Chemistry Exam: Thermodynamics of Ideal and Van der Waals Gases - Prof. Alan R. Esker, Exams of Physical Chemistry

Download Chemistry Exam: Thermodynamics of Ideal and Van der Waals Gases - Prof. Alan R. Esker and more Exams Physical Chemistry in PDF only on Docsity! Page 2 of 2 Chemistry 3615 First Exam October 2, 2013 _____________________________ Name Answer Sheet Circle the Correct Letter. If you change your mind, completely erase the wrong answer if you are using pencil. If you are using pen completely black out the wrong answer and clearly indicate your choice for the correct answer. If you need additional scratch paper, just ask. 1. A B C D E F G H I J K L 2. A B C D E F G H I J K L 3. A B C D E F G H I J K L 4. A B C D E F G H I J K L 5. A B C D E F G H I J K L 6. A B C D E F G H I J K L 7. A B C D E F G H I J K L 8. A B C D E F G H I J K L 9. A B C D E F G H I J K L 10. A B C D E F G H I J K L 11. A B C D E F G H I J K L 12. A B C D E F G H I J K L 13. A B C D E F G H I J K L 14. A B C D E F G H I J K L 15. A B C D E F G H I J K L 16. A B C D E F G H I J K L 17. A B C D E F G H I J K L 18. A B C D E F G H I J K L 19. A B C D E F G H I J K L 20. A B C D E F G H I J K L Page 5 of 22 Useful Relationships and Definitions pT V V 1 ¸ ¹ · ¨ © § w w D Tp V V 1 ¸̧ ¹ · ¨̈ © § w w  N FdzdW  dW = -pop dV ³ 2 1 V V opdVpW ¸ ¸ ¸ ¸ ¹ · ¨ ¨ ¨ ¨ © §  ¸ ¹ · ¨ © §   ... V b V RT ab 1 RT VpZ 2 2 ¸̧ ¸ ¸ ¸ ¸ ¸ ¹ · ¨̈ ¨ ¨ ¨ ¨ ¨ © § ¸ ¹ · ¨ © §  ¸ ¹ · ¨ © §  ...p RT ab2 RT a p RT ab RT 11 RT VpZ 2 3 z z x y 1 y x ¸ ¹ · ¨ © § w w ¸̧ ¹ · ¨̈ © § w w 1 x z z y y x yxz  ¸ ¹ · ¨ © § w w ¸ ¹ · ¨ © § w w ¸̧ ¹ · ¨̈ © § w w V V T UC ¸ ¹ · ¨ © § w w p p T HC ¸ ¹ · ¨ © § w w R = 8.314 J•mol-1•K-1 = = 0.08206 L•atm•mol-1•K-1 1 atm = 760 mm Hg = 760 Torr = 101325 Pa 0.001 m3 = 1 L = 1000 cm3 H JT p T ¸̧ ¹ · ¨̈ © § w w P V p C C J JpV = constant 1TV J = constant JJ Tp1 = constant dU = dQ + dW, 'U = Q + W H = U + pV (linear) R)5N3(RR 2 3CV  linear)-(non R)6N3(R 2 3R 2 3CV  F = 2 + C - P T dQdS ³ 2 1 T T i12 dTCTH)T(H ³ 2 1 T T i 12 dTT CTS)T(S S = k ln :k = R/6.02x1023 := !xy!x !y x y  ¸̧ ¹ · ¨̈ © § Page 8 of 22 Table 1.7. Selected equations of state Equation Reduced Form Critical Constants pc തܸ௖ Tc Perfect Gas ݌ = ܴܶ തܸ van der Waals ݌ = ܴܶ തܸ െ ܾ െ ܽ തܸଶ ݌௥ = 8 ௥ܶ 3 തܸ௥ െ 1 െ 3തܸ௥ଶ or ߨ = 8߬3߶ െ 1 െ 3 ߶ଶ ܽ 27ܾଶ 3b 8ܽ 27ܴܾ Berthelot ݌ = ܴܶതܸ െ ܾ െ ܽ ܶ തܸଶ ݌௥ = 8 ௥ܶ 3 തܸ௥ െ 1 െ 3 ௥ܶ തܸ௥ଶ or ߨ = 8߬3߶ െ 1 െ 3 ߬߶ଶ 1 12 ൬ 2ܴܽ 3ܾଷ൰ ଵ/ଶ 3b 2 3 ൬ 2ܽ 3ܴܾ൰ ଵ/ଶ Dieterici ݌ = ܴܶ݁ ି ௔ோ்௏ഥ തܸ െ ܾ ௥݌ = ݁ଶ ௥ܶ݁ ି ଶ ೝ்௏ഥೝ 2 തܸ௥ െ 1 or ߨ = ݁ ଶ߬݁ି ଶ ఛథ 2߶ െ 1 ܽ 4݁ଶܾଶ 2b ܽ 4ܴܾ Virial ݌ = ܴܶതܸ ൜1 + (ܶ)ܤ തܸ + (ܶ)ܥ തܸ ଶ ൠ Periodic Table of the Elements 18 ? He 2 130 14 15 16 17 | avn a 5 \ 6 ;7\ 8 \ 3 | 10 2 > Li | Be Bic |N)|O F | Ne ssa | 4919 com || i201 | ae0: |, 1800 || 10.60, 11/12 43 | 14) 16 \{ 17 3) Na Mg Si s || cl nol) 3 4 5S 6 PF 8B 9B 1 11 12 | 2652 | 2809 ,| so97 |, snr || asas 19 | 20) 22 (22/23 | 24 \f 25 | 26 | 27 | 28 | 29 | 30 |) 31 | 32 Bd | 35 4) K | Ca} Sc} Ti | V | Cr} Min) Fe |) Co} Ni} Cu Zn | Ga |) Ge Se || Br Lss.10_ | vo.8 | 04.96 || 17.87 | 50.94 | 52.00 || sas ) sass || 6355. 55.01 | 69.72 )| 761, | 7792 |, 7.96 || 79.80 (37 [ 38 |" 39 \ 40 41 | 42 \f 43 |f 44 | 45 | ab \l 47) 48 | a9 | SO “32 (53) 5) Rb | Si Y | Zr | Nb} Mo|| Te | Ru|| Rh} Pd || Ag Cd /) In || Sn Te || | 35.47 | 97.52 | egoi )| 91.22 | 9292 | 95.94 )| 981 | 1012 || 2029), 106.4 || 1079 1124 187 cars || 125 {55 [56 \ 57 ){ 72 / 73 | 74 \{ 75 \{ 76 \/ 77 |" 78 \ 79 | BO \f Bi yf 82> 84 \{ 85 ) 6 Cs | Ba| Lax Hf | Ta) W)) Re | Os|| Ir | Pt || Au) Hg |) TI | Pb Po || At (ize | 1373 | 1369) | aas_| 1309 | sana || 1862 1902 || 1922 } 195.1 || 197.0 | 2096 || 204. )| 207.2 203) )|_(210) | { 87 ( 88 ) 89 |{ 104/105) 106 |/ 207 \/ 108 | 109 7) Fr Ac ® Rf | Db) Sg) Bh) Hs |) Mt zes0 ) 2270 ) | s2say | casa} | (265) )| 4252) ||_@6 | 263 58 (59 |/ 60 |’ G1 / 62 || 63 | G4 \f 65 | 66 | G7 | 68 / G9 |) 70 | 72 6* Ce | Pr Tb | Dy) Ho) Er | Tm Lu saat [1209 || 442}, tase (aso || 1520} 1579 || ssn | 1505), 649 || 167 | 1609 |, 1720 || 756 90 ){ 91 \{ 92 \° 93 \f 94 \f 95 | 96 \f 97 \f 98 |’ 99 \f 100 {101 |” 102 }/ 103 ) 7% Th | Pall U cm)|| Bk | Cf | Es || Fm |Md) No |) Lr zazo | zat || aseo) 237 || 226 || zens | zara || agg || 2st: | asa j| ase.a_ | ase.a | pasar || (25a), Page 9 of 22 Page 10 of 22 The next three problems use the following information: 0.7500 moles of an ideal gas with a constant molar heat capacity at constant volume of (5/2)R is originally at 1000. K and the volume of the system is 0.1600 m3. The gas is subjected to a three step cycle. First, the gas is cooled isometrically to one-half of its original temperature. The gas is subsequently compressed isothermally and reversibly back to its original pressure. In a final step, the gas is returned isobarically to its original state? Hint, start by drawing a picture. You may assume that the heat capacity is independent of temperature and the gas behaves ideally for all processes. 1. What is the internal energy change in kJ for the isometric step? (A) -25.46 (B) -12.99 (C) -7.794 (D) -3.637 (E) 0 (F) 3.637 (G) 7.794 (H) 12.99 (I) 25.46 2. What is the energy change in the form of heat in kJ for the cycle? (A) -2.232 (B) -1.594 (C) -0.9567 (D) -0.3189 (E) 0 (F) 0.3189 (G) 0.9567 (H) 1.594 (I) 2.232 3. What is the work in kJ during the isobaric step? (A) -7.275 (B) -5.196 (C) -3.118 (D) -1.039 (E) 0 (F) 1.039 (G) 3.118 (H) 5.196 (I) 7.275 5. Consider the following equation of state: __ kT 3a V=—+b-as What is Ty for this equation of state? we eof of of © 3% «1 Ole a AT, Bae Bap = - p — Bae 9. a2 0% ean _ Rtee Rr ja tb Bap ee - —t ey ar Rt Rr RT" z . TE We tole MW dtavatwe of 2 (2 Teo then we will sek ~ jereud Cqunti? 9 for all Slopes af Zz. Oh tee spr et ‘ RT WE showever, 2 wt WE derivatne of ths Sipe be cau We wat +e find whet the ‘lashes F valve of he Slope we Gy howe with Hey eayua tion wecavse the beyhust slit vk Gan bast (5S related to the yy hest ene ~ ye vk Cm Wwe, j (3% -2 + 28 16 qT = i on 7 Rr RP 5» wes + > kT a = LRT ’ e T® RT ‘ , ~~ my 3 (a= bRT AY (te _ -? TER ~ Teny T - >| Ba x oR TE yw bot be prut te yorrselé het Ys i the May yr ™ CVvalvake et FRomd —ferwatwe we sot oh phy Ty, ints Ty ond mk iF a ty ative valve OF CY PRIS fon | Ye moog (Awe 5h Yow may not Owe frome in We Yow get Yo Kw you have Cx am): Yemen er ft, dul Ale Leak Ame O Fay SO mar vale Fry 70 Pen Parn Page 13 of 22 N ot e th at so lid li ne s r ep re se nt r ed uc ed te m pe ra tu re s. Page 14 of 22 N ot e th at so lid li ne s r ep re se nt r ed uc ed te m pe ra tu re s. T r = 1. 00 1. 05 1. 10 1. 15 1. 20 1. 30 1. 40 1. 50 1. 60 1. 80 2. 00 2. 50 3. 00 3. 50 4. 00 5. 00 6. 00 8. 00 10 .0 0 15 .0 0 Page 16 of 22 8. Figure I contains two isotherms (T = 600K), one for a perfect gas (PV=nRT) and one for a gas governed by Equation of State 1 (b !0). Figure II contains two isotherms (T = 300K), one for a perfect gas and one for a gas governed by Equation of State 2 (a > 0). (I) Equation of State 1 ݌ = ோ்௏ഥା௕ (II) Equation of State 2 ݌ = ோ்௏ഥ െ ௔ ௏ഥమ Which of the following statements is correct for any isothermal reversible expansion with the same initial and final molar volumes for the ideal and real gas in each case? (A) The molar work done by the ideal gas is larger for both Figure I and Figure II. (B) The molar work done by the ideal gas is larger for Figure I, but the molar work done by the real gas is larger for Figure II. (C) The molar work done by the real gas is larger for Figure I, but the molar work done by the ideal gas is larger for Figure II. (D) The molar work done by the real gas is larger for both Figure I and Figure II. (E) There is insufficient information to answer this problem. Page 17 of 22 9. A sample of nitrogen gas behaving ideally has a density of 0.0850 kg/m3 and an isothermal compressibility of 2.00 x 10-5 Pa-1. What is the value of the coefficient of thermal expansion in K-1? (A) 8.84 x 10-5 (B) 1.08 x 10-4 (C) 1.69 x 10-4 (D) 1.99 x 10-4 (E) 3.21 x 10-4 (F) 3.54 x 10-4 (G) 3.88 x 10-4 (H) 4.42 x 10-4 (I) 5.04 x 10-4 10. Substance A with a molar mass of 0.08380 kg/mol existing in a single phase gaseous state with a molar volume of 9.22 x 10-5 m3/mol is cooled into the two phase region where the mass density of the liquid (Ul) is 2413 kg/m3 and Ul/Ug = 3.76 (where Ug is the mass density of the gas. What is the mole fraction of the liquid? (A) 0.10 (B) 0.20 (C) 0.30 (D) 0.40 (E) 0.50 (F) 0.60 (G) 0.70 (H) 0.80 (I) 0.90 = 2t2 leg 10, Substance A with a molar mass of 0.08380 kg/mol existing in a single phase gaseous state with a molar volume tN Deh of 9.22 x 10° m'/mol is cooled into the two phase region where the mass density of the liquid (p)) is 2413 kg/m’ ms and py/ py = 3.76 (where 0, is the mass density of the gas. What is the mole fraction of the liquid? « (V-), (A) 0.10 (B) 0.20 (€)030 (E) 0.50 Xb (F) 0.60 (G)0.70 (H) 0.80 (0.90 VM a - 5 M = 0.03380 14 Veseay 7 22 ¥ 10 ™3/na\ = 241d M/y> ord R16 &» Eend : X Cale Feeeres of liqni a) Vr PR, 7 WNW/ a = 3.76 C5 R= c41.9585 /,3 we wut Vg anh Ve (Vv 2 ~) Vy = 0.0830 W wm} — 4.39879 x lot Jo\ mol 64.155 KB V>< +2 8 3g0 M 3 33 Ver 2 a 5 mm = 3.492955 Xo [eno 2AI3 by \e “4 X Ng - Vases (esesmn viet) Gate) = 0.404 ~ (04 . Je 7 3 t Vg- Vy (1.39579 Kio") — (492885 xis?) 7 oe LE: yo CE mEemdee LEVER FUE prs HE length fatal Jeayth Page 19 of 22 13. Consider the following unbalanced reaction. __ C4H8 (g) + __ O2 J ĺ__ CO2 (g) + __ H2O (g) If 14 g of C4H8 and 64 g of O2 react until the limiting reagent is consumed inside a 6.00 m3 reaction vessel, what is the mole fraction of the unreacted reactants in the resulting mixture if all gases behave ideally and isothermally at 450 K? (A) 0.1 (B) 0.2 (C) 0.3 (D) 0.4 (E) 0.5 (F) 0.6 (G) 0.7 (H) 0.8 (I) 0.9 14. Consider the two differentials (I and II) and the function (III): ݂݀ = + ݔ݀(ଶݕݔ) = ݂݀ (ܫ) ݕ݀(ଶݔݕ) + ݔ݀(ݕݔ2) ݂ (II) ݕ݀(ݕଶݔ) = ଶݔ + ݕݔ2 + ଶݕ െ (ܫܫܫ) 1 Indicate which of the following statements is correct or that none of the above are correct. (A) None are exact (B) Only I is exact (C) Only II is exact (D) Only III is exact (E) I and II are exact (F) I and III are exact (G) II and III are exact (H) I, II and III are exact 14. Consider the two differentials (I and II) and the function (IID: df = (xy?)dx +(yx*)dy(I) df = (2xy)dx + (x?y)dy (ID f =x? 4 2xy+y?-1 (ID Indicate which of the following statements is correct or that none of the above are correct. (A) None are exact (B) Only Lis exact (C) Only His exact — (D) Only Il is exact (E) | and II are exact @® and III are exact (G) IL and III are exact (H) I, Il and III are exact (x) Af = Cxy)de + yx) ay Wt ated the Secand deava frrss of wo wees Wx) MCX) these twos to be the Sune fr the Act erential to be exact Coren Eqaten 2D df ef r (sf dy 93] x fa (ae\ | _ thy ate both the 55 16) | = xy (8) S| = 24x Same ,So(I) *$ an exack oo di FEecen tial (2) dF = (2u)dx + CY) dy ot the Sane, ¢ dQ - 2 SO Beh BO) OLE: ce) ) ext di FF erential (x) fer edxye yr -l = FC x)y) e 2e f: (28) dx + B49 ae\ af 2 —\ 2. dx +2 — < tx tf Es y 5 x 2 (2) IS @xncek rae (aby). 2 ee ectadial PECGD,\- & [&G))* * fairer Page 20 of 22 15. Indicate which of the following true statements for a perfect gas undergoing the processes depicted in the figure is false for a van der Waals gas. You may assume all processes depicted in the figure are reversible processes. You may also assume that the heat capacities are independent of temperature and that the number of moles of gas in the system is constant. The complete cycle represents ABCDA. (A) ܳ஻஼ = οܷ஻஼ െ ஻ܹ஼ (B) ஽ܹ஺ = 0 (C) οܷ஼஽ = 0 (D) |ܳ஺஻஼஽஺| = ݈݁ܿݕܿ ݁݀݅ݏ݊݅ ܽ݁ݎܽ (E) ο ஺ܷ஻஼஽஺ = 0 16. Consider the provided thermodynamic cycle (ABCDA) in the form of volume versus temperature, for an ideal gas where all processes can be regarded as reversible and the heat capacity at constant volume and number of moles in the system can be regarded as constants. Indicate which of the following statements is incorrect. (A) ܳ஼஽ = )ҧ௏ܥ݊ ஽ܶ െ ஼ܶ) (B) ݌஽ > ஺݌ (C) ݄ܶ݁ ܿ݅݉ݎ݄݁ݐ݋ݔ݁ ݏ݅ ܤܣ ݏݏ݁ܿ݋ݎ݌ (D) ஻ܹ஼ < 0 (E) οܷ஻஺஽஼ = 0 p V 0 0 TC =TDD A B VA = VDVB pD pB = pC TA =TB C pA VC 0 0 D AB TA = TD VC = VD C V TTB = TC VA = VB