Pchem 11e student answers letter PDF

Preview

Summary

Download Pchem 11e student answers letter PDF

Description

Student Solutions Manual to Accompany Atkins’ Physical Chemistry ELEVENTH EDITION

Peter Bolgar Haydn Lloyd Aimee North Vladimiras Oleinikovas Stephanie Smith and James Keeler Department of Chemistry University of Cambridge UK

Numerical solutions to the problems compiled by Jack Entwistle Selwyn College and the Department of Chemistry University of Cambridge

Preface This document is a compilation of the numerical solutions to the (a) Exercises and the odd-numbered Discussion questions and Problems from the 11th edition of Atkins’ Physical Chemistry. Where a problem requests the derivation of a result or expression, and provided that expression is not too complex, we have also included such results.

Errors and omissions In such a complex undertaking some errors will no doubt have crept in, despite the authors’ best efforts. Readers who identify any errors or omissions are invited to pass them on to us by email to . Jack Entwistle James Keeler Cambridge, August 2018

1

1 The properties of gases 1A The perfect gas E1A.1(a) 810 Torr 0.962 atm E1A.2(a) no 24.4 atm E1A.3(a) 3.42 bar 3.38 atm E1A.4(a) 30 lb in−2 .

E1A.5(a) 0.0427 bar 4.27 × 105 Pa E1A.6(a) S8 . E1A.7(a) 6.2 kg E1A.8(a) x O2 = 0.240 x N 2 = 0.760 pO2 = 0.237 bar pN 2 = 0.750 bar x N 2 = 0.780 x O2 = 0.210 pN 2 = 0.770 bar pO2 = 0.207 bar E1A.9(a) 0.169 kg mol−1 E1A.10(a) θ = −273 ○ C E1A.11(a) x H 2 = 32 x N 2 = 31 pH 2 = 2.0 × 105 Pa pN 2 = 1.0 × 105 Pa ptot = 3.0×105 Pa P1A.1 1.15 × 105 Pa 8.315 J K−1 mol−1 P1A.3 0.082062 atm dm3 mol−1 K−1 P1A.5 p = ρRT/M 45.94 g mol−1 P1A.7 24.5 Pa 9.14 kPa 24.5 Pa P1A.9 between 0.27 km 3 and 0.41 km3 P1A.11 −2 Pa 0.25 atm

P1A.13 c CCl 3 F = 1.1 × 10−11 mol dm−3 c CCl 2 F 2 = 2.2 × 10−11 mol dm−3 10−13 mol dm−3 c CCl 2 F 2 = 1.6 × 10−12 mol dm−3

1B The kinetic model E1B.1(a) 9.975 E1B.2(a) υrms, H2 = 1.90 km s−1 υrms,O2 = 478 m s−1 E1B.3(a) 6.87 × 10−3 E1B.4(a) 1832 m s−1 E1B.5(a) υmp = 333 m s−1 υmean = 376 m s−1 υrel = 531 m s−1 E1B.6(a) 1.7 × 1010 s−1 E1B.7(a) 475 m s−1 82.9 nm 8.10 × 109 s−1 E1B.8(a) 0.20 Pa E1B.9(a) 1.4 × 10−6 m = 1.4 µm

P1B.3 υmean, new ≈ 0.493 υmean P1B.5 3.02 × 10−3 for n = 3 4.89 × 10−6 for n = 4 P1B.7 1.12 × 104 m s−1 5.04 × 103 m s−1

c CCl 3 F = 8.0 ×

2 P1B.9 0.0722 at 300 K P1B.11 9.7 × 1010 s−1

0.0134 at 1000 K

1C Real gases E1C.1(a) 0.99 atm 1.8 × 103 atm E1C.2(a) a = 0.0761 kg m 5 s−2 mol−2 3

E1C.3(a) 0.88 1.2 dm mol E1C.4(a) 140 atm

−1

b = 2.26 × 10−5 m3 mol−1

E1C.5(a) 50.7 atm 35.2 atm 0.695 E1C.6(a) 1.78 atm dm6 mol−2 0.0362 dm3 mol−1 153 pm E1C.7(a) 1.41 × 103 K 175 pm E1C.8(a) 8.7 atm 3.6 × 103 K 4.5 atm 2.6 × 103 K 0.18 atm E1C.9(a) 4.6 × 10−5 m3 mol−1 0.66 P1C.1 1.62 atm P1C.3 0.929 0.208 dm3 mol−1 P1C.5 501.0 K P1C.7 0.1353 dm3 mol−1 0.6957 0.5914

P1C.9 0.0594 dm3 mol−1 5.849 atm dm6 mol−2 . 20.48 atm P1C.11 0.03464 dm3 mol−1 1.262 atm dm6 mol−2 P1C.13 Vm = 3C/B T = B 2 /3CR p = B 3 /27C 2 3 ′ −1 P1C.15 B = 0.0868 atm B = 2.12 dm mol−1 bp 1.11 P1C.19 1 + RT P1C.21 −0.01324 dm3 mol−1 1.063 × 10−3 dm 6 mol−2 P1C.23 Vm = 13.6 dm3 mol−1 2% 2RT 1/2 I1.1 υ = ( ) M I1.3 0.071 dm3 mol−1

47 K

3

2 Internal energy 2A Internal energy E2A.1(a) 8.7 kJ mol−1 7.4 kJ mol−1 7.4 kJ mol−1 E2A.3(a) −76 J E2A.4(a) q = +2.68 kJ w = −2.68 kJ ∆U = 0 q = +1.62 kJ q = 0 w = 0 ∆U = 0 E2A.5(a) pf = 1.33 atm ∆ U = +1.25 kJ E2A.6(a) −88 J −1.7 × 102 J P2A.1 6.2 kJ mol−1 2 5 1 P2A.3 al 2 − bl 2 2 5 P2A.7 −1.7 kJ −1.8 kJ −1.5 kJ P2A.9 −1.5 kJ −1.6 kJ

w = −1.62 kJ

∆U = 0

q = +1.25 kJ w = 0

2B Enthalpy E2B.1(a) C p,m = 30 J K−1 mol−1 C V ,m = 22 J K−1 mol−1 E2B.2(a) −5.0 kJ mol−1 E2B.3(a) q p = +10.7 kJ w = −624 J ∆U = +10.1 kJ ∆H = +10.7 kJ

w = 0 ∆U = +10.1 kJ ∆H = +10.7 kJ E2B.4(a) q p = ∆H = +2.2 kJ ∆U = +1.6 kJ P2B.1 11 min P2B.3 62.2 kJ P2B.5 w = 0 ∆U = q V = +2.35 kJ ∆ H = 3.0 kJ

q V = +10.1 kJ

2C Thermochemistry E2C.1(a) q = ∆H = +22.5 kJ w = −1.6 kJ E2C.2(a) −4.57 × 103 kJ mol−1 E2C.3(a) −167 kJ mol−1 E2C.4(a) 1.58 kJ K−1 +3.07 K −1 E2C.5(a) ∆ r H −○ (3) = −114.40 kJ mol

∆U = +21 kJ

∆ r U −○ = −112 kJ mol−1

∆ f H −○ (H2 O, g) = −241.82 kJ mol−1 E2C.6(a) −1368 kJ mol−1 −1 E2C.7(a) ∆ r H −○ (298 K) = +131.29 kJ mol

∆ r U −○ (298 K) = +128.81 kJ mol−1

+134.1 kJ mol ∆ r U (478 K) = +130 kJ mol E2C.8(a) −394 kJ mol−1 P2C.1 37 K 4.1 kg −1

− ○

∆ f H −○ (HCl, g) = −92.31 kJ mol−1

−1

∆ r H −○ (478 K) =

4 P2C.3 +52.98 kJ mol−1 −32.56 kJ mol−1 P2C.5 −1.27 × 103 kJ mol−1 −1 ∆ f H −○ = +2355.1 kJ mol−1 P2C.7 ∆ c H −○ = −25966 kJ mol

P2C.9 −803 kJ mol−1 P2C.11 −2.80×103 kJ mol−1

−2.80×103 kJ mol−1

−1.27×103 kJ mol−1

2.69×103 kJ mol−1

2D State functions and exact differentials E2D.1(a) 501 Pa E2D.2(a) ∆Um = +130 J mol−1

E2D.3(a) +1.3 × 10 K E2D.4(a) +20 atm E2D.5(a) +44.2 J K−1 mol−1 P2D.1 0.80 m 1.6 m 2.8 m P2D.5 κ T R = α(Vm − b) P2D.9 23 K MPa−1 14 K MPa−1 −3

−1

q = +7.52 kJ mol−1

w = −7.39 kJ mol−1

2E Adiabatic changes E2E.1(a) With vibrational contribution γ ammonia = contribution γ ammonia = γ methane = E2E.2(a) 1.3 × 102 K E2E.3(a) Vf = 8.46 dm3 258 K −877 J 4 3

10 9

E2E.4(a) −194 J E2E.5(a) 9.7 kPa P2E.1 Tf = 194 K w ad = −2.79 kJ ∆ U = −2.79 kJ

2E Integrated activities I2.7 −2.6 kJ

γ methane =

13 12

Without vibrational

5

3 The second and third laws 3A Entropy E3A.1(a) not spontaneous E3A.2(a) +366 J +309 J

E3A.3(a) +3.1 J K−1 E3A.4(a) ∆S = +2.9 J K−1 ∆S sur = −2.9 J K−1 ∆ S tot = +2.9 J K−1 ∆ S = ∆ S sur = ∆ S tot = 0 E3A.5(a) 191 K

∆S tot = 0

∆S = +2.9 J K−1

∆S sur = 0

E3A.6(a) 24.1% P3A.1 q = +2.74 kJ w = −2.74 kJ

∆H = 0

∆S = +9.13 J K−1

∆S sur =

∆U = 0

−9.13 J K ∆S tot = 0 q = +1.66 kJ w = −1.66 kJ +9.13 J K−1 ∆S sur = −5.54 J K−1 ∆S tot = +3.59 J K−1 P3A.3 VB = 2.00 dm3 VC = 3.19 dm3 VD = 1.60 dm3 −1

−157 J q 4 = 0 ∣w ∣ = +58 J 27% Th P3A.5 ∣q∣ × ( − 1) Tc

∆U = 0

∆H = 0

q 1 = +215 J

q2 = 0

∆S = q3 =

3B Entropy changes accompanying specific processes E3B.1(a) +30 kJ mol−1 E3B.2(a) +87.8 J K−1 mol−1

−87.8 J K−1 mol−1

E3B.3(a) +4.55 J K mol E3B.4(a) 153 J K−1 mol−1 E3B.5(a) Tf = 298 K ∆S 1 = −31.0 J K−1 −1

E3B.6(a) −22.1 J K E3B.7(a) +87.3 J K−1 P3B.1 ∆S = −21.3 J K−1

−1

−1

∆S 2 = +33.7 J K−1

∆S sur = +21.7 J K−1

∆S tot = +2.7 J K−1

∆S tot = +0.4 J K−1

spontaneous

+110 J K−1 ∆S sur = −111 J K−1 ∆S tot = −1.5 J K−1 not spontaneous P3B.3 +10.7 J K−1 mol−1 (Tc + Th )2 m C p,m ln ( ) +22.6 J K−1 P3B.5 M 4(Tc × Th ) P3B.7 ∆S = +45.4 J K−1 ∆S = 0 J K−1 ∆S sur = +51.2 J K−1 P3B.9 +477 J K−1 mol−1 P3B.11 +7.5 × 102 J 6.11 × 103 J +6.86 kJ 68.6 s

3C The measurement of entropy E3C.1(a) 4.8 × 10−3 J K−1 mol−1

∆S =

6 E3C.2(a) −386.1 J K−1 mol−1 E3C.3(a) −99.38 J K−1 P3C.1 76.04 J K−1 mol−1

+92.6 J K−1 mol−1

−153.1 J K−1 mol−1

P3C.3 0.93 J K−1 mol−1 63.9 J K−1 mol−1 64.8 J K−1 mol−1 64.8 J K−1 mol−1 at 298 K 62.4 J K−1 mol−1 at 273 K P3C.5 +42.08 J K−1 mol−1 +41.16 kJ mol−1 at 298 K +41.15 J K−1 mol−1 +40.8 kJ mol−1 at 398 K P3C.7 89.0 J K−1 mol−1 at 100 K 173.8 J K−1 mol−1 at 200 K 243.9 J K−1 mol−1 at 300 K a P3C.9 a = 2.569 JK−4 mol−1 b = 2.080 JK−2 mol−1 S m (0)+ T 3 +bT 11.01 J K−1 mol−1 3

3D Concentrating on the system ∆ r G −○ = −521.5 kJ mol−1 ∆ r H −○ = +53.40 kJ mol E3D.1(a) ∆ r H −○ = −636.6 kJ mol −1 −1 − ○ − ○ ∆ r G −○ = −178.7 kJ mol−1 ∆ r G = +25.8 kJ mol ∆ r H = −224.3 kJ mol −1 E3D.2(a) −480.98 kJ mol E3D.3(a) 817.90 kJ mol−1 E3D.4(a) −522.1 kJ mol−1 +25.78 kJ mol−1 −178.6 kJ mol−1 E3D.5(a) −340 kJ mol−1 −1

−1

P3D.1 49.9 bar 900 K +50.7 J K−1 −11.5 J K−1 ∆UA = +24.0 kJ ∆UB = 0 +3.46 × 103 J 0 P3D.3 -47 kJ mol−1 −1 −1 ∆ r G2−○ = −961 kJ mol−1 ∆ r G −○ = +4 kJ mol P3D.5 ∆ r G1−○ = +965 kJ mol

3E Combining the First and Second Laws E3E.1(a) −17 J

E3E.2(a) −36.5 J K−1 E3E.3(a) −85.40 J E3E.4(a) +10 kJ +1.6 kJ mol−1

E3E.5(a) −1.6 × 102 J mol−1 E3E.6(a) +11 kJ mol−1 −1 ∆ r H −○ (298 K) = −565.96 kJ mol−1 ∆G(375 K) = P3E.1 ∆ r G −○ (298 K) = −514.38 kJ mol −501 kJ mol−1 P3E.3 22 kJ mol−1 ∂T ∂V ∂p ∂S ∂V ∂S P3E.5 ( ) = ( ) ( ) =( ) ( ) = −( ) ∂p S ∂S p ∂T V ∂V T ∂T p ∂p T pf RT a P3E.7 G m (pf ) = G m (pi ) + RT ln ( ) + b(pf − pi ) Vm = − G m (pf ) = pi p pRT pf pf a G m (pi ) + RT ln ( ) − ln ( ) RT pi pi

7 I3.1 −20.8 K +37.1 J K−1 mol−1 I3.3 +19.5 J K−1 mol−1

8

4 Physical transformations of pure substances 4A Phase diagrams of pure substances E4A.1(a) one phase two phases three phases two phases E4A.2(a) 0.71 J E4A.3(a) 4 E4A.4(a) area E4A.5(a) Two phases one phase one phase

4B Thermodynamic aspects of phase transitions E4B.1(a) ∆µ(liquid) = −65 J mol−1 E4B.2(a) −699 J mol−1

∆µ (solid) = −43 J mol−1

liquid

E4B.3(a) +70 J mol−1 E4B.4(a) 2.71 kPa E4B.5(a) 15.9 kJ mol−1 45.2 J K−1 mol−1 E4B.6(a) 304 K 31.2 ○ C E4B.7(a) 20.801 kJ mol−1 E4B.8(a) 34.08 kJ mol−1 350.4 K 77.30 ○ C E4B.9(a) 2.8 × 102 K 8.7 ○ C E4B.10(a) 9.6 × 10−5 K E4B.11(a) 25 g s−1 E4B.12(a) Water 1.7 kg Benzene 31 kg Mercury 1.4 g E4B.13(a) 49 kJ mol−1 4.9 × 102 K 2.2 × 102 ○ C 99 J K−1 mol−1 E4B.14(a) 273 K −0.35 ○ C P4B.1 −3.10 kJ mol−1 7.62 % P4B.3 9.08 atm 920 kPa P4B.5 −22.0 J K−1 mol−1 −109.9 J K−1 mol−1 P4B.7 234.4 K P4B.9 84 ○ C 38.0 kJ mol−1

+110 J mol−1

P4B.11 d ln p/dT = ∆ sub H/RT 2 31.7 kJ mol−1 P4B.13 1.31 kPa −1 1 R a P4B.15 T = ( ) 363 K 89.6 ○ C + T0 ∆ vap H H I4.1 (p/kPa) = 4.80+(3.18×104 )×[(T /K) − 278.65]

(p/kPa) = 4.80 × exp [−4.98 × 103 (

1 1 − )] T/K 278.65

(p/kPa) = 4.80×exp [−3.70 × 103 (

1 1 − )] T/K 278.65

9 I4.3 N = 17 I4.5 1.60 × 104 bar

10

5 Simple mixtures 5A The thermodynamic description of mixtures E5A.1(a) VB = (35.677 4 − 0.918 46 x + 0.051 975 x 2 ) cm3 mol−1 E5A.2(a) VB = 17.5 cm3 mol−1 VA = 18.1 cm 3

E5A.3(a) −1.2 J mol−1 E5A.4(a) +1.2 J K−1 −3.5 × 102 J E5A.5(a) 6.7 kPa E5A.6(a) 886.8 cm3 −1 E5A.7(a) 56.3 cm3 mol E5A.8(a) 6.4 ⋅ 103 kPa E5A.9(a) 3.7 × 10−3 mol dm−3 E5A.10(a) 3.4 × 10−3 mol kg−1 3.37 × 10−2 mol kg−1 E5A.11(a) 0.17 mol dm−3 P5A.3 +4.70 J K−1 mol−1 +4.711 J K−1 mol−1 P5A.7 4.2934 mol kg−1

0.01 J K−1 mol−1

5B The properties of solutions E5B.1(a) 1.3 × 102 kPa E5B.2(a) 84.9 g mol−1 E5B.3(a) 381 g mol−1 E5B.4(a) 273.08 K E5B.5(a) 273.06 K E5B.6(a) ∆ mix G = −3.10 × 103 J ∆ mix S = +10.4 J K−1 ∆ mix H = 0 E5B.7(a) 21 0.8600 E5B.8(a) 0.137 mol kg−1 24.3 g E5B.9(a) pB = 6.1 Torr pA = 32 Torr ptot = 38 Torr y CCl 4 = 0.84 y Br 2 = 0.16 E5B.10(a) x methylbenzene = 0.92 x 1,2−dimethylbenzene = 0.08 y methylbenzene = 0.97 y 1,2−dimethylbenzene = 0.03 E5B.11(a) x A = 0.267 x B = 0.733 58.6 kPa E5B.12(a) ideal y A = 0.830 y B = 0.170

P5B.3 Vpropionicacid = 75.6 cm 3 mol VTHF = 99.1 cm3 mol P5B.5 −4.64 kJ P5B.7 1.39 × 104 g mol−1 P5B.9 1.25 × 105 g mol−1 B = 1.23 × 104 mol−1 dm3 P5B.11 21 P5B.13 M J = 1.26 × 105 g mol−1 B = 4.80 × 104 mol−1 dm3 −1

−1

11

5C Phase diagrams of binary systems: liquids E5C.1(a) y M = 0.354

y M = 0.811 n 0.161 = 9.68 n 0.042

E5C.3(a) x P = 0.150 P5C.1 y B = 0.91 y MB = 0.085 P5C.3 6.4 kPa y B = 0.77 y MB = 0.23 P5C.5 625 Torr 500 Torr

x H = 0.5

ptot = 4.5 kPa

y H = 0.3

x H = 0.7

y H = 0.5

nl nv

= 1.1

5D Phase diagrams of binary systems: solids E5D.4(a) x B ≈ 0.25 T2 ≈ 190 ○ C n Ag3 Sn n Ag3 Sn E5D.6(a) 76% = 1.11 = 1.46 n Ag n Ag P5D.3 (species,phases): b(3,2), d(2,2), e(4,3), f(4,3), g(4,3), k(2,2) P5D.5 eutectics: x Si = 0.056 at 800 ○ C, x Si = 0.402 at 1268 ○ C, x Si = 0.694 at 1030 ○ C n Ca 2 Si n Si = 0.7 nnliqSi = 0.53 n CaSi = 0.67 n Ca−richl iq 2 = 10.6 302.5 ○ C P5D.7 x 1 = 0.167 x 2 = 0.805 nnx=0.805 x=0.167

5E Phase diagrams of ternary systems D5E.1 3 E5E.3(a) x CHCl 3 = 0.30 x CH 3 COOH = 0.20 x H 2 O = 0.50 two phase region with phase composition a ′2 being approximately 5 times more abundant than the phase with composition a2′′ E5E.5(a) 13 mol dm−3 24 mol dm−3

5F Activities E5F.1(a) 0.5903 E5F.2(a) a A = 0.833 a B = 0.125 γ A = 0.926 E5F.3(a) a P = 0.498 γ P = 1.24 a M = 0.667 γ M = 1.11 E5F.5(a) 0.9 E5F.6(a) 2.74 g 2.92 g E5F.7(a) 0.56 E5F.8(a) B = 1.96 I5.3 K C = 371 bar I5.5 56 µg 14 µg 1.7 × 102 µg

12

6 Chemical equilibrium 6A The equilibrium constant E6A.1(a) nA = 0.90 mol nB = 1.2 mol E6A.2(a) −64 kJ mol−1 E6A.3(a) exergonic E6A.6(a) K = 3.24 × 1091 K = 3.03 × 10−5 E6A.7(a) 1.4 × 1046

E6A.8(a) −44 kJ mol−1 105 5.84 × 105 E6A.9(a) 2.85 × 10−6

−33 kJ mol−1

E6A.10(a) K = K c × (c −○ RT/p−○ ) E6A.11(a) x A = 0.087 x B = 0.369 E6A.12(a) +12 kJ mol−1

−27 kJ mol−1

x C = 0.195

−4.4 kJ mol−1

+1.3 kJ mol−1

5.84×

x D = 0.347 0.32 +2.8 kJ mol−1

E6A.13(a) −14 kJ mol−1 E6A.14(a) −1.1 × 103 kJ mol−1

P6A.1 +4.48 kJ mol−1 0.101 atm 0.102 bar P6A.3 nH 2 = 6.67 × 10−3 mol nI 2 = 0.107 mol

nHI = 0.787 mol

6B The response of equilibria to the conditions E6B.1(a) 0.141 13.4 E6B.2(a) -68.26 kJ mol−1

9.22 × 1011

1.27 × 109

E6B.3(a) 1.5 × 103 K E6B.4(a) +2.77 kJ mol−1 −16.5 J K−1 mol−1 E6B.5(a) 50% E6B.6(a) x borneol = 0.904 x isoborneol = 0.096 E6B.7(a) +52.9 kJ mol−1 −52.9 kJ mol−1 E6B.8(a) 1109 K E6B.9(a) 3.07 − 6.48 kJ mol−1 70.2 kJ mol−1 110 J K−1 mol−1 P6B.1 −92.2 kJ mol−1 P6B.3 −23R(CT − B) +70.5 J K−1 mol−1 −1 ∆ r H −○ = +3.00 × 102 kJ mol−1 P6B.5 K = 2.79 × 10−6 ∆ r G −○ = +153 kJ mol −1 −1 +102 J K mol −1 P6B.7 K = 1.35 at 437 K K = 0.175 at 471 K ∆ r H −○ = −103 kJ mol

P6B.9 1.2 × 108 2.7 × 103 P6B.11 −225.34 kJ mol−1

∆ r S −○ =

13

6C Electrochemical cells E6C.1(a) +1.56 V +0.40 V −1.10 V E6C.2(a) +1.10 V +0.22 V +1.23 V E6C.3(a) −0.619 V E6C.4(a) −212 kJ mol−1 E6C.5(a) +0.030 V P6C.1 +1.23 V P6C.3 2.0

+1.09 V

6D Electrode potentials E6D.1(a) 6.4 × 109 1.5 × 1012 E6D.2(a) 8.445 × 10−17

E6D.3(a) −0.46 V ∆ r G −○ = +89 kJ mol +87 kJ mol−1 E6D.4(a) no P6D.1 +0.324 V +0.45 V P6D.3 −0.6111 V −0.22 V +0.4139 V P6D.5 −324 J K−1 mol−1 −571 kJ mol−1

−1

∆ r H −○ = +146.39 kJ mol−1

∆ r G −○ (308K) =

I6.1 −77 kJ mol−1 −1 − ○ = 1.0304 V ∆ G = −236.81 kJ mol −1 K = 7.11 × ∆ r G −○ = −198.84 kJ mol I6.3 Ecell r −1 1034 γ ± = 0.761 γ ± = 0.750 ∆ r H = −263 kJ mol ∆ r S − 87.2 J K−1 mol−1 I6.5 γ ±,1 = 0.501 γ ±,2 0.549 I6.9 41 % 77 % 41 % I6.11 +0.206 V

14

7 Quantum theory 7A The origins of quantum mechanics E7A.1(a) 9.7 × 10−6 m E7A.2(a) 580 K E7A.3(a) (5.49 × 10−2 ) × 3R E7A.4(a) 6.6 × 10−19 J 4.0 × 102 kJ mol−1 6.6 × 10−20 J 40 kJ mol−1 6.6 × 10−34 J 4.0 × 10−13 kJ mol−1 E7A.5(a) 330 zJ 199 kJ mol−1 360 zJ 217 kJ mol−1 496 zJ 298 kJ mol−1 E7A.6(a) 19.9 km s−1 20.8 km s−1 24.4 km s−1 E7A.7(a) 2.77 × 1018 2.77 × 1020

E7A.8(a) no electron ejection 3.19 × 10−19 J 837 km s−1 E7A.9(a) 21 m s−1 E7A.10(a) 7.27 × 106 m s−1 150 V

E7A.11(a) 2.4 × 10−2 m s−1 E7A.12(a) 332 pm E7A.13(a) 6.6 × 10−29 m 6.6 × 10−36 m 99.8 pm P7A.1 1.54 × 10−33 J m−3 2.51 × 10−4 J m−3 P7A.5 6.54 × 10−34 J s P7A.9 500 nm blue-green

7B Wavefunctions E7B.1(a) N = (2/L)1/2 E7B.2(a) N = (2a/π)1/4 E7B.3(a) can be normalized cannot be normalized E7B.4(a) 0 E7B.5(a) 1/4 E7B.6(a) length−1 E7B.7(a) cannot be normalized cannot be normalized can be normalized E7B.8(a) Maxima at x = L/4, 3L/4; Node at x = L/2 P7B.1 N = (2π)−1/2 N = (2π)−1/2 √ P7B.3 N = 2/ L x L y N = 2/L P7B.5 0.0183 P7B.7 2.00 × 10−2 6.91 × 10−3 6.58 × 10−6 0.5

P7B.9 8.95 × 10−6 P7B.11 x = ±a

1.21 × 10−6

15

7C Operators and observables E7C.6(a) L/2 E7C.7(a) 0 E7C.8(a) π π E7C.9(a) 1.05 × 10−28 m s−1 E7C.10(a) 7.01 × 10−10 m

1.05 × 10−27 m

P7C.1 Yes −1 Yes +1 No P7C.7 1/a P7C.11 ⟨x⟩ = 0 ⟨x 2 ⟩ = 1/4a ⟨p x ⟩ = 0 ⟨px2 ⟩ = ħ2 a P7C.13 −1/x 2

2x

∆x = (4a)−1/2

√ ∆p x = ħ a

7D Translational motion E7D.1(a) 3 × 10−25 kg m s−1 5 × 10−20 J 33 −1 E7D.2(a) e−i(2.7×10 m )x E7D.3(a) 1.8 × 10−19 J 1.1 × 102 kJ mol−1 102 kJ mol−1 4.1 eV 3.3 × 104 cm−1 E7D.5(a) 0.04 0 E7D.8(a) λC /2 E7D.9(a) L/6, L/2, 5L/6 0, L/3, 2L/3, L

1.1 eV

9.1 × 103 cm−1

6.6 × 10−19 J 4.0 ×

E7D.10(a) −0.174 2mkTL2 1 E7D.11(a) n = − 2 1.24 × 1016 h2 E7D.12(a) Maxima at (x, y):(L/4, L/4), (L/4, 3L/4), (3L/4, L/4), (3L/4, 3L/4); Nodes at x = L/2 and parallel to the y axis, y = L/2 and parallel to the x axis

E7D.13(a) (1, 4) E7D.14(a) 3 E7D.15(a) 0.84 P7D.1 6.2 × 10−41 J 2.2 × 109 1.8 × 10−30 J 2 P7D.3 ⟨x⟩ = L2 ⟨x 2 ⟩ = L3 − 2π1 2 P7D.5 3.30 × 10−19 J 4.98 × 1014 Hz lower P7D.11 1.20 × 106 P7D.15 n1 + n2 − 2

7E Vibrational motion E7E.1(a) 4.30 × 10−21 J E7E.2(a) 278 N m−1 E7E.3(a) 2.64 × 10−6 m E7E.5(a) 5.61 × 10−21 J

increases

16 E7E.6(a) 4.09 × 10−20 J 18.1 pm E7E.7(a) 3 4 E7E.8(a) y = −1, +1

1.29 × 10−20 J 32.2 pm

E7E.9(a) y = ±1 P7E.1 4.04 × 1014 Hz 5.63 × 1014 Hz P7E.3 ν 2 H 2 = 93.27 THz ν 3 H 2 = 76.15 THz P7E.5 2.99 × 103 cm−1 k f = µ(2π ν˜ c)2 1902 N m−1 P7E.7 1420 cm−1 P7E.9 g = (mk f )1/2 /2ħ E = 21ħ(k f /m)1/2 P7E.13 P = 0.112 P7E.17 υ = 0

2080 cm−1

7F Rotational motion E7F.1(a) 21/2 ħ −ħ, 0, ħ E7F.3(a) N = (2π)−1/2 E7F.5(a) 3.32 × 10−22 J E7F.6(a) 2.11 × 10−22 J E7F.7(a) 4.22 × 10−22 J

E7F.8(a) 1.49 × 10−34 J s E7F.10(a) 3 θ = π/2, 0.684, 2.46 E7F.11(a) ϕ = π/2, 3π/2 yz plane ϕ = 0, π xz plane E7F.12(a) 7 E7F.14(a) θ = π/4 θ = 0.420 P7F.1 7.88 × 10−19 J 5.273 × 10−34 J s 5.23 × 1014 Hz P7F.3 is separable P7F.5 E 0,0 = 0 E 2,−1 = 6ħ2 /2I E 3,+3 = 12ħ2 /2I J z(0,0) = 0 J z(2,−1) = −ħ J z(3,+3) = 3ħ I7.1 +74.81 kJ mol−1 +80.8... J K −1 mol−1 T = 812 K 2.9 × 10−6 m 1.84 × 10−6

17

8 Atomic structure and spectra 8A Hydrogenic Atoms E8A.1(a) 1 9 25 E8A.2(a) N = (a03π)−1/2 E8A.3(a) Z 3 /(8πa 30 ) E8A.4(a) r = 4a 0 /Z E8A.5(a) 0.347a 0 √ E8A.6(a) r = (3 ± 3)(3a 0 /2Z) E8A.7(a) θ = π/2 ϕ = π/2 √ E8A.8(a) (3 + 5)(a 0 /Z) E8A.9(a) 4a 0 /Z E8A.10(a) 3 subshells 9 orbitals E8A.12(a) 0 P8A.1 x = 0, y = 0, z = 2a 0 /Z P8A.3 −2.179 27 × 10−18 J √ P8A.5 Radial nodes: 3s at r = (3a 0 /2Z)(3 ± 3), 3p at r = 6a 0 /Z , 3d none Anuglar nodes: 3s none, 3p yz plane, 3d xz and yz plane ⟨r⟩ = (27a 0 )/(2Z) P8A.7 σ = 2.66a 0 1 Z 2 e 4 me × P8A.9 − 32π2 ε02 ħ2 n 2 P8A.11 2a 0,H 12 E h,H

8B Many-electron atoms E8B.2(a) 14 E8B.4(a) [Ar] 3d8 E8B.5(a) Li P8B.1 a 0 /126

8C Atomic spectra E8C.1(a) n2 = 2 n2 = ∞ E8C.2(a) 3.29 × 105 cm−1 30.4 nm 9.87 PHz E8C.3(a) forbidden allowed allowed E8C.4(a) 2 P1/2 , 2 P3/2 E8C.5(a) j = 25, 23 j = 72 , 25 E8C.6(a) l = 1

18 E8C.7(a) L = 2 S = 0 J = 2 E8C.8(a) S = 1, 0 3, 1 S = 23, 12 4, 1 E8C.9(a) M S = 0 S = 0 M S = 0, ±1 S = 1 E8C.10(a) 3 D3 , 3 D2 , 3 D1 , 1 D2 3 D1 E8C.11(a) J = 0 1 J = 23, 21 4 2 J = 2, 1, 0 5, 3, 1 E8C.12(a) 2 S1/2 2 P3/2 , 2 P1/2 ˜ E8C.13(a) −(3/2)hcA˜ +hc A

E8C.14(a) allowed forbidden allowed P8C.1 n1 = 6 for n2 = 8, 9 and 10 λ = 7502.5 nm, 5908.3 ...