ _ _

t = 0.098 hr = 5.88 min = 353 s 1 0 )ac o ns t a n t p r e s s u r eb a t c hr e a c t or t=0.0549 hr = 3.29 min = 198 s

_ _ __ _ _ _ _ _ __ _ _ _

CHE 304 (Spring 2007) __________________ LAST NAME, FIRST Quiz #4 Note: Your answers must be correct to 3 significant figures and have the appropriate units. I. The gas phase reaction

AB

has a unimolecular reaction rate constant of 0.0025 min-1 at 90oF. This reaction is to be carried out in parallel tubes 10 ft long and 1 in. inside diameter under a pressure of 150 psia at 260 oF. A and B each have molecular weights of 64. Ideal gas constant R = 10.73 psiaft3/lbmoloR = 1.99 Btu/lbmoloR. The conversion of A is 80%. 1) If 1500 lb/hr of B is required, determine the feed flow rate of A in lbmol/min ____________ FA0 = 0.488 lbmol/min 2) If the activation energy of the reaction is 35,000 Btu/lbmol, the rate constant at 260oF is k = 4.75 min-1 3) If the reaction rate constant at 260oF is 52.6 min-1 and the feed flow rate of A is 1.0 lbmol/min, the required volume of the reactor is V = 1.58 ft3 4) If the reaction rate constant at 260oF is 52.6 min-1, the feed flow rate of A is 1.0 lbmol/min, and there is also an inert flow rate of 1.0 lbmol/min, the required volume of the reactor is V =3.16 ft3 5) If the required volume of the reactor is 1.5 ft3, the number of tubes needed is nt = 28

____________

II. Th eg a sp h a s ec a t a l y z e dh y d r o g e n a t i o no fo c r e s o lt o2 me t h y l c y c l o h e x a n o n ei sg i v e nb y o c r e s o l ( A)+2 H2( B) 2 me t h y l c y c l o h e x a n o n e ( C) Th er e a c t i o nr a t eo nan i c k e l s i l i c ac a t a l y s twa sf o u n dt ob e oC PB,whe r r ek=1 . 7 4mo lo fo c r e s ol / ( k gc a t mi na t m)a t1 7 0 A =k

Th er e a c t i o nmi x t u r ee n t e r st h ep a c k e d b e dr e a c t o ra tat o t a lpr e s s u r eo f5a t m.Th emo l a rf e e d c o n s i s t so f6 7 % H2 a n d3 3 % oc r e s ola tat ot a lmo l a rr a t eo f4 0mo l / mi n . 6) Ne g l e c t i n gp r e s s u r ed r o p ,wr i t et h ec o nc e n t r a t i o nofCA i nt e r mo fCA0a n dX. CA = CA0

(1  X ) (1  2 X / 3)

7) If the pressure drop is not negligible, we need to solve the following ODEs (1  X ) (1  2 X / 3) dX dy = 0.435 y, and =  0.34 , where y = P/P0 2y (1  2 X / 3) dw dw

The above two ODEs can be solved using the following Matlab statements and function A) wspan=0:.1:4.8; [w,xy]=ode45('f4d22b',wspan,[0 0]);

B) wspan=0:.1:4.8; [w,xy]=ode45('f4d22b',wspan,[0 1]);

function wx = f4d22b(W,xy) X=xy(1);y=xy(2); wx(1,1)=0.435*(1-X)*y/(1-2*X/3); wx(2,1)=-0.34*(1-2*X/3)/(2*y);

function wx = f4d22b(W,xy) X=xy(1);y=xy(2); wx(1,1)=0.435*(1-X)*y/(1-2*X/3); wx(2,1)=-0.34*(1-2*X/3)/(2*y);

C) wspan=0:.1:4.8; [w,xy]=ode45('f4d22b',wspan,[0 1]);

D) None of the above

function wx = f4d22(W,xy) X=xy(1);y=xy(2); wx(1,1)=0.435*(1-X)*y/(1-2*X/3); wx(2,1)=-0.34*(1-2*X/3)/(2*y);

I I I .A f e r me nt a t i o nbr ot hc o n s i s t so fa na q u e o u ss o l u t i o no fn u t r i e n t sa n dc e l l s .Ast h ec e l l s g r o w,t h e yc l u s t e ri n t os p h e r i c a lp e l l e t so fr a d i u sR( t ) .Ona v e r a g e ,t h ec e l ld e ns i t yi n s i d ea p e l l e ti s0. 0 4mgo fc e l lma s sp e rc u b i cmi l l i me t e ro fp e l l e tv ol u me .Th ed i s s o l v e do x y g e n c m3.Th ec e l l su t i l i z eo x y g e na tar a t eo f1 . 2mmo lof c on c e n t r a t i o ni nt heb r ot hi s5g/ o x y g e np e rh o u rpe rgr a mo fc e l lma s s ,v i aaz e r o or d e rr e a c t i o n.Th ed i ffu s i o nc o e ffic i e n t fo xy g e nwi t hi nt h ep e l l e ti s1 . 81 0-5c DAB o m2/ s .Th ec e l l sa n db r o t hh a v ed e n s i t i e sc l o s et o t h a tofwa t e r .Th e r ei safin i t ec o n v e c t i v er e s i s t a nc et oma s st r a ns f e rt ot h es u r f a c eoft h e p e l l e t ,s u c ht h a tt h eflu xt ot h es ur f a c ei sgi v e nb y mo l a rflu x= ( C kB  CP) c wh e r eCB i st heb r o t ho x y g e nc o nc e nt r a t i o na n dCP i st h e( u nkn o wn )c o n c e n t r a t i o no fo x y g e n a tt hep e l l e ts u r f a c e . 8) Determine the reaction rate, R, per unit volume of the cell in mol/(cm3s) R = 1.33 10-8 mol/(cm3s) 9 mo ma n d2 k / DAB=4d e t e r mi neCP( g / c m3) 9) I fR = 2.51 0 l /(cm3s), R=5 . 01 0-2c cR

/ c m3 CP = 3.15 1 0-6g

10) If R is the reaction rate per unit cell volume, the differential equation for the concentration of oxygen, CA, i nt h es p he r i c a lp e l l e ti s D D d  2 dC A  d  2 dC A  A) AB r r  +R = 0  R =0 B) AB 2 r dr  dr  dr  r dr  C)

D AB d  2 dC A  r   R = 0 Ans dr  r 2 dr 

D)No n eo ft hea b o v e

CHE 304 (Spring 2007) __________________ LAST NAME, FIRST Quiz #5 Note: Your answers must be correct to 3 significant figures and have the appropriate units. do fs e wa g eo uto fas e we r I.A we l l mi x e ds e wa g el a g o o n( as h a l l o wp o n d )i sr e c e i vi n g4 3 0m3/ 5 2 p i p e .Th el a g o o nh a sas u r f a c ea r e ao f1 0m a n dad e p to f1 . 0m.Th ep o l l u t a n tc o n c e n t r a t i o ni n t h er a ws e wa g ed i s c h a r g i n gi nt ot hel a g o o ni s2 5 0g/ m3.Th eo r g a n i cma t t e r( p o l l u t a n t )i nt h e s e wa g ed e gr a d e sb i o l o g i c a l l yi nt h el a g oo na c c o r d i n gt ofir s t o r d e rki n e t i c s .Th er e a c t i o nr a t e c o n s t a nti s0 . 0 70/ d .As s umi n gn oo t he rwa t e rl o s s e so rg a i n s ,fin dt h es t e a d ys t a t ec o n c e n t r a t i o n o ft h ep o l l u t a n ti nt hel a g o one fflu e n t . CA = 14.5 g/m3 r II.Ana i r b o r n es p he r i c a lc e l l u l a ro r g a n i s m,0 . 01 5c mi nd i a me t e r( D) ,u t i l i z e s4 0 . 0mo lO2 pe h o u r ,p e rgr a mo fc e l lma s s .As s u meS h=k DAB =4( b a s e donDAB i nt h eg a sp h a s e . ) mD/ As s u mez e r o o r d e rki n e t i c sf o rr e s p i r a t i o n .Thed i ffu s i onc oe ffic i e n t t o h r r o O ug ht he 2f 2 c e l l u l a rma t e r i a li s1 0-5 c m2/ sa n dt h ed i ffu s i o nc o e ffic i e nt f i o n r a O i r i s 0 . 1 8 c m / s a t 2 2 9 8oK.Thee q ui l i b r i u mc o n c e n t r a t i o n( CA)o fO2 i nt hec e l l u l a rma t e r i a l si sr e l a t e dt ot h e . 01 0-6pA( p a r t i a lO2 pr e s s u r e( p b yt h er e l a t i o nCA( mo l / c m3)=7 a t m) .De n s i t yo fc e l li s1 A) 3 t m/ mo l oK g / c m .Ai ri sa t1a t m wi t h21mol e% o x y g e n . Ga sc o n s t a n tRg=8 2. 0 6c m3a na i ra tt h es u r f a c eo ft h e 2 )Ats t e a d ys t a t e ,d e t e r mi n et h ec o n c e n t r a t i o no fo x y g e n( mo l / c m3)i c e l l u l a ro r g a n i s m. k / c m3 10-6g m = 8.01 3 )I ft h ec o n c e n t r a t i o no fo x y g e ni na i ra tt h es u r f a c eo ft h ec e l l u l a ro r g a n i s mi s8 . 51 0-6 3 3 mo l / c m ,t h ec o n c e n t r a t i ono fo x y g e n( mol / c m )i nt h ec e l la tt h es u r f a c eo ft h ec e l l u l a r o r g a n i s mi s _ _ _ __ _ _ _ _ _ _ 6 3 mo l / c m CAs|cell = 1.455 1 0

CH2 ) ,i st ob ep r o d u c e di nawe l l s t i r r e ds e mi b a t c hr e a c t o r I I I .He xa me t h y l e n et e t r a a mn i e ,N4( 6 o b ya dd i n g2 0Ca q u e o u sa mmon i as o l u t i o na tac o ns t a n tr a t eo f2 5l i t e r s / mi nt oa ni n i t i a lc ha r g e o ff o r ma l i ns o l u t i o n: 6 HCHO+4 NH3>N4( CH2) H2O 6+6 ( A) ( B) Th er e a c t i o ni si n s t a n t a n e o u s ,i r r e v e r s i bl e ,a n de x ot h e r mi c .Th ei ni t i a lc h a r g eo ff o r ma l i n s o l u t i o ni s5 0 0 0l i t e r s wi t h af o r ma l d e h y d ec o n c e n t r a t i o n ,CAi ,o f2 0 . 0 mol / l i t e r .Th e c o n c e n t r a t i o no fa mmo n i ai nt h es o l ut i o ni sCB =1 2 . 0mo l / l i t e r .He a tc a p a c i t yo fb o t ha mmon i a oC.He a n df or ma l i ns ol u t i oni s1 0 0 0c a l / l i t e r CH2) . T h e a to fr e a c t i o ni s7 4 . 6k c a l / mo lo fN4( 6 i n i t i a lt e mp e r a t u r eo ff o r ma l i ns o l u t i o ni nt h er e a c t o ri s2 5oC. 4 )Th er a t eo fh e a tg e n e r a t e db yt hec h e mi c a lr e a c t i o ni s

__ _ _ _ _ _ __ _ _ _

5 59 5kc a l / mi n 5 )Ti mer e q u i r e df o rc o mp l e t ec o n s u mp t i o no ff o r ma l d e h y d ei s

_ _ _ _ __ _ _ _ _ _ _

t = 222 min I V.Th efir s to r d e rr e a c t i o nA  Bi sc a r r i e do u ti na na d i a b a t i cCSTRwi t hAC l / l i t e r 0=2mo a n dT0=3 00oK.I ti sf o un dt h a t5 0 %c o n v e r s i oni so b t a i n e dwi t h ( =V/ Q)= 4mi n ,a n dt he r e a c t o rt e mp e r a t u r ei s3 5 0oK. s 6 )Th er e a c t i o nr a t ec o n s t a n tka t3 50oKi _ _ _ __ _ _ _ _ _ _ k=0 . 2 5mi n-1 7 )Th er e a c t i o ni si nwa t e rwi t h Cp=1 00 0c a l / l i t e r oK.Fi n dt h eh e a to fr e a c t i o n. _ _ _ __ _ _ _ _ _ _

Hr =  50kc a l / mo l

V.Th ei r r e v e r s i b l e ,l i q u i d p h a s er e a c t i o nA  Bi st ob ec a r r i e do u ti na ni d e a lPFR.Th ei n l e t c o n c e n t r a t i o no fA,CA0,i s2 , 5 0 0mo l / m3,a n dt hef e e dt e mp e r a t u r ei s1 50oC.Th ef r a c t i o n a l c o n v e r s i o no fA i nt h er e a c t o re fflu e n tmu s tb ea tl e a s t0 . 9 0 .Th er e a c t o rwi l lo pe r a t e s1 . 4 0 1 0-4 i s o t h e r ma l l ya t1 5 0oC.Th er e a c t i o ni ss e c o n do r de ri nA.Th er a t ec o n s t a n ta t1 5 0oCi ( molAs ) .At1 5 0oCHRx= 1 65k J / mo l . Th eflo wr a t et ot h er e a c t o ri s0 . 0 13m m3/ / s . 8 )De t e r mi n et hev o l u meo ft h ePFRr e q u i r e df o r90 %c on v e r s i o n.

_ _ _ _ __ _ _ _ _ _

V= 0. 2 5 7m3 9 )De t e r mi n et her a t e( k J / mi n )a twhi c hh e a ti sr e mo v e df r o mt h ewh ol er e a c t o r ._ _ _ __ _ _ _ _ _ _ 5 Q =2.2310 kJ/min

10

VI )( 1 0 )Th ef o l l o wi n gMATLABp r o gr a mc a ne v a l u a t e ( 1) n n 0

A. x = 2; sum = 1; For n=0:10 sum = sum + (1)^n*x^n/factorial(2*n+1); end B. (Ans.) x = 2; sum = 1; z = 1; For n=1:10 z = z*x/(2*n)/(2*n+1); sum = sum+z end

xn f o rx=2 (2 n  1)!

C. x = 2; sum = 1; z = x; For n=1:10 z = z*x/(2*n+1); sum = sum+z end D. None of the above...