Molecular Thermodynamics CEM 484
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Date Created: 09/19/15
CEM 484 Problem Set 6 Spring 2011 due Wednesday March 23 1 A reversible cycle is completed in three steps an isothermal expansion at T2 from V1 to V2 cooling at constant volume V2 from T2 to T1 and adiabatic compression back to the initial state a Sketch a diagram of this cycle using T and V as coordinates b A nonideal gas obeying the van der Waals equation of state is carried through this cycle Compute A8 for each step and show that AS 0 for the nonideal gas in this cycle Assume EV for this gas is constant I A bottle of champagne at a temperature of 280K is placed in a refrigerator that releases its heat into a room at a constant temperature of 300K the efficiency of the refrigerator is 05 times the corresponding Carnot ef ciency How many joules of electric energy are required to cool the bottle to a temperature of 276K Assume that the heat capacity ofthe lled bottle is equal to that of 10 kg of water and independent oftemperature A The following reactions might be used to power rockets 1 I H2g302g H20g 3 u CH30Hl 504g gt 002g 2H20g iii H2g F2g a 2HFg a Calculate the enthalpy changes at 25 C for each of these reactions per kilogram of reactants b Since the thrust is greater when the molar mass ofthe exhaust gas is lower divide the heat per kilogram by the molar mass ofthe product orthe average molar mass in the case of reaction ii and arrange the above reactions in order of effectiveness on the basis ofthrust A In principle methanol can be produced from methane in two steps or one O CH 4g H20g a COg 3H2 g C0g 2H2g CH30H g CH4g H20g CH30Hg H2g What is Ar at 500K for each of these reactions From the standpoint of heat balance would it be better to develop a process to carry out the overall reaction in two separate reactors or in a single reactor over 5 What is Aj for H2ga 2Hg at 298 1000 and 3000 K E398 1147 JKmol for Hg 6 Ifthe Gibbs energy varies with temperature according to b c G T a T T2 how will enthalpy and entropy vary with temperature Check that these three equations are consistent 7 At 298 K for H2g E 130684 JKmol A 0 kJmol and A 0 kJmol What are the values of the molar entropy enthalpy of formation and Gibbs energy of formation at 10392 bar assuming that H2 is an ideal gas 8 Ammonia isto be oxidized to NO2g to make nitric acid What temperature will be reached if the only reaction is 7 3 NH3g 202g N02g 5H20g and a stoichiometric amount of oxygen is used 1339 A 139 J 9 i a 7 g aw g e e e EU 7 f a CAME 3M f emu lL boT 63 LLJYKJ 5752 a W L39 T 47 K3 worlc Maw n 2 1 col bottle 09 3403143 423 Him f f Ar E33 3 A QQ9 99093 4 24 RVML Arm mm W W 40quot 525 V Z E dquot W7quot i r 7 3 17347 34 I 593 a a e 13 I 14 r75 3 v A92 L gem m5 my 39 2 2 c9 Ark3 2133 13 m5 5 at 241 745 H Fr YkIM f i Arbkgm a 53k5x725amp Dooi 7 i WhigwiwlwW 03973331quot v f 39 VQP cocwgcha 349 e e LQJ 0 QPWCcocsD 462 3910lQRT 1CquotLlD5L LD 7 iOs395 75 hQ g 443r44 5 gzgmg 1 ng 3 29 4 Agyigiaaf fL2 i f A Srilq 4 444 W 9 77 7 2142 i 530 41 796433 1 ZPJZeg 0LT zea W Mi ioIs 421590 29 a3 ML 1quot 939 7 L036 LLCuLM Hp 3 3 cage 6 253 A E2 a Ag i Wg 63503 MA 1 k r quotquot T 7 77 2gtLMMT 7 1471quot 241 lg 3 4187Mh ME EFWWWBVZ 5301 73quot F 6419 59 7 i 2 H33 T 98 3513 quot33 337 i 7 if 7 x r AME 15 Ar 0 CW7 441 i 1 J 7 4 f f W Wquot Gc3ggk e 3 6T5Q5TC L A 1 T F39 3971 CEM 484 Spring 2011 Problem Set 7 due Wednesday March 30 2011 1 a What is the maximum ame temperature that an be realized by a propane torch using 02g as the oxidant Assume that the combustion of C3H8 is carried out at 1 bar external pressure and that the initial temperature ofthe gases is 298 K b What will the maximum ame temperature be ifthe oxidant is air Assume that air is 80 N2 20 02 mole percent 2 The sublimation pressures of CO2 at 13885 Kand 15875 K are 133 x10393 bar and 266 x 10392 bar respectively Estimate the molar enthalpy of sublimation of CO2 3 The pressures at the solidliquid equilibrium line of propane are given by the empirical equation P 718 238565T1283 where P is in bars and T in Kelvin Given that Tfus 8546 K and AM 353 kJmol calculate AMV at 8546 K 4 The vapor pressures of solid and liquid Hi can be expressed empirically as 19020 and 29062K lan torr T 25957K 1n Pliqt0rr 17572 Calculate the ratio of the slopes ofthe solidgas equilibrium curve and the liquidgas equilibrium curve at the triple point Given that the normal melting point Tfus 222 K and the critical temperature and pressure are given by To 424 K amp Pc 830 bar use the data in the previous problem to sketch the phase diagram of Hi 01 6 Considerthe phase change Cgraphite Cdiamond Given that A5 Jmol18953363T calculate Ar and Aj Calculate the pressure at which diamond and graphite are in equilibrium with each other at 298 K Take the density ofdiamond and graphite to be 351 gmL and 225 gmL respectively Also assume that these densities are independent of pressure 7 The CRC Handbook of Chemistry and Physics gives the densities of many aqueous solutions as a function ofthe mass percentage of solute lfwe denote the density by p and the mass percentage of component 2 by A2 the Handbook gives p pA2 in gmL a Show that the quantity V n1M1 n2M2pA2 is the volume ofthe solution containing n1 moles of component 1 and n2 moles of component 2 where M1 and M2 are the molar masses ofcomponents 1 and 2 respectively b Show that M 1 A2 dpltA2gt PO42 PA2 61142 in 5 o ltI M2 1 A2 100dpA2 P042 PA2 dAz c Show that V n1l71 n2l72 3CDLC quot I fHLO a Timmg 7 Ark quotMEW Wigg H39h y M Egg SAQK COD 13551 ALP quot A4 39 Mama 7 4 Li c gem Wm 7103 a lagL 1295332 up Q I 1 o 3 o 3043 PPm4 dquot c we 329 201 2 I LCP CM 73 3 a 99Hilltgg pzqngu CiQLLD ags 1123 f LM3339C U7KJM i a 245 w Mww agx a ee Cg y y 2 mtg v 020 023 9 330 ra 99 2owkCQ a Mmw 20m Ziqs wao xw2Y17d 9 What 1 41 143 2 0 77 inlaysQ ML 7 new 25119 14 mm gt4Z SEF lie 939 lei 77 TL 4 quotl wf 5 AME quot4 3 35440 75 a 87751715392751 39 iQLY Moquot 1333quot 3731 9 7sz u 1252571397j3 7 W H 7 7 7 3 7 7 4g 2128323m39I071 ampT F quot W A4qu u 7 0amp7 Axgw mw 353019 x Lin 7 3061 19Tl391731 jo c S st39mM Loo 19M 3 7024 39 Qltw A 2 mama 3419016 7 t PU J 2 L 1W g 557 K 17572 T 1610 LK 9016 1259511 L H572 T 1 HS 3103quot T T QHR K J P3 HOQ39LK W0ze 7 53 lHLHC i 3924l ci 2010E ST C T 53 1QDC J cic l wr fe010K 11061 CU W T LL W wa s 7 iysZTai 7 5 74 393 g d J I Ai W5 ig j i ljS h QT 4 923 2 Envy P 6 Tlee y k 7 1 533 Hi 3 GUI 4 Q1 3 32 V lt M W 7 fag 136 wf kar 7406 03 is THE JsrrvaM D 03th GM MM t K S 08 Law ZILK hp 3 A0693 45351714 413311 T 59373 K T gov 4 22155 K93 1 mapha 3Mb 1 I oo 2001k 9 300 Loo 290 2 K Clt wrm Q mowwb i APEquot CFMIA ms 3343 i lt3 Arcf 31 139 7 7 1 Z0 1 I A1 AzmArg 0 AFquot g Arv 150 i A f i i H i 1 Wm V60 quotta lm 7x 3TILCL C4 3 5 7 43539taiK9Kw Looovy i w w g xU 331103 Law 1391wa 51 i Ari Li LLR S 7va 7 P k O 22397 3 tQ lm Mo Wde 7amp1 7 7 Bar 7 W A 7 7 64A qq J LL1mr L JLi le st if 7 41 00639 C 7 183 iitwto lpgwgt M2 Ma 5 x 10413 7 2 P oar 4 At 4 massCi 4 39 f d mes AL LM Lw r lt 06 n7 1 nLPIL L35 17f z 1 m x2112 mkm T654411 s nf Lrgl i aw A Tia 1 L 1 z km1quot39 mg v 3 0042 ME A aml T39R ni A1 1 1 399 7 rm 1 dhl 139 LVN 1 LMQ 3 M ML 711 71 mi 3 47 t m 56 gi d q L 924 a 1577 IA 9 EM m i i i Alphgg 05L 9 5le mg Tpl L i 4 gdga lg 44 45 mi 2 n 4 mm az Illt1me Vi 7 z 7l 2 731A 4 a 7quot qrL L ijJ ri 7 iIMwo MIMMLL 7 LWF 7 nm1g100 M1 7 AmMLmY A Loo mJu Am 64 1e VJ L ThJquotl 7 I 42 Tim 7J2 K i b f 4 62454237 V4294 17 E jLL 394 fl VL W Arms ltm j quot l h L W LE to if ntmk4 z39 i anL m44 m 1 CEM 484 Spring 2011 Problem Set 7 due Wednesday March 30 2011 1 a What is the maximum flame temperature that an be realized by a propane torch using 029 as the oxidant Assume that the combustion of C3H8 is carried out at 1 bar external pressure and that the initial temperature of the gases is 298 K b What will the maximum flame temperature be if the oxidant is air Assume that air is 80 N2 20 02 mole percent 2 The sublimation pressures of C02 at 13885 K and 15875 K are 133 x 103 bar and 266 x 10392 bar respectively Estimate the molar enthalpy of sublimation of C02 3 The pressures at the solidliquid equilibrium line of propane are given by the empirical equa on P 718 238565T1283 where P is in bars and T in Kelvin Given that Tfus 8546 K and AME 353 kJmol calculate AMV at 8546 K 4 The vapor pressures of solid and liquid Hi can be expressed empirically as 62 In P torr 2 19020 and In P39iqt0rr 259397K 17572 Calculate the ratio of the slopes of the solidgas equilibrium curve and the liquid gas equilibrium curve at the triple point 5 Given that the normal melting point Tfus 222 K and the critical temperature and pressure are given by Tc 424 K amp Pc 830 bar use the data in the previous problem to sketch the phase diagram of HI 6 Consider the phase change C graphite a C diamond Given that AEOJmol189533637 calculate Argo and AEO Calculate the pressure at which diamond and graphite are in equilibrium with each other at 298 K Take the density of diamond and graphite to be 351 gmL and 225 gmL respectively Also assume that these densities are independent of pressure 7 The CRC Handbook of Chemistry and Physics gives the densities of many aqueous solutions as a function of the mass percentage of solute If we denote the density by p and the mass percentage of component 2 by A2 the Handbook gives p pA2 in gmL CEM 484 Spring 2011 Problem Set 9 due Friday April 22 1 A1 L reaction vessel containing 0233 moles of N2 and 0341 moles of PC5 is heated to 250 l C The total pressure at equilibrium is 2933 bar Assuming that all gases are ideal calculate the equilibrium constant K for the only reaction that occurs PCls g PClgg Clzg 2 In the synthesis of methanol by CO g 2H2 g a CH30H g at 500K calculate the total pressure required for 90 conversion to CH30H if CO and H2 are initially in a 12 molar ratio K 609 X 103 3 Water vapor is passed over coal assumed to be pure graphite in this problem at 1000K Assuming that the only reaction that occurs is the water gas reaction C graphite H2O g a CO g H2 g K 252 Calculate the equilibrium pressures of H20 CO and H2 at a constant total pressure of 1 0 bar Remember that the activity of a solid in this heterogeneous equilibrium is equal to one 4 The equilibrium constant for the reaction N2g3H2g 2NH3g is 350 at 400 K when partial pressures are expressed in bars Assume that the gases are ideal a What is the equilibrium composition and equilibrium volume when 025 moles of N2 are mixed with 075 moles of H2 at a temperature of 400 K and when a constant total pressure of1 bar is maintained b What is the equilibrium composition and equilibrium total pressure if the initial mixture of gases from part a is placed in a 3326 Ltank at 400K 5 a Use the thermochemical data and gas law data given below to calculate Kp forthe synthesis of methanol from carbon monoxide and hydrogen at 400 K and a constant total pressure of 100 bar Considerthe thermochemical data to be independent of COg 2H2g gt CH3OHg 798W mole Kmal temperature over the temperature range ofthe problem and the gases to be described by the truncated virial equation of state Z1BP b Calculate the equilibrium partial pressure of methanol under the conditions of part a if the reaction is started with a stoichiometric 12 molar ratio of CO and H2 0 What would the equilibrium partial pressure of methanol be ifthe gases were considered to be ideal W WWHW 7i7i7 i 7 WWWi if W K3 60 X153 Xanadu LKquot r 7 w39 29quot 239 W g n fu r quot jig fax 1 13402 be 10333015731 404 W3 3 r i 0 al gg i 6amp3amp253 i f h fieS 5 5 5 7 mi J quoti 39 S 339 if K 2523 Ben 91 has 2 no 3391 H7 1524L g 7W 1 f h f i m 6 1n 1z 35131 oK eh S frag z XiVELJ P 39th A if 7 7 if m 4 quot quot A A 1 u 1 1 1 1ft u gunquot 7 7 i allf k f E g i 36 O 7 Q Hi 149 3ampLC53E T 1M aqil sn 7 12525 179 25 w i i 7 iiil A 74A 7 W llz 3KO FNEEV 7 J23 E 7 L r 3 gt3 3 x x 9 74 74 295 JsF3 gtny 7 7 n2 ua W W Qilii2 I Vi WV 3520 2 Hiquot 1 2 457 st 7 quotAQQSES 3553533 2 3amp533 K kg quot M39 a 39aKSEE S 1 quot f 54 7 I I 2 7 J 1 4 510 A 0376 ll1 35 x Gimme wwgnplp if A f g f f g f V 4 gi 3 a i M a 7 ins w QLSW i V 46quot i H A i 103331l19ou3 a 6731 i 32cJ i 719 2s 6 75f m v gm quot16195754 3 9 f Lj SF 8635 13393 C i 30 CZ57 fo idC 3390 iJ 7t51193 I m2 s0 3 57 MS 0 30 6X 6 I PM 12651 z gigs covaa dmwQ Y 33 14 ALWFM Q0 f lo 53329 CbgOHCgA 333LKXQ39Cno mm WW 0 Aruzocv39 w 1 a 4 T i 33gsmp ArZquot quotIa lgg HooK 33Q3TgtL lgt a 0001 loo yak I HfL H HYLoTM J quotszetno 3 Hw A K a 3 T9quot 1 0235 A H BP P7 I R T V PT i 331 P Knew QVMP 1 B quotdp 5quot lb 1quot 212479 lt BRT39PI hr RTLE aTR IA A cur quot A 7 3Prbu5 5 ab 73 0 J V 549 m do 73 7 9917 5quot11101 5 Mason 8 0139 4514 xlo q Lax 441 Y a e os S L 391 Igua f v a CM 39A Y0 1 e 1 Lou K 3 Vegan f 043C LLt L 1 1 Ym 1L MINI055 392 J A gt V 3 b 39 39 130 45 a quot 39 Z M 7 A LES Q399 139 K Chemistry 484 Spring 2011 Problem Set 2 due Wednesday Jan 26 2011 L What mass of N2 gas is present in a 500 L container at 400 K under 200 bar of N2 pressure if a the gas is ideal and b the gas obeys the van der Waals equation of state for N2 a 137 L2barmol2 and b 00387 Lmol N Use the van der Waals equation and the RedlichKwong equation to calculate the value of the pressure of 10 mole of ethane at 4000 K confined to a volume of 8326 cm3 The experimental value is 400 bar vdW constants a 55818 L2barmol2 b 0065144 L mol for RK A 98831 L2barT12mol2 and B 0045153 Lmol 0 Butane liquid and vapor coexist at 3700 K and 1435 bar The densities of the liquid and vapor phases are 8128 molL and 06313 molL respectively Use the van der Waals equation the RedlichKwong equation and the PengRobinson equation to calculate these densities o 1644 L2barmol2 and 3 007245 Lmol for the PengRobinson equation for VdW a 13888 L2barmol2 and b 011641 Lmol and for R K A 29016 L2barK1 2mol2 and B 008068 Lmol A a Manipulate the DieterICI equation of state into a Virial expansion in The equation a of state is PeRT 7l b RT where a and b are constants analogous to those defined for a van der Waals gas Recall that X x2 x x4 e 1x 2 3 4 039 Calculate the value of the second virial coefficient at t 100 50 0 100 and 150 C for Ar using the van der Waals coef cients a 1363 L2barmol2 and b 003219 Lmol O In terms of intermolecular forces what does it mean when the second virial coef cient is positive What does it mean when the second virial coefficient is negative Draw a graph of the second virial coef cient ofAr as a function of temperature and comment on the temperature dependence 0 Calculate the value of the third virial coef cient ofAr at 0 C and 50 0 assuming the Van der Waals equation is a correct description 01 Calculate the Boyle temperature of Ne assuming it is described by the van der Waals equation of state a 021666 L2barmol2 and b 0017383 Lmol O A gas is represented by the equation of state 1 b PRT12 3 V V V over where a and b are constants Derive expressions for the critical volume temperature and pressure in terms of R a and b 7 a The density of 02 as a function of pressure at 27315 K is listed below lP bar p250 l0500 p750 l1000 lp gL l0356985 l0714154 l1 071485 l1 428962 Use these data to determine B2vT ofoxygen at this temperature Take the atomic mass of the oxygen atom to be 15999 and the value of the gas constant R 831451 JKmol 0083145 LbarmolK b Using the hybrid sphere potential section 167 ofthe text to model B2vT where Uroo forrSo C 66 forrgto r Determine the values of the hardsphere diameter 6 and the coefficient of the 1r6 term Ce in the potential energy expression The Boyle temperature for O2 is 4059K PMS L 39 0 4 i A Pvth f if 7 4 g lgi hgx 2g f0oY3Lw1Azoalt AAAL k WA 1 i f 7 3q a L P 27quot M aw V Q 7139 Ms lo V1 h V1 ET q 1 404 1 Vii A v P ri7 la3 KT 7 K 07 i 45 V P V V P 1 R 3v 7 CF y A 0 V a J 3 39 v 311L015 quot f 30065 lt1 039 l J 3 O in lt So a La MMLamp gt hark OAnc vwi Vs 45 1 a MML M Z 5 j W V 14 113 V hi 001 3011 i 39 w l L M9 J m M 05121 quotitem4 M Lx D 45am P fr 14 f 7 6 7W7 V 6 L 39 Em C 91033 Igggtu oo t5 a X 373 A M1 4143351 wmgquot W 1 If wBac LH 1 026763 Aquot M 21gt co 56413 P 3723 bu Mam 72345 MA PV ng iza v L e quotL v3LV av ci 3 2 v 1 P T9 P 393 1 V beru 4 1171190 P 3 P p n 1L 3 i 39 L w x V C GAMMA 033M337o601 3838 uz V ML f35 6 ur I q 3s 4r Bla gtogsw V f3339 fw 3 L V quot QL JSCV 094 1 A 011313 2o 3 me 73 E l gagsc fsz n 0113 36gt x 71 Sawjv v u 1752 D M v 39 3 this A V vu may l7 w J r WMI W I p rv R 1397 39 3 u I d Agiritad A 7 f A a 3quot V vu1173911 342 5574M e M 7 V 71quot V0 campg 4 4 77mm quot L M J F 12 35 7A Mkwv 39P 427 gt4 176 7 7 1 1170385 In A Rama 2 sn 1 T H WM 3 PVZC39V33 PBWv w BB 4 V g 2 RTVWHD TVI TM 7 7 39 PV M Raft PW w AnsVQ lwm 3 7T7 Z7 PVZQ QTVL EC Qg hn 143 0 TNL V F U S E3 E5 L 34 E 233 gl A o P L39T U 9 3 WP 3 lqu 1 13 5quot a I r V 0033mgt37o0 139 43 1 mfo XOWAB mashr ZQmewXu gvo K M 6os3 Lif37 o 3049 m L a w W H2ng j Q39 513 ofa xewb A A any 41 a V quot21LIV 4 04X21V 39jg o C in I 9114 3703772 aowyj 2 153 e 7 535 43 J p 1 M 38 w 7 m 5L 7 shaLO Q Ly 9 1 1 Q6 rg 1 4 d mgi 4 ship 31 4711 14d9 Ayia74ia g EELAMA w 7142922 Vim 2 W29 442 AL 2 m ltVAgt 4 pf g gt6 s W Md w w w AT 429 w j A QM gto mRVJAki Via w w 371 gagDP 439 v pgDd lt02 v2 6 70 Z L zQ m 31 1 O7245j gt ZEBMQWQCO7ZVIgt P P M L3539 A 4lt 1 h H35 03 200 2 ML RTE 3 lt r 03 375077 I 5 7quot z 737 wlqBy 39 n zd gt JL IG7 4539 gltc 00752945 4339 00786 1gt 2 U L199 082190 I my 3 4 3 14 34 JAIL MK x I e lgtltgtfr M 2 2 0 Llt gt AILM 9 gt la1 Lc32 151gI739 VJKV leTMV MT KT M77 B1f L U f R 1 13 1 41g1ggL L Mm erw le y f 53 RA Er 4 47 A r7312 003mi JZT me 52 3x3 73 7 Q 573 C M7413K 1 oaag nm 000 LMCL Q amwm 741114 M too 200 goo awequot t L l l f 1 51 11 139WT WW quot z W m w vi gagg mui M 6 0 6ch u g VA La P HT 5 7 2 5quot ariaquot1 x7 if V q q la 15 v RT VA rawU Jr 5 50 127 k 7 AL 111 kw r51 paer 5 QA1lle K JarLC ux Ra H QDL V MR 7 V 7 8213 10336 LMD v 03 4 W 7 W W 6 W71 Mm M 74 MW 754v 31V 5 a 1 O ILL RT 7 W govt2139 0 1 03 1431 2 m i m MWO173 3Z m COd MM K W VII 239 7 gt A5902 8 LEJ 2er 4 97341 3H1ij 53440 KartL T 92 V e l 2 O Ele if Balazv 9a VATILQL 1 M U i V 3 RT 4 35 v 395 61 a k A 39 RM E Z 3M5 Law W 3W W in M Lm X 7 Um 0312 9ky iolj rig 2 mm 3 L j 47 0 3 7L37215r WHEN 4 j T wl m eo9WLHJ Log V r 39 M W Blvdr 911 c gu 0711 C 3 3 kgquot c3quots aria zafgvj zgy zo W Exam ZhrMC CL ag g osak gag r 3 a x 3Q lHOSCi39ka r 7 M 7 i7 7 i 3 2 O O7LH J 1 if Cg M L 3 hi l crg K 3 q 1 QWUA Y gtf qu 455511 Z 7 l 3 3ampsz L N 0 A 01 0 Chemistry 484 Problem Set 1 Spring 2011 Due Wednesday January 19 2011 Calculate the value of the pressure in bars exerted by a 420 foot column of water Take the density of water to be 100 gmL A surface science experiment is carried out in a high vacuum chamber where the pressure is 103912torr mm Hg How many molecules are there in a 100 cm3 volume inside such an apparatus at 298 K What is the corresponding molar volume at this pressure and temperature 100 g of N2 are mixed with 50 g of O2 and held at 25 C at 0750 bar a What are the mole fractions of N2 and 02 b what are the partial pressures of N2 and 02 c What is the volume of the ideal mixture A mixture of H2 and N2 gas has a density of 0216 gL at 300 K and 500 torr What is the mole fraction composition of the mixture It takes 03625 g of N2 to fill a glass container at 2982 K and 00100 bar pressure It takes 09175 g of an unknown homonuclear diatomic gas to fill the same bulb under the same conditions What is the identity of this gas Nitrogen tetroxide is partially dissociated in the gas phase according to the reaction N 204 9 lt 2 N02 9 A mass of 2315 g of N2O4 is placed in a 050 L container at 353 K and dissociates to an equilibrium mixture with a total pressure of 2130 bar a what are the mole fractions of N204 and N02 at equilibrium b What percentage of N204 dissociated Assume the gases are ideal 1 P m 90m 1 Hag moonr 43 7 599113 lt7 My 53 1 263m 5L 1 Hiogh g eh v Km 7 Z M 0009 lDoetcc3j I Yrvamgk ig r 1 4st s 7 J A 7 1 oru P 49639 Em Hm I139 U 2 h 1 lo 1250 ht03L A 39 nob 1 Sgimo ioe arm iuz u wax V 4 quotHi 773 Lco k lgggql i E39Sfmo meQF I A i V v 13K 0 M IMJL 91 7 5amp357 n 180339 Siege 4 INA A A V U 7 U to b m 31030 gtrr w XQ L O Q q 0 35 1151 x x l cum 0304 I V Ra 39 JP c ajl 7 1 W V EE x J s 3 01 721 LL 9 RT i W A5 7quot CMXquot 33 Q 7 rueL KDYQ n1 WM Yo 1 2x 2Y gtlt CEM 484 l A P 01 O 1 Spring 2011 Problem Set 5 due Monday February 28 A 100 mole sample ofa monatomic ideal gas in a balloon is initially at P1 100 bar and T1 300K The system is then heated to 400K at constant pressure Calculate the nal volume AH AU q and w for an ideal gas 5p 5R2 The value of 5p for a sample of an ideal gas was found to vary with temperature according to the expression CPU Kmol 2017 03665T Calculate q w AU and AH for 100 mole ofthe gas when the temperature is raised from 25 C to 200 C a at constant pressure and b at constant volume When 0500g of propane C3H3 was burned in a bomb calorimeter of heat capacity or calorimeter constant Coal 641 JK the temperature rose from 29800 K to 31015 K Assuming that a stoichiometric amount of 02g was initially placed in the bomb and that the reaction went to completion calculate a the standard molar internal energy of combustion and b the standard molar enthalpy of combustion One mole of helium gas undergoes an isenthalpic expansion AH 0 from an initial temperature and pressure of 700 K and 1000 bar to a final pressure of 1 00 bar Calculate the nal temperature ofthe gas if it can be described by a truncated van der Waals equation of state nT P b where b 0024 Lmol Assume that 5p 208 JKmol and is independent oftemperature A 250g sample of methane gas at 250Kthat occupies a volume of 1 400 L expands to a nal temperature and volume of 150K and 730 L Calculate the change in entropy for this gas sample assuming that it obeys a the ideal gas equation of state and b the van der Waals equation for CH4 a 228 L2barmol2 and b 428 x 10392 Lmol CV 2705 JKmol One mole of ammonia expands adiabatically and reversibly from an initial temperature and volume of 200K and 01 L to a nal volume of 200L What is the nal temperature ofthe gas Assume that ammonia behavesas a van der Waals gas for NH3 a 4225 L2barmol2 b 00371 Lmol and CV 273 JKmol Determine A8 for the compression of 4000L of CeH5I at a constant temperature of 300Kto a nal volume of3910L The coef cient ofthermal expansion or 124 x 10394 K391 and the isothermal compressibility K 921 x 10396 barl L100 c f 3994 7 7 3D bL LM v w vvv mu 7 V 2w 7 Lava 0770 83V 77L A r N 7 V Mn M m quotWKquot mm w N 4 V 7 AH F ALL H a ALPAH 25W 27073903 7 Pixt H143 7 120 80 lbart 3w322 11Ei3J vux MST 44 L1 we 203935 H 4QL ifI jffif Hoot3N 1 33r a 0 bmwwmmWMWWHwwV mwwmwmmm V w J it ko A M W A M m 772a TM 7quot 950 473K W Q73 AHz 9P4r nygoQT A 1017 0 3 877gta67 W 7 24gt lt n 1 TL hwn w 7 T Wm 1 35 6Mgt75 1S7CI Loco Zr MW Aw 21572 qu AUV AL 4PM 1 24 T A x 9T5 2726 kr N2 7 143 7 W l M L457 kamn 473233 ALT Kw N 00 Ll gt2 M39jg LQXDN gzyz gg quot 9 wa um Zuni gm CP CvzmQ a CV CP KR Hum AU O 33 WTm quot O 4 ltTZamp WW W mw 7 Uh w Hq L a 43 73 H H823 23 a 249 n3 4 46233 B i z i r ltDo7aT 1 4730 x 3aw f 163 Jq 7 7 h la ATMMH V WWgtMAH 3 V H 9W 15ng 3 Qvo ai lom AQEMZARM 39 Mil Ii BLOJSK g gmg 2e a JugWBLELB 0 ML 77395 AV 77363 W omwkgug amp Ash AM a AORT Ama Rgszz mquzr 2 aocH W 12me 94 O X W 77f 1697K le 3ltotl4w2 034 h MQ PM M AW 77T 31 7 ltQ0341MX310 6 6 o hd qyey mm 77 10 1 36223 N 78 0395 1 7 2 H 7370I 7 Q ovto rj 1 oUI Mcggy 7 LL64 7amp3 au 1 744 sz 393139 P 3 T 7og 06b w 7 1 Alida pl d jLgl amp T I Li 696 39 3d fHJQ gj vg a 557739 if 2 Li fquot 39ii1 ifiii Pcv m39 nnfi f Loo 9 l 14 r v l z if 7 Wk 15645730 L 6 5 Cu fMo 7M CV Elna44TWV14 m Q 1 g lwgwggmwv wmwAka3ampFampvnw 3 V T F 3i l 33 w V BM 3T1 V Maw 7 h 193 Wk 1512K 72 Cu 723 A3 3 nghq y 17ng I H 9 5523 250 4 6 7 751007 N 2411 AQAV K 230 400 EOE ZNL 33quot 32 f 317 71 C V 2 gt it Q u RAvL a A 406 KM wazll 4 D aquot 4424 zk39tfsm 4 XH MT Why Aquot Von L Vquot A e 2 JAE LgtT V hb marA 2 3 wag Q54quot3M3 27b3 h mama 0313 v E V1390 QJZ 643 Moo me sxwuLN mag no 3 2 K K i TL 10 O L AX39S 41 Ag 0 lt gtde 4 51r r 200Koq K g3 ESL T V nb 6 TS 047 734V m Ni 3900 0 477 7 was i 7 Zoom H 7 7 7 V r r maid 100L lab CV Tm 397 mL M 2 Q q l 73lt 3 tom 3 373AGEQB 2 474 E 010103739 1732A71 1 411 K wL CEM 484 Spring 2011 Problem Set 8 due Wednesday April 6 2011 1 Trichloroacetic acid TCA dissolves readily in water to yield a solution that shows a large increase in volume The data given below are from an experiment where small amounts of TCA were added to 5000 mL of pure water at 25 C moles TCA Solution Volume mL added 000 5000 00156 539 00316 553 00455 556 00626 572 00785 586 00975 604 01091 614 a Construct a plot of the moles of TCA nTCA added vs total solution volume and fit these data to a polynomial in nTCA Both third and fourth order polynomials will do a decent job of fitting the data b Using the polynomial expression you derived in a derive an expression for the partial molar volume of the solute 17m in terms of the moles of TCA added c Construct a plot of 17m vs nTCA What is the average value of 17m found over this range of concentrations 2 a The vapor pressures of pure tetrachloromethane component 1 and trichloroethylene component 2 between 768 C and 872 C can be expressed empirically by the formulas 279078 9 23454 lnP1 t0rr 158401 and lnP2 t0rr 150124 t2264 t1927 where t is the Celsius temperature Assuming that tetrachloromethane and trichloroethylene form an ideal solution at all compositions calculate the values of X1 and Y1 that give rise to a solution with a normal boiling point of 820 l C b Use the data in part a to create a crude 3 solution points boiling temperature composition diagram of a tetrachloromethane trichloroethylene solution c What is the normal boiling temperature ofa solution where X2 070 3 Suppose the vapor pressures ofthe two components of a binary solution are given by P1 X1131eX 2 and P2 XZPeX 22 Given that P1 750 and P2 160 torr calculate the total vapor pressure and the composition ofthe vapor phase at X1 040 4 Ethanol and methanol form very nearly ideal solutions At 20 C the vapor pressure of ethanol is 593 kPa and that of methanol is 11 83 kPa a Calculate the mole fractions of ethanol and methanol in a solution obtained by mixing 100g of each b Calculate the partial pressures and the total vapor pressure ofthe solution c Calculate the mole fraction of methanol in the vapor 5 lfthe vapor pressures ofthe two components in a binary solution are given by Pl X1Plsng RT and P2 XzfgelezRT show that AG RT L XllnX1X21nX2X1X2 AmGw wn1n2 w A S AmSR XllnX1X21nX2 Rn1n2 and A H A H L XIXZ w m wn1 n2 A solution that satis es these equations is known as a regular solution The w term can be modeled in terms of intermolecular forces using a statistical thermodynamical model 6 Suppose we express the vapor pressures of the components ofa binary solution by P1 Xleeo Xg and P2 Xnge xi use the GibbsDuhem equation to show that or must equal 5 7 The Henry s Law constants for oxygen and nitrogen in water at 0 C are 254 x 104 bar and 545 x 104 bar respectively Calculate the lowering ofthe freezing point ofwater by dissolved air with 80 N2 and 20 02 by volume at 1 bar pressure 8 If 684g of sucrose M 342 gmole is dissolved in a 1000g ofwater a what is the vapor pressure at 20 l C b What is the freezing point The vapor pressure of pure water at 20 C is 23149 kPa PM SM 5 Solqu39M 4 944491 tEX wa JQJ a 17 M 7 M77 Mai44 a imla i mLJL gt 413031 K 05 I o 324 no 33 no iii07 509 V 5mm 110 n lomqmr n 8Pxo3 6300 1i 3 Kyle h 139 I 39IErr c Su aH M 1PM 2 Mmg I no 0 IQ gal n A me m Volume mL Problem Set 8 pmblem 1 50 if 7 V 77 0106 0f08 11 004 062 moles TCA added