Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
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Focus 1
The properties of gases
Answers to exercises
Topic 1A The perfect gas
1A.1 (a) 810 Torr
(b) 0.962 atm
(c) 0.222 atm
(d) 1.03 Γ 105 Pa
1A.2 92 kPa
1A.3 2.25 kPa
1A.4 4.33 mmol
1A.5 660 bar
1A.6 10.0 atm
1A.7 418 kPa
1A.8 173 kPa
1A.9 β243.6 β
1A.10 394 K
1A.11 (a) 3.6 m3
(b) 178 m3
1A.12 3.4 Γ 105 m3
1A.13 benzene 0.355οΌ toluene 0.645
1A.14 (a) 1.32 Γ 10β3m3
(b) 61.2 Γ 103 Pa
Topic 1B The kinetic model of gases
1B.1 (a) 493 m sβ1
(b) 615 m sβ1
1B.2 (a) π£mean(79 K) = 647 m sβ1
π£mean(315 K) = 1.29 km sβ1
π£mean(1500 K) = 2.82 km sβ1
(b) π£mean(79 K) = 323 m sβ1
π£mean(315 K) = 645 m sβ1
π£mean(1500 K) = 1.41 km sβ1
1B.3 3.72
1B.4 πN2 0.80 g
πHe 0.30 g
1B.5 65 mPa
1B.6 π = 0.97 ΞΌm
π = 120 Γ 103
1B.7 (a) 7.0 Γ 1010
(b) 7.0 Γ 108
(c) 7.0 Γ 104
1B.9 (a) 6.8 nm
(b) 68 nm
(c) 6.8 mm
Topic 1C Real gases
1C.1 πc = 0.242
1C.2 CH4 πc = 0.288
C2H6 πc = 0.274
C3H8 πc = 0.276
1C.3 2.15 MPa
1C.4 β3.37 Γ 10β5 m3molβ1
1C.5 β3.49 Γ 10β8 Paβ1
1C.6 (a) (i) 101 kPa
(ii) 83.1 MPa
(b) (i) 101 kPa
(ii) 206 MPa
1C.7 β0.608 MPa
1C.8 π = 4.6 Γ 10β5 m3 molβ1
π = 0.66
1C.9 1842 K
Answers to problems
1.1 0.50 m3
1.2 28.82 g molβ1
130 kg
1.3 6.8 kPa
1.4 713 Torr
1.5 π₯N2= 0.7809
π₯O2= 0.2094
π₯Ar = 0.0098
1.6 132 g molβ1
1.7 16.4 g molβ1
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
ANSWERS TO END OF CHAPTER EXERCISES
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1.8 (a) πH2= 200 kPa
πN2= 100 kPa
(b) 300 kPa
1.9 (a) 72 K
(b) 943 m sβ1
1.10 1.0 Γ 1013 sβ1
1.11 0.57 dm3 molβ1
1.12 π = 0.656 Pa m6molβ2
π = 5.54 Γ 10β5 m3 molβ1
1.13 π = 0.321 Pa m6 molβ2
π = 6.50 Γ 10β5 m3molβ1
π = 1.86 Γ 10β10 m
1.14 π = π. πππ ππ π¦π π¦π¨π₯βπ
π = π. π Γ ππβππ¦π π¦π¨π₯βπ
Answers to projects
1.1 (d) π β 10β2
1.2 (a) 720 Mbar
(d) 0.21 Mbar
(e) 0.029 Mbar
1.3 (c) 1030 K
1.4 (c) πc = 101.3 bar
πc = 0.1327 dm3 molβ1
πc = 431.3 K
Focus 2
The First Law of thermodynamics
Answers to exercises
Topic 2A Work
2A.1 (a) π€expansion = β0.10 J
(b) π€expansion = β100 J
(a) π€compression = +0.10 J
(b) π€compression = +100 J
2A.2 β5.5 kJ
2A.3 (a) β99 J
(b) β167 J
2A.4 +123 J
2A.5 +29.9 J
2A.6 β1.25 kJ
2A.7 (a) 0
(b) β783 J
2A.8 β100 J
Topic 2B Heat
2B.1 23.7 J Kβ1
2B.2 (a) 27 J Kβ1
(b) 0.45 J Kβ1gβ1
(c) 25 J Kβ1molβ1
2B.3 42 kJ
2B.4 87 kJ
2B.5 πΆπ,m = 29.9 J Kβ1molβ1
πΆπ,m = 38.2 J Kβ1molβ1
Topic 2C Internal energy
2C.1 β41 kJ
2C.2 +42.5 J
Topic 2D Enthalpy
2D.1 +20 kJ
2D.2 0
2D.3 (a) exothermic
(b) endothermic
(c) endothermic
(d) endothermic
(e) endothermic
2D.4 Ξπ» = ππ = β1.2 kJ
πΆπ = 80 J Kβ1
2D.5 Ξπ» = ππ = +2.2 kJ
Ξπ = +1.6 kJ
2D.6 28.25 J Kβ1molβ1
Topic 2E Physical change
2E.1 1740 kJ molβ1
2E.2 19.5 kJ molβ1
2E.3 +492 kJ molβ1
2E.4 +2.83 Γ 104 kJ
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
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2E.5 (a) +2.44 kJ molβ1
(b) +2.26 kJ molβ1
2E.6 +93 kJ molβ1
2E.7 ππ = Ξπ» = +80.0 kJ
π€ = β5.20 kJ
Ξπ = +74.8 kJ
2E.8 2.58 kJ molβ1
2E.9 +239 kJ molβ1
Topic 2F Chemical change
2F.1 β124 kJ molβ1
2F.2 (a) 388 kJ molβ1
(b) smaller
(c) Ξfπ»o β 38 kJ molβ1
2F.3 398 kJ molβ1
2F.4 (a) +16 kJ molβ1
(b) β772 kJ molβ1
2F.5 (a) β1560 kJ molβ1
(b) +51.88 kJ gβ1
(c) methane: +55.5 kJ gβ1
ethane is less exothermic
2F.6 β4564.7 kJ molβ1
2F.7 β85 kJ molβ1
2F.8 (a) β3290 kJ
(b) β2710 kJ
2F.9 β432 kJ molβ1
2F.10 +225 kJ molβ1
Answers to problems
2.1 +920 kJ
610 s
2.2 (a) 37 K
(b) 4.1 kg
2.3 +774 J
2.4 +1.86 kJ
2.5 (a) 175 kJ molβ1
(b) 274 kJ molβ1
(c) 150 kJ molβ1
(d) 449 kJ molβ1
2.6 +2.468 kJ molβ1
2.7 (a) 20.83 J Kβ1molβ1
(b) (i) +641 J molβ1
(ii) +458 J molβ1
2.8 +39.8 kJ molβ1
2.9 2.38 kJ molβ1
2.10 +40.88 kJ molβ1
2.11 +1152 kJ
2.12 4.22 kJ Kβ1
+0.768 K
2.13 (a) β2800 kJ molβ1
(b) β2800 kJ molβ1
(c) β1.27 Γ 103 kJ molβ1
2.14 (a) β1333 kJ molβ1
(b) β1331 kJ molβ1
(c) β815 kJ molβ1
2.15 +112.27 kJ molβ1
2.16 β382.96 kJ molβ1
2.17 (a) β57.29 kJ molβ1
(b) β28.6 kJ molβ1
(c) β138.2 kJ molβ1
(d) β32.88 kJ molβ1
(e) β55.84 kJ molβ1
2.19 (a) +1.9 kJ molβ1
(b) +30.6 kJ molβ1
2.20 (a) β2205 kJ molβ1
(b) β2200 kJ molβ1
2.21 +11.3 kJ molβ1
2.22 β56.98 kJ molβ1
2.23 (a) decrease
(b) increase
(c) decrease
2.24 (a) increase
(b) increase
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
ANSWERS TO END OF CHAPTER EXERCISES
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2.25 +7.04 J molβ1
Answers to projects
2.1 (a) more negative
(b) more positive
2.2 (a) π€ = βππ (πi + ππi) ln(πf/πi) + ππ π(πf β πi)
(b) w more negative
2.3 (a) Ξπm = ΒΌππ4
(b) πΆπ,m = π + 2ππ
2.4 (a) +818 J molβ1
2.6 (a) 40000 K
2.7 π = 29.74 J Kβ1molβ1
π = 2.51 Γ 10β2 J Kβ2molβ1
π = β1.55 Γ 105 J K molβ1
2.9 (a) 7.4 per cent
(b) 40 kJ
(c) 15 m
(d) blood temperature, 37 C
(e) 25 kJ
(f) 9.1 m
Focus 3
The Second Law of thermodynamics
Answers to exercises
Topic 3A Entropy
3A.1 (a) +1.7 J Kβ1
(b) +1.2 J Kβ1
3A.2 +0.41 J Kβ1
3A.3 1470 K
Topic 3B Entropy changes
3B.1 +14 J Kβ1molβ1
3B.2 2.89 dm3
3B.3 +23.6 J Kβ1
3B.4 β93.0 J Kβ1
3B.5 β45.1 kJ
β165 J Kβ1
3B.6 (a) +120 J Kβ1
(b) β120 J Kβ1
3B.7 +0.95 J Kβ1molβ1
3B.8 (a) +122 J Kβ1
(b) +130 J Kβ1
(c) +606 J Kβ1
The total entropy change of the system:
+858 J Kβ1
3B.9 (a) +85 J Kβ1molβ1
(b) +34 kJ molβ1
3B.10 (a) +87.8 J Kβ1molβ1
(b) β87.8 J Kβ1molβ1
Topic 3C Absolute entropy
3C.1 6.69 mJ Kβ1molβ1
3C.3 +11.5 J Kβ1molβ1
Topic 3D The Gibbs energy
3D.1 (a) positive
(b) negative
(c) positive
3D.2 (a) β412.9 J Kβ1molβ1
(b) +92.6 J Kβ1molβ1
(c) β153.1 J Kβ1molβ1
(d) β21.0 J Kβ1molβ1
(e) +512.0 J Kβ1molβ1
3D.3 (a) β198.72 J Kβ1 molβ1
(b) +309 J Kβ1 molβ1
Answers to problems
3.1 (a) +33 J Kβ1
3.2 β7.9 J Kβ1molβ1
3.3 0.63 πi
3.5 +5.1 J Kβ1
3.6 +79 J Kβ1molβ1
3.7 (b) 4.1 Γ 10β23 J Kβ1
3.8 (c) 3.37 J Kβ1 molβ1
3.9 4.0 Γ 10β4J Kβ1molβ1
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
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3.10 0.256 J Kβ1molβ1
3.11 +5.03 kJ Kβ1
3.12 (a) β0.69 J Kβ1molβ1
(b) +0.14 J Kβ1molβ1
3.13 (a) β93 kJ molβ1
(b) Yes
(c) +300 J Kβ1molβ1
3.14 0.41 g
3.15 +17 J
3.16 8.2 Γ 1023molecules
Answers to projects
3.1 (a) 3.3 kW
(b) 180 kW
3.2 Ξπ = π ln(πf/πi) + π(πf β πi)
βΒ½π(πfβ2 β πi
β2)
3.3 (b) 2.02 Γ 10β22 J Kβ1molβ1
(d) π
π< 0.01
3.4 (a) Yes
(b) 0.46 mol
(c) β12 W mβ3
(d) battery: β150 Γ 103 W mβ3
computer battery
Focus 4
Physical transformation
Answers to exercises
Topic 4A The thermodynamics of transition
4A.2 graphite
4A.3 No
4A.4 (a) +2.7 kJ molβ1
(b) β20 kJ molβ1
4A.5 +4.2 kJ molβ1
4A.6 β3.5 kJ molβ1
Topic 4B Phase diagrams of pure substances
4B.1 (a) 7.9 kg
(b) 15 kg
(c) 1.1 g
4B.2 0.709 atm
which is equivalent to 0.719 bar
4B.3 331 K
4B.4 758 mbar
4B.5 36.7 kJ molβ1
4B.6 A: 15.15 B: unchanged
4B.7 1
4B.8 2
Topic 4C Partial molar quantities
4C.1 886.8 cm3
4C.2 96.9 cm3
4C.3 +1.8 kJ molβ1
4C.4 +32.631 J molβ1
4C.5 (a) β1.31 kJ molβ1
(b) +4.38 J Kβ1molβ1
(c) spontaneous
4C.6 (a) ΞπΊm β 1.40 kJ molβ1
Ξπm + 4.71 J Kβ1molβ1
(b) spontaneous
4C.7 4.99 kPa
Topic 4D Solutions
4D.1 17.5 g
4D.2 8.92 Γ 10β2 mol kgβ1
4D.3 πsucrose = 0.403 mol dmβ3
πsucrose = 0.388 mol kgβ1
4D.4 1.80 Γ 10β3
4D.5 β37 J molβ1
4D.6 π₯CO2= 4.8 Γ 10β3
4D.7 129 kPa
4D.8 7985 Pa
4D.9 (a) 1.3 mmol dmβ3
(b) 17.0 mmol dmβ3
4D.10 πN2= 0.51 mmol kgβ1
πO2= 0.28 mmol kgβ1
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
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4D.11 34.3 mmol dmβ3
4D.12 π₯T = 0.93 π₯X οΌ0.07
π¦T = 0.97 π¦X = 0.03
4D.13 +5.6 kJ molβ1
Topic 4E Colligative properties
4E.1 59.1 g molβ1
4E.2 +0.061 K
4E.3 +0.36 K
4E.4 207 g molβ1
Topic 4F Phase diagrams of mixtures
4F.1 πβ²
πβ²β² = 0.31
4F.2 πEβ² (aq) = 0.050 mol dmβ3
πEβ² (org) = 0.0075 mol dmβ3
4F.3 0.25
Answers to problems
4.1 (b) 711 K
4.3 (a) β0.1346 bar Kβ1
(b) +135.6 bar
4.4 (a) 31.69 kJ molβ1
(b) 341.7 K
4.5 353 K
4.6 3.0 Torr
4.11 2.30 kPa
4.12 (a) 171.03 Torr
(b) 6.92 Torr
(c) π¦eth = 0.96111
π¦chl = 0.03889
(d) 692 Torr
4.13 (a) 43.95 Torr
(b) 1.13 Torr
(c) 22.6 kPa
4.14 6.41 Γ 103 kPa
4.15 A: πΎHβ² = 861 Torr
B: πΎHβ² = 1103 Torr
4.16 A: KH = 242 Torr
B: KH = 397 Torr
4.17 0.11 C
4.18 π = 88.19 kg molβ1
4.19 13.9 kg molβ1
4.20 (a) yT = 0.36
(b) yT = 0.81
4.21 (a) 0.150
(b) πβ²
πβ²β² = 9.81
4.22 (a) 0.345
(b) πβ²
πβ²β² = 0.135
4.25 (c) 5% tin by mass
(d) No Ag3Sn in the solid
(e) 20% Ag3Sn by mass
Answers to projects
4.1 (a) 6.4 kPa
(c) 5.7 kPa
4.2 (b) greater
(c) 0.69 per cent
4.3 (a) π₯ethanol = 0.072
(b) 53.1039 cm3 mol
-1
4.4 (a) πwater/cm3 molβ1 =
18.068 + 6.557 Γ 10β3π2 β 1.018 Γ 10β3π3
4.5 (a) 4.4 cm3O2
(b) 4.0 atm: 56 ΞΌg N2,
1.0 atm: 14 ΞΌg N2
(c) 170 ΞΌg N2
Focus 5
Chemical change
Answers to exercises
Topic 5A The thermodynamics of reaction
5A.1 (a) π = πCO2(g)
6
[CH3COCOOH]2πO2(g)5 Γ (πo2/πo)
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
ANSWERS TO END OF CHAPTER EXERCISES
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(b) π = [FeSO4]
[PbSO4]
(c) π = [HCl]2
πH2(g)Γ
πo
πo2
(d) π = [CuCl2]
[CuCl]2 Γ πo
5A.2 +12.3 kJ molβ1
5A.3 +6.8 kJ molβ1
5A.4 β25.1 kJ molβ1
5A.5 +26 kJ molβ1
5A.7 β14.4 kJ molβ1
formation of NH3
5A.8 2.31
5A.9 (a) 5.2 Γ 1011
(b) 850
5A.10 1
5A.11 β2.42 kJ molβ1
5A.12 3.01
5A.13 glucose-1-phosphate 3.4 Γ 103
glucose-6-phosphate 2.5 Γ 102
glucose-3-phosphate 36
Topic 5B The equilibrium constant
5B.1 πCO2= 10.2 kPa
5B.2 3.3 Γ 106
5B.3 6.94
5B.4 3.1 Γ 10β3
5B.5 4.31 Γ 1043
Topic 5C Response to conditions
5C.1 (a) 52.9 kJ molβ1
(b) β52.9 kJ molβ1
5C.2 β92.2 kJ molβ1
5C.3 πΎ = 7.23 Γ 1011
5C.4 (a) products
(b) products
(c) reactants
(d) products
Topic 5D Proton transfer equilibria
5D.3 (a) pH = 4.8
pOH = 9. 2
(b) pH = 2.8
pOH = 11.2
(c) pH = 13.3
pOH = 0.7
(d) pH = 4.3
pOH = 9.7
5D.4 (a) 9.5 mmol dmβ3
pH = 2.0
(b) 5.01 Γ 10β13mol dmβ3
pH = 12.3
(c) 53 mmol dmβ3
pH = 1.3
Topic 5E Polyprotic acids
5E.1 (a) 9.7 Γ 10β4
(b) 3.8 Γ 10β10
5E.2 (a) π(H2S) = 1.0
π(HSβ) = 1.3 Γ 10β3
π(S2β) = 9.2 Γ 10β14
undissociated (H2S) form
(b) π(H2S) = 7.7 Γ 10β4
π(HSβ) = 1.0
π(S2β) = 7.1 Γ 10β5
HSβ ions
Topic 5F Acidβbase equilibria of salts in water
5F.1 4.36
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
ANSWERS TO END OF CHAPTER EXERCISES
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5F.2 (a) acidic
NH4+(aq) + H2O(l) β H3O+(aq) + NH3(aq)
(b) basic
H2O(l) + CO32β(aq) β HCO3
(aq) + OHβ(aq)
(c) basic
H2O(l) + Fβ (aq) β HF(aq) + OHβ(aq)
(d) neutral
(e) acidic
[Al(H2O)6]3+(aq) + H2O(l) β
[Al(H2O)5OH]2+(aq) + H3O+(aq)
(f) acidic
[Co(H2O)6]2+(aq) + H2O(l) β
[Co(H2O)OH]+(aq) + H3O+(aq)
5F.3 (a) pH 2β4
(b) pH 3β5
(c) pH 11.5β13.5
(d) pH 6β8
(e) pH 5β7
5F.4 (a) H3PO4 and NaH2PO4
(b) NaH2PO4 and Na2HPO4, or
NaHSO3 and Na2SO3
Topic 5G Solubility equilibria
5G.2 (a) 1.0 Γ 10β5 mol dmβ3
(b) 1.2 Γ 10β4 mol dmβ3
(c) 9.3 Γ 10β11 mol dmβ3
(d) 6.9 Γ 10β7 mol dmβ3
5G.3 (a) 5.5 Γ 10β10mol dmβ3
(b) 3.2 Γ 10β3 mol dmβ3
(c) 1.6 Γ 10β7 mol dmβ3
(d) 2.5 Γ 10β7 mol dmβ3
Topic 5H Ions in solution
5H.1 1.35
5H.3 7.63 mS m2molβ1
5H.4 347 ΞΌm sβ1
Topic 5I Electrochemical cells
5I.2 (a) π£ = 2
(b) π£ = 2
(c) π£ = 4
(d) π£ = 2
(e) π£ = 2
(f) π£ = 1
5I.3 β212 kJ molβ1
5I.4 +7.7 kJ molβ1
Topic 5J Standard potentials
5J.1 Exercise 5I.1
(a) 0
(b) 0
(c) +0.87 V
(d) β0.27 V
(e) β0.62 V
(f) +1.67 V
Exercise 5I.2
(a) +0.08 V
(b) +0.27 V
(c) +1.23 V
(d) +0.695 V
(e) +0.54 V
(f) +0.37 V
5J.2 πΈβ = +1.14 V
ΞrπΊβ = β440 kJ molβ1
5J.3 110
5J.4 0.320 V
Answers to problems
5.1 (a) β91.14 kJ molβ1
(b) +594.6 kJ molβ1
(c) β66.8 kJ molβ1
(d) +99.8 kJ molβ1
(e) β415.80 kJ molβ1
5.2 +279 kJ molβ1
5.3 (a) β32 kJ molβ1
(b) (i) β49 kJ molβ1
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
ANSWERS TO END OF CHAPTER EXERCISES
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(ii) β67 kJ molβ1
5.4 β0.7 kJ molβ1
5.5 (a) exergonic
(b) endergonic
(c) endergonic
(d) exergonic
5.6 (a) 1120 K
(b) 397 K
5.7 1500 K
5.8 (a) K > 1
(b) K < 1
(c) K > 1
(d) K > 1
(e) K > 1
5.10 πΎr1/πΎr2 = 1.4 Γ 1046
5.11 β245 kJ molβ1
5.12 0.0958, 0.9042
5.13 πNH3(g) = 1.93 bar
πH3(g) = 1.10 bar
πN3(g) = 0.03 bar
5.14 2.7 Γ 10β4bar
5.15 (a) βPCl5β = 0.016 mol dmβ3
[PCl3] = [Cl2] = 0.013 mol dmβ3
(b) 45 per cent
5.16 πH2(g) β 0.20 bar
πN2(g) β 0.20 bar
πNH3(g) = 7.6 Γ 10β5 bar
5.17 +41.1 kJ molβ1
5.19 (a) 9.24
(b) β12.9 kJ molβ1
(c) +161 kJ molβ1
(d) +248 J Kβ1molβ1
5.20 β187.78 kJ molβ1
5.21 (a) +12.50 kJ molβ1
(b) +9.05 kJ molβ1
(c) β8.6 J Kβ1molβ1
5.22 (a) [H3O+] = 1.6 Γ 10β7 mol dmβ3
pH = 6.8
(b) [OHβ] = 1.6 Γ 10β7 mol dmβ3
pOH = 6.8
5.23 (a) 2 D2O(l) β D3O+(aq) + OD
β(aq)
(b) 14.9
(c) 3.67 Γ 10β8 mol dmβ3
(d) 7.43
(e) pD + pOD = pπΎw = 14.9
5.24 ideal: pH = 0.30
πΎH3O+ = 0.769: pH = 0.42
5.26 +57.2 kJ molβ1
π.28 pπΎa = 8.02
5.29 (a) 5 per cent
(b) 0.34 per cent
(c) 2.4 per cent
5.30 (a) pH = 1.94
pOH = 12.1
7.4 per cent
(b) pH = 3.7
pOH = 10.3
81 per cent
(c) pH = 0.84
pOH = 13.16
58 per cent
5.31 (a) pH = 6.6
(b) pH = 2.1
(c) pH = 1.5
5.32 [(COOH)2] = 0.08 mol dmβ3
[HOOCCO2β] = 0.07 mol dmβ3
[(CO2)22β] = 6.5 Γ 10β5 mol dmβ3
[H3O+] = 0.07 mol dmβ3
[OHβ] = 1.4 Γ 10β13 mol dmβ3
5.33 [H2S] = 0.065 mol dmβ3
[HSβ] = 9.2 Γ 10β5mol dmβ3
[S2β] = 7.1 Γ 10β15mol dmβ3
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
ANSWERS TO END OF CHAPTER EXERCISES
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[H3O+] = 9.2 Γ 10β5mol dmβ3
[OHβ] = 1.1 Γ 10β10 mol dmβ3
π.35 pH = 9.2
5.36 pH = 4.8
5.38 (a) [acid]
[base]= 1.6 Γ 10β5
(b) [acid]
[base]= 1
(c) [acid]
[base]= 5.0
5.40 pH = 2.71
5.41 (a) pH = 5.1
(b) pH = 9.1
(c) pH = 2.7
5.42 (a) pH = 2.9
(b) pH = 4.6
(c) 12.5 cm3
(d) pH = 4.75
(e) 25.0 cm3
(f) pH = 8.72
5.43 πΎa = 6.92 Γ 10β6
pKa = 5.16
pH = 3.38
5.44 8.00
5.46 (a) pKa = 3.08
πΎa = 8.32 Γ 10β4
(b) pH = 2.78
5.47 pH = 8.3
5.48 (a) pH = 4.75
(b) pH = 5.0
(c) pH = 4.1
5.49 ΞsπΊo = +241 kJ molβ1
5.50 π = 1.25 Γ 10β5 mol dmβ3
5.51 (b) increase
5.52 (a) 2.73 g
(b) 2.92 g
5.53 0.015 mol kgβ1 MgF2
πΎΒ±,MgF2= 0.538
πMg2+ = 0.0081
πFβ = 0.016
0.025 mol kgβ1 NaCl
πΎΒ±,NaCl = 0.733
πNa+ = 0.018
πClβ = 0.018
5.54 π΅ = 2.022
5.55 13.83 mS m2molβ1
5.56 (a) 12.6 mS m2 molβ1
(b) 210 S mol1/2m1/2
5.57 1.364 Γ 10β5 mol dmβ3
5.58 3.70
5.59 4.85
5.60 +28 mV
5.61 β1.18 V
5.62 (a) +1.23 V
(b) +1.11 V
5.63 (a) right-hand
(b) +1.06 V
5.64 (a) β1.20 V
(b) β 1.19 V
5.65 (a) β394 kJ molβ1
(b) β787 kJ molβ1
(c) +75 kJ molβ1
(d) β284 kJ molβ1
(e) β291 kJ molβ1
(f) +498 kJ molβ1
5.66 (a) πΈcello = β0.46 V
ΞrπΊo = +88.8 kJ molβ1
Ξrπ»o = +146.39 kJ molβ1
(b) +86.9 kJ molβ1
5.67 (a) πΈcello = +1.57 V
ΞrπΊo = β606 kJ molβ1
(b) β604 kJ molβ1
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5.70 (a) β40 kJ molβ1
(b) +29.7 kJ molβ1
(c) β313 kJ molβ1
5.71 (a) +0.324 V
(b) +0.45 V
5.72 +0.56 V
5.73 (a) 6.4 Γ 109
(b) 1.3 Γ 107
(c) 9.4 Γ 1043
(d) 1.1 Γ 1025
(e) 8.2 Γ 10β7
(f) 3.4 Γ 1013
5.75 (a) +0.94 V
(b) {1.51 + 0.041 Γ ln(10βpH)} V
5.76 +0.22 V
5.77 (a) β0.6119 V
(b) β0.22 V
(d) +0.41 V
(e) pπΎa = 10.28
5.79 Ξrπo = β324 J Kβ1molβ1
Ξrπ»o = β571 kJ molβ1
Answers to projects
5.3 (b) +0.2234 V
5.4 (b) +0.206 V
Focus 6
Chemical kinetics
Answers to exercises
Topic 6A Empirical chemical kinetics
6A.1 1.2 mmol dmβ3
6A.2 A: 1.6 mol dmβ3sβ1
B: 0.80 mol dmβ3sβ1
D: 2.4 mol dmβ3sβ1
6A.3 0.80 mol dmβ3sβ1
Topic 6B Rate laws
6B.1 molβ2dm6 sβ1
6B.2 πr1: molβ1dm3sβ1
πr2: molβ1dm3
6B.3 πr1: kPaβ1/2sβ1
πr2: dimensionless
6B.4 3.7 Γ 106 dm3molβ1sβ1
Topic 6C Integrated rate laws
6C.1 1.58 Γ 10β3 sβ1
6C.2 1.12 Γ 10β4sβ1
6C.5 (a) 14 Pa sβ1
(b) 1.5 Γ 103s
6C.7 1326 s
6C.8 3100 a
6C.9 (a) 0.63 ΞΌg
(b) 0.16 ΞΌg
6C.10 (a) 0.138 mol dmβ3
(b) 0.095 mol dmβ3
6C.11 13.6 s
6C.12 π‘1/2 = 5.70 h
(a) 78.4 kPa
(b) 77.6 kPa
Topic 6D The temperature dependence of
reaction rates
6D.1 7.5 Γ 10β14molβ1dm3sβ1
6D.2 (a) 1.86 Γ 1023a
(b) 75.8 s
6D.3 π΄ = 1.37 Γ 1015dm3molβ1sβ1
6D.4 298.86 K
6D.5 52 kJ mol1
6D.6 35.9 kJ molβ1
6D.7 121 kJ molβ1
6D.8 β21.6 kJ molβ1
6D.9 (a) 27.2 kJ molβ1
(b) 54.3 kJ molβ1
6D.10 π΄ = 1.44 Γ 1012 molβ1 dm3 sβ1
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6D.11 0.8 nm2
Topic 6E The approach to equilibrium
6E.1 7.5 Γ 105 sβ1
6E.2 23.8 msβ1
6E.3 21 ms
Topic 6F Reaction mechanisms
6F.1 39.1 d
6F.2 increase
6F.3 1.89 Γ 10β6 Paβ1sβ1
Topic 6G Reactions in solution
6G.1 (a) 6.61 Γ 106 m3molβ1sβ1
(b) 3.0 Γ 107 m3molβ1sβ1
6G.2 (a) β3.1 Γ 1016 mol mβ2sβ1
(b) 1.6 Γ 10β11mol
6G.3 (a) 27 h
(b) 2.7 Γ 103 h
(c) 3.0 Γ 103 a
6G.4 π = 1 Γ 106
6G.5 17 kJ molβ1
Topic 6H Homogeneous catalysis
6H.1 5.6 Γ 1022
6H.2 1.62 mmol dmβ3
6H.3 πcat = 1.18 Γ 105 sβ1
π = 7.9 Γ 106 molβ1dm3sβ1
Topic 6I Heterogeneous catalysis
6I.1 172 m2
6I.2 (a) 60 Pa
(b) 4.9 kPa
6I.3 (a) 0.068
(b) 0.42
Answers to problems
6.1 (a) first order
(b) 4.977 s1
6.2 (a) complex: first order
Y: second order
(b) 1.9 mol1
dm3 s1
6.3 (a) π£ = ππ[ICl][H2]
(b) kr = 0.162 mol1
dm3 s1
(c) 20.6 Γ 10β7mol dmβ3sβ1
6.4 0.248 s1
6.5
(a) second order
(b) 7.80 Γ 10β3
dm3 mol
β1 s
β1
6.6 (a) second order
(b) 1.32 dm3 mol
β1 s
β1
6.9 second order
0.287 molβ1dm3minβ1
6.10 πΈa = 272 kJ molβ1
6.11 πΈa = 180 kJ molβ1
A = 2.11 molβ1
dm3 s
β1
6.12
(a) π(20 β) = 1.7 Γ 10β20
(b) π(200 β) = 5.6 Γ 10β13
π΄ = 3 Γ 1011 molβ1dm3sβ1
6.13 (a) 126 kJ molβ1
(b) Ξπβ‘ = 0
6.15 πr,eff = 7.12 Γ 105 sβ1
πrβ² = 4.00 Γ 1010 molβ1 dm3sβ1
6.16 {πb(πa/πaβ² )1/2}[A2]1/2[B]
6.19 (a) 3 ClO(aq) ClO3(aq) + 2 Cl(aq)
(b) first step
6.26 πΎM = 1.11 ΞΌmol dmβ3
π£max = 2.31 ΞΌmol dmβ3 sβ1
πcat = 1.2 Γ 102 sβ1
6.27 πΎM = 87 mmol dmβ3
π£max = 16 ΞΌmol dmβ3 sβ1
6.28 πΌ = 2.809 Paβ1
πβ = 0.5659 cm3
6.29 gold: zeroth order
Platinum: first order
6.33 π = 165
πmon = 13.1 cm3
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Answers to projects
6.1 (a) 1
[A]0β[B]0ln (
[B]/[B]0
[A]/[A]0) = πrπ‘
(b) 1
[A]β
1
[A]0= πrπ‘
6.2 (b) πΈa = 105.1 kJ molβ1
ΞrπΊo = β26.6 kJ molβ1
Ξrπ»o = β34.3 kJ molβ1
6.6 (a) πΎM = 24.9 mmol dmβ3
π£max = 4.80 mol dmβ3sβ1
(b) πΎM = 25.0 mmol dmβ3
π£max = 4.81 mol dmβ3sβ1
(c) πΎM = 25.0 mmol dmβ3
π£max = 4.80 molβ1 dm3sβ1
Focus 7
Quantum theory
Answers to exercises
Topic 7A The emergence of quantum theory
7A.1 3.05 Γ 10β19 J
7A.2 8.226 Γ 104 cmβ1
7A.3 (a) 6.6 Γ 10β19 J
4.0 Γ 102 kJ molβ1
(b) 3.3 Γ 10β20 J
20 kJ molβ1
(c) 1.3 Γ 10β33 J
7.8 Γ 10β13 kJ molβ1
7A.4 (a) πΈ(750 nm) = 2.65 Γ 10β19 J
(b) π(250 nm) = 9.96 Γ 105 m sβ1
7A.5 (a) 6.6 Γ 10β31m
(b) 6.6 Γ 10β39 m
(c) 99.7 pm
7A.6 1.3 Γ 106 m sβ1
7A.7 4 Γ 10β36m
7A.8 (a) 1.10 Γ 10β27 kg m sβ1
(b) 9.5 Γ 10β24 kg m sβ1
(c) 3.31 Γ 10β36 kg m sβ1
7A.9 2.2 Γ 10β24 m sβ1
Topic 7B The dynamics of microscopic systems
7B.1 Ξπ₯ β₯ 0.900 nm
7B.2 Ξπ£ β₯ 2.1 Γ 10β29 m sβ1
7B.3 Ξπ₯ β₯ 1.1 Γ 10β26 m
7B.4 Ξπ₯ = 100 Γ 10β12 m
Ξπ£ β₯ 5.8 Γ 105 m sβ1
Topic 7C Translation
7C.1 (a) π₯ = πΏ/2
(b) π₯ = 3πΏ/4
(c) π₯ = 5πΏ/6
7C.2 9.84 Γ 10β23 J
7C.3 πΏ = 1.00 Γ 10β9 m
Topic 7D Rotation
7D.1 π = 0: β
π = 1: 628 pm
π = 2: 314 pm
7D.2 (a) 4.34 Γ 10β47 kg m2
(b) 1.55 mm
7D.3 6
7D.4 ml = β4, β3, β2, β1, 0, +1, +2, +3
7D.5 6.65 Γ 10β22 J
Topic 7E Vibration
7E.1 0.04 N mβ1
7E.2 6.90 Γ 1013 sβ1
7E.3 7.94 Γ 10β6 N mβ1
Answers to problems
7.1 2.52 eV
7.2 (a) 1.23 nm
(b) 38.8 pm
(c) 3.88 pm
7.3 (a) 6.1 Γ 10β4 N
(b) 6.1 Γ 10β10 Pa
(c) 1600 s
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ANSWERS TO END OF CHAPTER EXERCISES
14
7.5 π₯ = Β±0.5887/π1/2
7.7 (a) 1.8 Γ 10β4
(b) 5.9 Γ 10β5
7.8 5h2 / 8mL
2: (1,4) (2,2)
5h2 / 4mL
2: (1,6) (3,2)
7.9 πΏ/4 , 3πΏ/4
7.10 (a) 2.2 Γ 10β20 J
(b) 9.2 ΞΌm
7.12 (a) 0.22
(b) 9.5 Γ 10β3
7.13 8.79 Γ 1011sβ1
7.14 2.10 Γ 10β22 J
7.15 0.707
Answers to projects
7.1 (a) π₯ = 0.1 to π₯ = 0.2 nm:
π(π₯) = 1.84 Γ 10β4, 3.8 per cent
x = 4.9 to x = 5.2 nm:
π(π₯) = 2.36 Γ 10β4, 74.9 per cent
(b) 0.196
(c) 0.609
(d) 0.196
7.2 (a) (i) π(π₯) = (π/Ο)1/4eβππ₯2/2
(ii) x = 0
(b) (i) π(π₯) = (4π3/Ο)1/4π₯eβππ₯2/2
(ii) x = Β±1/a1/2
7.3 (a) 6.432 Γ 1013 sβ1
(b) 2146 cmβ1
(c) π C13 O16 2098 cmβ1
π C12 O18 2094 cmβ1
π C13 O18 2045 cmβ1
Focus 8
Atomic structure
Answers to exercises
Topic 8A Hydrogenic atoms
8A.1 4.10296 Γ 10β5cm = 410.296 nm
8A.2 π2 = 5
8A.3 π2 = 6
8A.4 1.00047
8A.5 27 cmβ1
8A.6 n1 = 2 n2 = 4
8A.7 16
8A.8 (a) 0, 0 angular node, 0 radial nodes
(b) 0, 0 angular node, 2 radial nodes
(c) 61/2β, 2 angular nodes,
0 radial nodes
(d) 21/2β, 1 angular node, 0 radial nodes
(e) 21/2β, 1 angular node, 1 radial node
8A.9 (a) 1
(b) 9
(c) 49
8A.10 (a) 2
(b) 14
(c) 22
8A.11 0, 180, 90, 270
8A.12 (a) (π π 1)
(b) l
(c) (π 1)
Topic 8B Many-electron atoms
8B.2 (a) [He]2s2p3
(b) [Ar]3d2
(c) [Ar]3d5
Topic 8C Periodic trends of atomic properties
8C.2 349 kJ molβ1
Topic 8D Atomic spectroscopy
8D.1 (b), (c), (e)
8D.3 nd, ng
8D.4 (a) πΏ = 2, 1, 0
(b) πΏ = 4,3, 2, 1, 0
8D.5 S = 2, 1, 0
8D.6 (a) 1S0
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15
(b) 3F4,
3F3,
3F2
(c) 5S2
(d) 5P3, 5P2,
5P1
8D.7 3F,
1F,
3D,
1D,
3P,
1P
8D.8 (a) 3F term,
the lowest level:
3F2
(b) 5
8D.9 [Ar]3d1
π½ = 5/2, 3/2
2D3/2, lowest in energy
8D.10 3F2
8D.11 Al: 2P1/2
Cl: 2P3/2
8D.12 (a), (c)
Answers to problems
8.1 n = 3 2: He3 + 15238.6 cmβ1
He4 + 15239.3 cmβ1
n = 2 1: He3 + 82288.5 cmβ1
He4 + 82292.3 cmβ1
8.2 122.31 eV
8.3 (a) n = 7 6 12368 nm
n = β 6 3282 nm
(b) n = 8 6 7503 nm
n = 9 6 5908 nm
(c) 12368 nm
8.4 (a) 397.13 nm
(b) 3.400 eV
8.5 (a) 109740 cmβ1
(b) n = 3 2 137170 cmβ1
n = 4 2 185180 cmβ1
(c) 122.5 eV
8.6 14.0 eV
8.7 0.602 π0
8.8 (a) 0.262 a0, 2.530 a0
(b) 0.090 a0, 3.845 a0
8.9 (a) 1.4 Γ 10β5
(b) 1.1 Γ 10β4
8.10 (a) 1.9 π0 , 7.10 π0
(b) 1.87 π0, 6.61 π0, 15.5 π0
8.11 Fe2+
8.12 2.142 meV
Answers to projects
8.1 (a) π = π0
(b) (i) 2.69 Γ 10β7
(ii) 2.47 Γ 10β8
(iii) 0
(c) 5.24 a0
(d) 5.236 π0
8.3 (a) receding, 338 km sβ1
Focus 9
The chemical bond
Answers to exercises
Topic 9A Valence bond theory
9A.1 1870 kJ molβ1
9A.2 πCβH = πC(1)πH(2) + πC(2)πH(1)
9A.3 π1(Ο-bond) =
π2pπ§A(1)π2pπ§B(2) + π2pπ§A(2)π2pπ§B(1)
π2(Ο-bond) =
π2pπ₯A(1)π2pπ₯B(2) + π2pπ₯A(2)π2pπ₯B(1)
π3(Ο-bond) =
π2pπ¦A(1)π2pπ¦B(2) + π2pyA(2)π2pπ¦B(1)
9A.5 210 times
9B.2 F2β: Β½
F2: 1
F2+: 1Β½
9B.3 O2+: 2Β½
O2: 2
O2β: 1Β½
O22β: 1
O2+ < O2 < O2
β < O2
2β
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9B.4
(a) H2β: 1Οg
21Οu1
(b) Li2: 1Οg2
(c) Be2: 1Οg2 1Οu
2
(d) C2: 1Οg2 1Οu
2 1Οu4
(e) N2: 1Οg2 1Οu
2 2Οg2 1Οu
4
(f) O2: 1Οg2 1Οu
2 2Οg2 1Οu
4 1Οg 2
9B.5 C2 stronger
9B.6 32 molecular orbitals
Topic 9C Molecular orbital theory:
heteronuclear diatomics
9C.1 (a) nonpolar
(b) polarized
9C.2 (a) C2, CN
(b) NO, O2, F2
9C.3 N2 is shorter
Topic 9D Molecular orbital theory:
polyatomic molecules
9D.1 β6.26 eV
604 kJ molβ1
ππ.2 6πΌ + 8π½
9D.3 0
9D.4 (a) β2π½
(b) β1.24π½
(c) β2π½
Answers to problems
9.2 bond angle for SO2 is 120
9.8 CO: 1Ο2 2Ο2 3Ο2 1Ο4
NO: 1Ο2 2Ο2 3Ο2 1Ο4 2Ο1
CNβ: 1Ο2 2Ο2 3Ο2 1Ο4
9.9 XeF+ will have a shorter bond length than
XeF
9.11 1u
2g (two)
3u (two)
4g
9.12 (a) 6.00 eV
(b) 2.70 eV
9.13 (a) ethene β30750 cmβ1
butadiene β37280 cmβ1
hexatriene β44660 cmβ1
octatetraene β47370 cmβ1
(b) β71910 cmβ1
9.14 (a) benzene: πΌ + 2π½, πΌ + π½,
πΌ + π½, πΌ β π½, πΌ β π½, πΌ β 2π½
Cyclooctatetraene:
πΌ + 2π½, πΌ + β2π½, πΌ + β2π½,
πΌ, πΌ, πΌ β β2π½, πΌ β β2π½, πΌ β 2π½
(b) benzene: 2π½
hexatriene: 0.988π½
(c) cyclooctatetraene: 1.657π½
octatetraene: 1.516π½
9.15 πΌ + β2π½: bonding
πΌ: non β bonding
πΌ β β2π½: antibonding
9.16 (a) C6H6β: 1Οu
2 2Οg4 1Οu
1
7πΌ + 7π½
(b) C6H6+: 1Οu
2 2Οg3
5πΌ + 7π½
Answers to projects
9.2 (c) Ο/4, βΟ/4
9.3 (b) (π /π0) = 2.11
(c) π1 = Β±(0.356π΄ + 0.934π΅)
π2 = Β±(0.934π΄ β 0.356π΅)
Focus 10
Molecular interactions
Answers to exercises
Topic 10A Electric properties of molecules
10A.1 β36 J molβ1
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
ANSWERS TO END OF CHAPTER EXERCISES
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10A.2 (a) 1.78 D, 5.9 Γ 10β30C m
(b) 0.94 D, 3.1 Γ 10β30C m
(c) 0.76 D, 2.5 Γ 10β30C m
10A.3 π/D = β0.89
10A.4 1.17 D
10A.5 (a) C2 m
2 J
β1
(b) (C2 m
2 J
β1) / (C
2 J
β1 m
β1) = m
3
Topic 10B Interactions between molecules
10B.1 β5.22 Γ 10β24 J
10B.2 π(π) = β1.9 Γ 10β27 J
πm(π) = β1.19 Γ 10β3 J molβ1
10B.3 479 pm
10B.4 π = 700 pm
πAπ = 12.6 kJ molβ1
Answers to problems
10.1 non-polar
10.2 (a) 1,2-dimethylbenzene: 0.69 D
1,3-dimethylbenzene: 0.40 D
1,4-dimethylbenzene: non-polar
(b) (i) 0.80 D
(ii) 0.40 D
(iii) non-polar
10.3 (a) 1.41 D
(b) 2.44 D
(c) 1.06 D
(d) 1.69 D
10.4 π = 37 D
π = 11.8Β°
10.5 1.17 Γ 10β29 C m = 3.50 D
10.7 (a) 476 kJ molβ1
(b) 87.4 kJ molβ1
10.9 (a) 3.72 kJ molβ1
(b) β0.365 J molβ1
10.10 196 pm
10.11 π(π) = β1.6 Γ 10β26 J
πm(π) = β9.6 Γ 10β3J molβ1
ππ.12 π(π) = β7.0 Γ 10β20 J,
πm(π) = β42 kJ molβ1
10.14 250 to 410 pm
10.16 (a) 11.6 kJ molβ1
(c) 2.12 Γ 1012 sβ1
Focus 11
Molecular spectroscopy
Answers to exercises
11A.1 (a) 6.78 Γ 1014 Hz
(b) 22600 cmβ1
11A.2 (a) 2.94 Γ 10β3 cmβ1
(b) 3.41 m
11A.3 (a) 1.48 Γ 104 dm3 molβ1 cmβ1
(b) 0.9506%
11A.4 (a) 55 dm3 molβ1 cmβ1
(b) 0.048
11A.5 659.999936 nm
7.02 Γ 107 m sβ1
11A.6 8.3 Γ 105 K
11A.7 (a) 53 ps
(b) 5.3 ps
(c) 160 ps
11A.8 (a) 53 cmβ1
(b) 0.27 cmβ1
Topic 11B Rotational spectroscopy
11B.1 3.6 Γ 1033
11B.2 (a) (i) 4.601 Γ 10β48 kg m2
(ii) 9.194 Γ 10β48 kg m2
(iii), (iv) 7.150 Γ 10β46 kg m2
(b) (i) 1.824 Γ 1012 Hz
60.84 cmβ1
(ii) 9.126 Γ 1011 Hz
30.44 cmβ1
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ANSWERS TO END OF CHAPTER EXERCISES
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(iii), (iv) 1.174 Γ 1010 Hz
0.3915 cmβ1
11B.3 (b) 2.66 Γ 109 sβ1
0.0888 cmβ1
11B.4 πΌβ₯ = 4πBπB2
πΌβ₯ = 2πBπB2
11B.5 π΄ = 5.149 GHz
π΅ = 10.30 GHz
11B.6 (a) 289
(b) 17
11B.7 232.1 pm
11B.8 Β½
11B.9 (a) 10
(b) 19
11B.10 474 K
11B.11 (a) (i) (ii) (iii),(iv)
(b) all
11B.13 (a) 636 GHz
(b) 21.2 cmβ1
11B.14 5990749.416 MHz
11B.15 116.2 pm
11B.16 20643 cmβ1
Topic 11C Vibrational spectroscopy
11C.1 (a) 4.49 Γ 1013 Hz
(b) 4.39 Γ 1013 Hz
11C.2 (a) 3
(b) 4
(c) 48
(d) 54
11C.3 329 N mβ1
11C.4 (a) (i) HF: 967.4 N mβ1
(ii) HCl: 515.8 N mβ1
(iii) HBr: 411.8 N mβ1
(iv) HI: 314.3 N mβ1
(b) DF: 2930 cmβ1
DCl: 2114 cmβ1
DBr: 1874 cmβ1
DI: 1634 cmβ1
11C.6 3724.66 cmβ1
11C.7 π₯e = 0.0062
11C.8 2699.9 cmβ1
Topic 11D Electronic spectroscopy
11D.1 [A] = 0.56 mol dmβ3
[B] = 0.16 mol dm
β3
11D.2 1.737 Γ 10β15 J
11D.3 50.8 nm
11D.4 1.602 Γ 10β15 J
11D.5 (a) 2.04 Γ 10β19 J
(b) 669 km sβ1
Topic 11E The decay of excited states
11E.2 0.57
11E.3 4.7 nm
Answers to problems
11.1 33 ΞΌg dmβ3
11.2 (a) 162 pm
(b) 179 GHz
11.3 (b) 3.2645 GHz
(c) 237.6 pm
11.4 οΏ½ΜοΏ½ = 0.2029 cmβ1
οΏ½ΜοΏ½ = 6.233 Γ 10β8 cmβ1
11.5 ROC = 116.28 pm
RCS = 155.97 pm
11.9 (b) 126.5 pm
11.11 πQ = 5.16 Γ 106 molβ1 dm3 sβ1
11.12 kF = 1.276 1010
molβ1
dm3 s
β1
11.13 kQ =9.146 109 mol
β1 dm
3 s
β1
π‘1/2 = 0.172 ΞΌs
11.14 407 ps
11.15 3.49 nm
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ANSWERS TO END OF CHAPTER EXERCISES
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Answers to projects
11.1 (a) 4200
(b) 588 nm
11.2 π½max = (ππ/βπ΅)1/2 β Β½
11.5 2.6 nm
Focus 12
Statistical thermodynamics
Answers to exercises
Topic 12A The Boltzmann distribution
12A.1 π2
π1= 0.37
12A.2 524 K
12A.3 π5
π0= 7.4
Topic 12B The partition function
12B.1 (a) π = 1 + 6eβ2π/ππ + 3eβ5π/ππ
(b) π = 1
(c) π = 10
12B.2 (a) πT = 1.45 Γ 1027
(b) πT = 6.49 Γ 1027
12B.3 (a) πT = 3.2 Γ 104
(b) πT = 6.2 Γ 1027
12B.4 (a) πR = 19.5
(b) πR = 265
12B.5 eqn 12B.6: πV = 1.39
eqn 12B.7: πV = 0.789
12B.6 πE = 4.23
Topic 12C The origin of thermodynamic
properties
12C.1 οΏ½Μ οΏ½ = (5eβπ/ππ+9eβ3π/ππ
1+5eβπ/ππ+9eβ3π/ππ) π
12C.2 (a) 1.25 kJ molβ1
(b) 2.08 kJ molβ1
12C.3 β37.4 kJ molβ1
Answers to problems
12.1 (a) π4
π2= 1.753
(b) π4
π2= 2.27
12.2 (a) ππ = β ππ½π½=0 eβππ½/ππ: ππ = 24.816,
Using eqn 12B.5: πR = 24.474
12.4 11350 K
12.5 (a) 1.401 (at 500 K)
(b) 3.147 (at 1000 K )
12.6 1.28 Γ 1034
12.7 (a) qE = 5
(c) 6.730
12.8 (a) πE = 1.293 (at 10 K )
πE = 7.825 (at 298 K )
12.9 πV = 2.14
πm = 14.6 J Kβ1molβ1
ππ.10 183.1 J Kβ1molβ1
12.11 (a) Sκ(Xe) > S
κ(Ne)
(b) Sκ(D2O) > S
κ(H2O)
(c) Sκ(graphite) > S
κ(diamond)
12.12 β54.3 kJ molβ1
12.13 πΎ = 1.336 Γ 10β25
12.14 πΎ = 1.951 Γ 10β11
Focus 13
Magnetic Resonance
Answers to exercises
Topic 13A Nuclear magnetic resonance
13A.1 (a) Tβ1 Hz
(c) A s kgβ1
13A.2 πΈ3/2 = β1.949 Γ 10β26 J
πΈ1/2 = β6.498 Γ 10β27 J
πΈβ1/2 = 6.498 Γ 10β27 J
πΈβ3/2 = 1.949 Γ 10β26 J
13A.3 2.263
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
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13A.4 (a) 2.9 Γ 10β5
(c) 7.3 Γ 10β6
13A.5 300.5 MHz
13A.6 18.79 T
Topic 13B The information in NMR spectra
13B.1 3.17 kHz
13B.2 (a) 9.1 ΞΌT
(b) 38 ΞΌT
13B.3 (a) 11
(b) 5
13B.4 (a) 2.4 kHz
(b) 6.0 kHz
13B.5 octet
13B.6 3.78 ms
Topic 13C Electron paramagnetic resonance
13C.1 4.64 Γ 10β24 J
13C.2 (a) 9.02 Γ 10β4
(b) 2.7 Γ 10β3
13C.3 9.25 GHz, 32.4 mm
13C.4 2.0022
13C.5 π = 64.5 MHz
13C.6 (a) 1:3:3:1
(b) 1:3:6:7:6:3:1
13C.7 (a) 331.9 mT
(b) 1.201 T
13C.8 terminal: 0.64
central: 0.180
Answers to problems
13.8 (a) π΄β² = 1.9 Hz
π΅β² = β1.4 Hz
πΆβ² = 6.4 Hz
(b) 109 Β°
13.9 2600 sβ1
13.10 64 sβ1
13.12 1
13.13 π 0.011 mT: 0.0049
π 0.172 mT: 0.0764
π 0.272 mT: 0.1209
π 0.450 mT: 0.2000
π 0.108 mT: 0.0480
π 0.112 mT: 0.0498
Focus 14
Macromolecules and aggregates
Answers to exercises
Topic 14A Biological and synthetic
macromolecules
14A.1 οΏ½Μ οΏ½n = 95 kg molβ1
οΏ½Μ οΏ½w = 93 kg molβ1
14A.2 3.4
14A.3 (a) 0.880 ΞΌm
(b) 31.1 nm
(c) 12.7 nm
14A.4 π c = 2.74 ΞΌm
π rms = 29.1 nm
14A.5 13000
14A.6 β0.042 J Kβ1molβ1
14A.7 8 aJ
Topic 14B Mesophases and disperse systems
14B.1 5.8 cm
14B.2 23 mN mβ1
14B.3 (a) 1.4 kPa
(b) 0.14 kPa
14B.4 97 mmol mβ2
Answers to problems
14.1 οΏ½Μ οΏ½n = 20 kg molβ1
οΏ½Μ οΏ½w = 22 kg molβ1
14.2 οΏ½Μ οΏ½w/οΏ½Μ οΏ½n = 1.27
14.4 β± = 1.37 pN
14.6 pH = 6.9
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
ANSWERS TO END OF CHAPTER EXERCISES
21
14.7 68 ΞΌJ
Answers to projects
14.1 (a) β¨π 2β©1/2 = 10.9 nm
(b) β¨π β© = 10.0 nm
(c) π β = 8.89 nm
14.3 (a) 2.70 pN
Focus 15
Solids
Answers to exercises
Topic 15A Crystal structure
15A.1 π = 0.396 nm3
π = 2.41 Γ 103kg mβ3
15A.2 π = 3.9
π = 4.01 Γ 103 kg mβ3
πππ.3 (a) 221 pm
(b) 110 pm
15A.4 {1 1 1} 330 pm, {2 1 1} 234 pm,
{1 0 0} 572 pm
15A.5 {1 2 3} 135 pm
{2 3 6} 70 pm
15A.6 564 pm
15A.7 π = 363 pm
π = 564 pm
15A.8 112 pm
15A.9 1.28 mV
15A.10 66.1 pm
15A.11 π = 798 pm
Topic 15B Bonding in solids
15B.1 (a) zinc-blende
(b) zinc blende
(c) rock-salt
15B.2 ΞLπ»κ(SrO)
ΞLπ»κ(CaO)= 0.947
15B.3 3000 kJ molβ1
Topic 15C The properties of solids
15C.3 549 nm
Answers to problems
15.2 (321). (111). (122). (32Μ 2Μ ).
15.6 bcc
15.7 (b) 8.97 Γ 103 kg mβ3
15.8 0.740
15.9 0.740 g cmβ3
15.10 520 nm
15.11 (a) 424 nm
(b) 600 nm
15.12 (a) less dense
(b) 92 per cent
15.15 π = βππ§2π2Ο
48π0π
15.16 β8.16 Γ 10β18 J
15.18 +3500 kJ molβ1
15.19 +2421 kJ molβ1