P3-4 (a) Note: This problem can have many solutions as data fitting can be done in many ways. Using Arrhenius Equation For Fire flies: T(in K)

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1 # Hnc "r k " K ( $ is th rquird rat law. P- Solution is in th dcoding algorithm availabl sparatly from th author. P-4 (a Not: This problm can hav many solutions as data fitting can b don in many ways. Using rrhnius Equation or ir flis: T(in K /T lashs/ min ln(flash s/min Plotting ln(flashs/min vs /T, w gt a straight lin. S Polymath program P-4-firflis.pol. or rickts: T(in K /T chrips/ ln(chirps/ x0 min min Plotting ln(chirps/min Vs /T, w gt a straight lin. oth, irflis and rickts data follow th rrhnius Modl. ln y + /T, and hav th sam activation nrgy. S Polymath program P-4-crickts.pol. P-4 (b or Honyb: T(in K /T x0 V(cm/s ln(v Plotting ln(v Vs /T, almost straight lin. ln(v 44.6.E4/T t T 40 o (K V 6.4cm/s t T -5 o (68K V 0.005cm/s(ut b would not b aliv at this tmpratur S Polymath program P-4-bs.pol. -5

2 P-4 (c or ants: T(in K /T x0 V(cm/s ln(v Plotting ln(v Vs /T, almost straight lin. S Polymath program P-4-ants.pol. So activity of bs, ants, crickts and firflis follow rrhnius modl. So activity incrass with an incras in tmpratur. ctivation nrgis for firflis and crickts ar almost th sam. Insct ctivation Enrgy rickt 550 irfly nt Honyb 4800 P-4 (d Thr is a limit to tmpratur for which data for any on of h insct can b xtrapolat. Data which would b hlpful is th maximum and th minimum tmpratur that ths inscts can ndur bfor dath. Thrfor, vn if xtrapolation givs us a valu that looks rasonabl, at crtain tmpratur it could b uslss. P-5 Thr ar two compting ffcts that bring about th maximum in th corrosion rat: Tmpratur and HN-H S 4 concntration. Th corrosion rat incrass with incrasing tmpratur and incrasing concntration of HN-H S 4 complx. Th tmpratur incrass as w go from top to bottom of th column and consquntly th rat of corrosion should incras. Howvr, th HN concntrations (and th HN-HS4 complx dcras as w go from top to bottom of th column. Thr is virtually no HN in th bottom of th column. Ths two opposing factors rsults in th maximum of th corrosion rat somwhr around th middl of th column. P-6 ntidot did not dissolv from glass at low tmpraturs. P-7 (a If a raction rat doubls for an incras in 0, at T T lt k k and at T T T +0, lt k k k. Thn with k -E/RT E / RT E / RT in gnral, k and k, or -6

3 P-0 (a H 6 H 4 + H Rat law: -r H 4 + / H 4 Rat law: -r k H 6 k H / 4 0 (H (H H 6 + H H + Rat law: -r k[ /K ] 4 n- 4 H 0 I- 4 H 0 Rat law: -r k[ /K c ] n 4 H 0 i 4 H 0 5 H H H 9 H H 4 H 9 + H 5 H + + D Rat law: -r k[ D /K ] P-0 (b + ( -r k ( -r k ( -r k (4 - -r k P-0 (c ( H 6 H 4 + H Rat law: -r ( H + r Hr Rat law: -r Hr ( H + I HI Rat law: k k H + k H 6 / r Hr r r k H H I P- (a Liquid phas raction, H --H H - H + H H --H + lb/ft.47 lb/ft Stoichiomtric Tabl: Spcis Symbol Initial hang Rmaining Ethyln oxid lb/ft - (- (- lb/ft Watr.47 lb/ft, - ( -.47 (.47- lb/ft Glycol 0 lb/ft Rat law: -r k -9

4 Isothrmal, isobaric, catalytic gas phas oxidation, H H 4 Stoichiomtric tabl: Spcis Symbol Entring hang Laving H 4 - (- - ( - H y T + # $ y " 0. ( P ( 6atm yt y 0.09 RT atm. " # 0.08 $ ( 5K. K ( " ( " 0.09( " v v + " 0. " 0. ( " # $ v v + 0. ( 0.046( 0.09( v v + " 0. If th raction follow lmntary rat law 0.5 $ 0.09 # " $$ # " $ Rat law: r k # r k $ ( # 0. $$ ( ( # 0. $ ( P- (d Isothrmal, isobaric, catalytic gas phas raction in a PR 6 H 6 + H 6 H 0 + Stoichiomtric tabl: Spcis Symbol Entring hang Laving nzn - (- H - ( - 6 H

5 y T + " y# ( $ $ $ P " 6atm " T y # $ / # $ RT atm. " # 0.08 $ ( 44.K. K ( " ( " 0.055( " v v ( + # $ # $ " " ( ( ( # 0.( # v v ( + " $ # ( v v ( + " # " # $ $ ( ( If th raction follow lmntary rat law. Rat law: r k ( r k " # $ or a fluidizd STR: 0 W r W k 5 0 ( k " # $ kgcat min T 70o at 00K xp E "" 5xp "" k k # # $ $ $ $ R T T kgcat min atm -

6 0 0 * v 0 v 0 5 /min W v 0 0 ( k " # $ at 0.8 W.4" 0 kg of T 70o k k xp E R T $ $ ( " " 5xp T ## ( $ $ "" ## kgcat min atm 0 0 * v 0 v 0 5 /min W v 0 0 ( k " # $ at W 4.4" 0 kg of catalyst P- H 4 + H 4 + Stoichiomtric tabl for th givn problm will b as follows ssuming gas phas Spcis Symbol Entring hang Laving H (- 0 Θ 0 -/ 0 0 (Θ / N I I Θ I Θ I H " 0 0 " I I, I " # I #

7 y 0 0 T 0 0.0, " y 0 # $0.5 0 y 0 P RT 0 v 0.04 (" 0.04(" 0 (+ # " 0.5 ( v " 0 " (" " 0.5 v 0 " " 0.5 P- (a Lt N Nibroanalin NH D mmonium hlorid + " -r k + D P- (b Spcis Entring hang Laving (- 0 Θ 0 6.6/ (Θ D 0 0 D 0 P- (c or batch systm, N /V -r kn N /V P- (d r k - N N N ( (, ( V V0 V0 v v0 N N N " " " ( (, ( V V0 V0 v0 r ( 0 ( k " " "

8 k.8 m 0 (.8 ( (.67 r k P- ( t 0 and T K 0 m k # k ( r 0 k $ k min m " m min k r m min t 0 and T 5 98K # $ E # k k $ xp R T T "" ( cal 7 m k xp k.min cal.987. K 6 m.0" 0 k.min -r k k/m min ( # ## $ # $ k k0 xp E # $ " (, R * T0 T + - cal " 7 m # xp $ k # k min cal ( $ #.987 * 46K 56K + $ #, K $ - m k 0.05 k min r k m k k k min m m k " " # r 0.05 $ $ r P- (f r k (-(θ - -5

9 t 0.90 and T 88 46K at T K m $ k $ r " k.min " # m # k t 0.90 and T 5 98K ( 6 m ( k r.0" 0.8 k.min # # $ m $ 6 k." 0 t 0.90 and T 88 56K P- (g /min m $ k $ r " k.min " # m # k or STR at 5 o -r V t 88 o, -r " r ( " M 0.9 / min 0. ". 0 V " r 6 k." 0 k ( " M m / min 0..79m ( 0.9 (.67 ( 0.9 ( 0.9 (.67 ( 0.9 ( 0.9 (.67 ( 0.9 P-4 6 H 6 + a + bnh c( 4.4 H 7. N dh + To calculat th yilds of biomass, you must first balanc th raction quation by finding th cofficints a, b, c, d, and. This can b don with mass balancs on ach lmnt involvd in th raction. nc all th cofficints ar found, you can thn calculat th yild cofficints by simply assuming th raction -6

10 , + ( "r N.6 ". + # ". + (. * + $ -. ( or batch systm, constant volum. " " N N N H # r k $ $ " ( ( 40 *( # # " + $ $, - " # rn.6 * # # $ + [ ] P-6 (a Liquid phas raction assum constant volum Rat Law (rvrsibl raction: " # r k $ # K Stoichiomtry: (, ( 0, 0 0 To find th quilibrium convrsion, st -r 0, combin stoichiomtry and th rat law, and solv for. K ( K 0 0 " # $ K 0.80 To find th quilibrium concntrations, substitut th quilibrium convrsion into th stiochiomtric rlations. 0 ( ( ( ( * P-6 (b Stoichiomtry: -9

11 0 ( y 0 " # and 0 0 N N " " 0 V V + + N N V V 0 0 ombin and solv for. K 0 ( + ( + ( # ( + ( + " $ 0 0 $ + 7 K 0 7 " # $ K Equilibrium concntrations: P 0 atm RT0 atm " ( K 400 # 0.08 $ K ( ( ( P-6 (c Sam raction, rat law, and initial concntration as part (b gas phas, batch raction. Stoichiomtry: N N ( ( 0 0 V V0 N N 0 0 V V0 ombin and solv for ( ( K Equilibrium concntrations -0

12 ( 0.05( ( 0.05( P-6 (d Gas phas raction in a constant prssur, batch ractor Rat law (rvrsibl raction: " # r k $ # K Stoichiomtry: 0 ( y 0 " # and 0 0 N N " " 0 V V + + N N V V 0 0 ombin and solv for : 0 ( + ( + K0 " 0 # $ Equilibrium concntrations: ( ( ( P-7 Givn: Gas phas raction + 8 in a batch ractor fittd with a piston such that V 0.P 0 ( ft k.0 lb r k sc N 0 N 0 at t 0 V ft T R onstant -