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Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
ANSWERS TO END OF CHAPTER EXERCISES
1
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 × 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 −243.6 ℃
1A.10 394 K
1A.11 (a) 3.6 m3
(b) 178 m3
1A.12 3.4 × 105 m3
1A.13 benzene 0.355, toluene 0.645
1A.14 (a) 1.32 × 10−3m3
(b) 61.2 × 103 Pa
Topic 1B The kinetic model of gases
1B.1 (a) 493 m s−1
(b) 615 m s−1
1B.2 (a) 𝑣mean(79 K) = 647 m s−1
𝑣mean(315 K) = 1.29 km s−1
𝑣mean(1500 K) = 2.82 km s−1
(b) 𝑣mean(79 K) = 323 m s−1
𝑣mean(315 K) = 645 m s−1
𝑣mean(1500 K) = 1.41 km s−1
1B.3 3.72
1B.4 𝑚N2 0.80 g
𝑚He 0.30 g
1B.5 65 mPa
1B.6 𝜆 = 0.97 μm
𝑁 = 120 × 103
1B.7 (a) 7.0 × 1010
(b) 7.0 × 108
(c) 7.0 × 104
1B.9 (a) 6.8 nm
(b) 68 nm
(c) 6.8 mm
Topic 1C Real gases
1C.1 𝑍c = 0.242
1C.2 CH4 𝑍c = 0.288
C2H6 𝑍c = 0.274
C3H8 𝑍c = 0.276
1C.3 2.15 MPa
1C.4 −3.37 × 10−5 m3mol−1
1C.5 −3.49 × 10−8 Pa−1
1C.6 (a) (i) 101 kPa
(ii) 83.1 MPa
(b) (i) 101 kPa
(ii) 206 MPa
1C.7 −0.608 MPa
1C.8 𝑏 = 4.6 × 10−5 m3 mol−1
𝑍 = 0.66
1C.9 1842 K
Answers to problems
1.1 0.50 m3
1.2 28.82 g mol−1
130 kg
1.3 6.8 kPa
1.4 713 Torr
1.5 𝑥N2= 0.7809
𝑥O2= 0.2094
𝑥Ar = 0.0098
1.6 132 g mol−1
1.7 16.4 g mol−1
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
ANSWERS TO END OF CHAPTER EXERCISES
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1.8 (a) 𝑝H2= 200 kPa
𝑝N2= 100 kPa
(b) 300 kPa
1.9 (a) 72 K
(b) 943 m s−1
1.10 1.0 × 1013 s−1
1.11 0.57 dm3 mol−1
1.12 𝑎 = 0.656 Pa m6mol−2
𝑏 = 5.54 × 10−5 m3 mol−1
1.13 𝑎 = 0.321 Pa m6 mol−2
𝑏 = 6.50 × 10−5 m3mol−1
𝑟 = 1.86 × 10−10 m
1.14 𝑎 = 𝟎. 𝟏𝟐𝟖 𝐏𝐚 𝐦𝟔 𝐦𝐨𝐥−𝟐
𝑏 = 𝟑. 𝟓 × 𝟏𝟎−𝟓𝐦𝟑 𝐦𝐨𝐥−𝟏
Answers to projects
1.1 (d) 𝑓 ≈ 10−2
1.2 (a) 720 Mbar
(d) 0.21 Mbar
(e) 0.029 Mbar
1.3 (c) 1030 K
1.4 (c) 𝑝c = 101.3 bar
𝑉c = 0.1327 dm3 mol−1
𝑇c = 431.3 K
Focus 2
The First Law of thermodynamics
Answers to exercises
Topic 2A Work
2A.1 (a) 𝑤expansion = −0.10 J
(b) 𝑤expansion = −100 J
(a) 𝑤compression = +0.10 J
(b) 𝑤compression = +100 J
2A.2 −5.5 kJ
2A.3 (a) −99 J
(b) −167 J
2A.4 +123 J
2A.5 +29.9 J
2A.6 −1.25 kJ
2A.7 (a) 0
(b) −783 J
2A.8 −100 J
Topic 2B Heat
2B.1 23.7 J K−1
2B.2 (a) 27 J K−1
(b) 0.45 J K−1g−1
(c) 25 J K−1mol−1
2B.3 42 kJ
2B.4 87 kJ
2B.5 𝐶𝑉,m = 29.9 J K−1mol−1
𝐶𝑝,m = 38.2 J K−1mol−1
Topic 2C Internal energy
2C.1 −41 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 Δ𝐻 = 𝑞𝑝 = −1.2 kJ
𝐶𝑝 = 80 J K−1
2D.5 Δ𝐻 = 𝑞𝑝 = +2.2 kJ
Δ𝑈 = +1.6 kJ
2D.6 28.25 J K−1mol−1
Topic 2E Physical change
2E.1 1740 kJ mol−1
2E.2 19.5 kJ mol−1
2E.3 +492 kJ mol−1
2E.4 +2.83 × 104 kJ
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
ANSWERS TO END OF CHAPTER EXERCISES
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2E.5 (a) +2.44 kJ mol−1
(b) +2.26 kJ mol−1
2E.6 +93 kJ mol−1
2E.7 𝑞𝑝 = Δ𝐻 = +80.0 kJ
𝑤 = −5.20 kJ
Δ𝑈 = +74.8 kJ
2E.8 2.58 kJ mol−1
2E.9 +239 kJ mol−1
Topic 2F Chemical change
2F.1 −124 kJ mol−1
2F.2 (a) 388 kJ mol−1
(b) smaller
(c) Δf𝐻o − 38 kJ mol−1
2F.3 398 kJ mol−1
2F.4 (a) +16 kJ mol−1
(b) −772 kJ mol−1
2F.5 (a) −1560 kJ mol−1
(b) +51.88 kJ g−1
(c) methane: +55.5 kJ g−1
ethane is less exothermic
2F.6 −4564.7 kJ mol−1
2F.7 −85 kJ mol−1
2F.8 (a) −3290 kJ
(b) −2710 kJ
2F.9 −432 kJ mol−1
2F.10 +225 kJ mol−1
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 mol−1
(b) 274 kJ mol−1
(c) 150 kJ mol−1
(d) 449 kJ mol−1
2.6 +2.468 kJ mol−1
2.7 (a) 20.83 J K−1mol−1
(b) (i) +641 J mol−1
(ii) +458 J mol−1
2.8 +39.8 kJ mol−1
2.9 2.38 kJ mol−1
2.10 +40.88 kJ mol−1
2.11 +1152 kJ
2.12 4.22 kJ K−1
+0.768 K
2.13 (a) −2800 kJ mol−1
(b) −2800 kJ mol−1
(c) −1.27 × 103 kJ mol−1
2.14 (a) −1333 kJ mol−1
(b) −1331 kJ mol−1
(c) −815 kJ mol−1
2.15 +112.27 kJ mol−1
2.16 −382.96 kJ mol−1
2.17 (a) −57.29 kJ mol−1
(b) −28.6 kJ mol−1
(c) −138.2 kJ mol−1
(d) −32.88 kJ mol−1
(e) −55.84 kJ mol−1
2.19 (a) +1.9 kJ mol−1
(b) +30.6 kJ mol−1
2.20 (a) −2205 kJ mol−1
(b) −2200 kJ mol−1
2.21 +11.3 kJ mol−1
2.22 −56.98 kJ mol−1
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 mol−1
Answers to projects
2.1 (a) more negative
(b) more positive
2.2 (a) 𝑤 = −𝑛𝑅(𝑇i + 𝑐𝑉i) ln(𝑉f/𝑉i) + 𝑛𝑅𝑐(𝑉f − 𝑉i)
(b) w more negative
2.3 (a) Δ𝑈m = ¼𝑎𝑇4
(b) 𝐶𝑉,m = 𝑏 + 2𝑐𝑇
2.4 (a) +818 J mol−1
2.6 (a) 40000 K
2.7 𝑎 = 29.74 J K−1mol−1
𝑏 = 2.51 × 10−2 J K−2mol−1
𝑐 = −1.55 × 105 J K mol−1
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 K−1
(b) +1.2 J K−1
3A.2 +0.41 J K−1
3A.3 1470 K
Topic 3B Entropy changes
3B.1 +14 J K−1mol−1
3B.2 2.89 dm3
3B.3 +23.6 J K−1
3B.4 −93.0 J K−1
3B.5 −45.1 kJ
−165 J K−1
3B.6 (a) +120 J K−1
(b) −120 J K−1
3B.7 +0.95 J K−1mol−1
3B.8 (a) +122 J K−1
(b) +130 J K−1
(c) +606 J K−1
The total entropy change of the system:
+858 J K−1
3B.9 (a) +85 J K−1mol−1
(b) +34 kJ mol−1
3B.10 (a) +87.8 J K−1mol−1
(b) −87.8 J K−1mol−1
Topic 3C Absolute entropy
3C.1 6.69 mJ K−1mol−1
3C.3 +11.5 J K−1mol−1
Topic 3D The Gibbs energy
3D.1 (a) positive
(b) negative
(c) positive
3D.2 (a) −412.9 J K−1mol−1
(b) +92.6 J K−1mol−1
(c) −153.1 J K−1mol−1
(d) −21.0 J K−1mol−1
(e) +512.0 J K−1mol−1
3D.3 (a) −198.72 J K−1 mol–1
(b) +309 J K−1 mol−1
Answers to problems
3.1 (a) +33 J K−1
3.2 −7.9 J K−1mol−1
3.3 0.63 𝑇i
3.5 +5.1 J K−1
3.6 +79 J K−1mol−1
3.7 (b) 4.1 × 10−23 J K−1
3.8 (c) 3.37 J K−1 mol−1
3.9 4.0 × 10−4J K−1mol−1
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
ANSWERS TO END OF CHAPTER EXERCISES
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3.10 0.256 J K−1mol−1
3.11 +5.03 kJ K−1
3.12 (a) −0.69 J K−1mol−1
(b) +0.14 J K−1mol−1
3.13 (a) −93 kJ mol−1
(b) Yes
(c) +300 J K−1mol−1
3.14 0.41 g
3.15 +17 J
3.16 8.2 × 1023molecules
Answers to projects
3.1 (a) 3.3 kW
(b) 180 kW
3.2 Δ𝑆 = 𝑎 ln(𝑇f/𝑇i) + 𝑏(𝑇f − 𝑇i)
−½𝑐(𝑇f−2 − 𝑇i
−2)
3.3 (b) 2.02 × 10−22 J K−1mol−1
(d) 𝑄
𝑁< 0.01
3.4 (a) Yes
(b) 0.46 mol
(c) −12 W m−3
(d) battery: −150 × 103 W m−3
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 mol−1
(b) −20 kJ mol−1
4A.5 +4.2 kJ mol−1
4A.6 −3.5 kJ mol−1
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 mol−1
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 mol−1
4C.4 +32.631 J mol−1
4C.5 (a) −1.31 kJ mol−1
(b) +4.38 J K−1mol−1
(c) spontaneous
4C.6 (a) Δ𝐺m − 1.40 kJ mol−1
Δ𝑆m + 4.71 J K−1mol−1
(b) spontaneous
4C.7 4.99 kPa
Topic 4D Solutions
4D.1 17.5 g
4D.2 8.92 × 10−2 mol kg−1
4D.3 𝑐sucrose = 0.403 mol dm−3
𝑏sucrose = 0.388 mol kg−1
4D.4 1.80 × 10−3
4D.5 −37 J mol−1
4D.6 𝑥CO2= 4.8 × 10−3
4D.7 129 kPa
4D.8 7985 Pa
4D.9 (a) 1.3 mmol dm−3
(b) 17.0 mmol dm−3
4D.10 𝑏N2= 0.51 mmol kg−1
𝑏O2= 0.28 mmol kg−1
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
ANSWERS TO END OF CHAPTER EXERCISES
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4D.11 34.3 mmol dm−3
4D.12 𝑥T = 0.93 𝑥X =0.07
𝑦T = 0.97 𝑦X = 0.03
4D.13 +5.6 kJ mol−1
Topic 4E Colligative properties
4E.1 59.1 g mol−1
4E.2 +0.061 K
4E.3 +0.36 K
4E.4 207 g mol−1
Topic 4F Phase diagrams of mixtures
4F.1 𝑛′
𝑛′′ = 0.31
4F.2 𝑐E′ (aq) = 0.050 mol dm−3
𝑐E′ (org) = 0.0075 mol dm−3
4F.3 0.25
Answers to problems
4.1 (b) 711 K
4.3 (a) −0.1346 bar K−1
(b) +135.6 bar
4.4 (a) 31.69 kJ mol−1
(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) 𝑦eth = 0.96111
𝑦chl = 0.03889
(d) 692 Torr
4.13 (a) 43.95 Torr
(b) 1.13 Torr
(c) 22.6 kPa
4.14 6.41 × 103 kPa
4.15 A: 𝐾H′ = 861 Torr
B: 𝐾H′ = 1103 Torr
4.16 A: KH = 242 Torr
B: KH = 397 Torr
4.17 0.11 C
4.18 𝑀 = 88.19 kg mol−1
4.19 13.9 kg mol−1
4.20 (a) yT = 0.36
(b) yT = 0.81
4.21 (a) 0.150
(b) 𝑛′
𝑛′′ = 9.81
4.22 (a) 0.345
(b) 𝑛′
𝑛′′ = 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) 𝑥ethanol = 0.072
(b) 53.1039 cm3 mol
-1
4.4 (a) 𝑉water/cm3 mol−1 =
18.068 + 6.557 × 10−3𝑏2 − 1.018 × 10−3𝑏3
4.5 (a) 4.4 cm3O2
(b) 4.0 atm: 56 μg N2,
1.0 atm: 14 μg N2
(c) 170 μg N2
Focus 5
Chemical change
Answers to exercises
Topic 5A The thermodynamics of reaction
5A.1 (a) 𝑄 = 𝑝CO2(g)
6
[CH3COCOOH]2𝑝O2(g)5 × (𝑐o2/𝑝o)
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
ANSWERS TO END OF CHAPTER EXERCISES
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(b) 𝑄 = [FeSO4]
[PbSO4]
(c) 𝑄 = [HCl]2
𝑝H2(g)×
𝑝o
𝑐o2
(d) 𝑄 = [CuCl2]
[CuCl]2 × 𝑐o
5A.2 +12.3 kJ mol−1
5A.3 +6.8 kJ mol−1
5A.4 −25.1 kJ mol−1
5A.5 +26 kJ mol−1
5A.7 −14.4 kJ mol−1
formation of NH3
5A.8 2.31
5A.9 (a) 5.2 × 1011
(b) 850
5A.10 1
5A.11 −2.42 kJ mol−1
5A.12 3.01
5A.13 glucose-1-phosphate 3.4 × 103
glucose-6-phosphate 2.5 × 102
glucose-3-phosphate 36
Topic 5B The equilibrium constant
5B.1 𝑝CO2= 10.2 kPa
5B.2 3.3 × 106
5B.3 6.94
5B.4 3.1 × 10−3
5B.5 4.31 × 1043
Topic 5C Response to conditions
5C.1 (a) 52.9 kJ mol−1
(b) −52.9 kJ mol−1
5C.2 −92.2 kJ mol−1
5C.3 𝐾 = 7.23 × 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 dm−3
pH = 2.0
(b) 5.01 × 10−13mol dm−3
pH = 12.3
(c) 53 mmol dm−3
pH = 1.3
Topic 5E Polyprotic acids
5E.1 (a) 9.7 × 10−4
(b) 3.8 × 10−10
5E.2 (a) 𝑓(H2S) = 1.0
𝑓(HS−) = 1.3 × 10−3
𝑓(S2−) = 9.2 × 10−14
undissociated (H2S) form
(b) 𝑓(H2S) = 7.7 × 10−4
𝑓(HS−) = 1.0
𝑓(S2−) = 7.1 × 10−5
HS– ions
Topic 5F Acid–base equilibria of salts in water
5F.1 4.36
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
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5F.2 (a) acidic
NH4+(aq) + H2O(l) ⇌ H3O+(aq) + NH3(aq)
(b) basic
H2O(l) + CO32–(aq) ⇌ HCO3
(aq) + OH–(aq)
(c) basic
H2O(l) + F– (aq) ⇌ HF(aq) + OH–(aq)
(d) neutral
(e) acidic
[Al(H2O)6]3+(aq) + H2O(l) ⇌
[Al(H2O)5OH]2+(aq) + H3O+(aq)
(f) acidic
[Co(H2O)6]2+(aq) + H2O(l) ⇌
[Co(H2O)OH]+(aq) + H3O+(aq)
5F.3 (a) pH 2–4
(b) pH 3–5
(c) pH 11.5–13.5
(d) pH 6–8
(e) pH 5–7
5F.4 (a) H3PO4 and NaH2PO4
(b) NaH2PO4 and Na2HPO4, or
NaHSO3 and Na2SO3
Topic 5G Solubility equilibria
5G.2 (a) 1.0 × 10−5 mol dm−3
(b) 1.2 × 10−4 mol dm−3
(c) 9.3 × 10−11 mol dm−3
(d) 6.9 × 10−7 mol dm−3
5G.3 (a) 5.5 × 10−10mol dm−3
(b) 3.2 × 10−3 mol dm−3
(c) 1.6 × 10−7 mol dm−3
(d) 2.5 × 10−7 mol dm−3
Topic 5H Ions in solution
5H.1 1.35
5H.3 7.63 mS m2mol−1
5H.4 347 μm s−1
Topic 5I Electrochemical cells
5I.2 (a) 𝑣 = 2
(b) 𝑣 = 2
(c) 𝑣 = 4
(d) 𝑣 = 2
(e) 𝑣 = 2
(f) 𝑣 = 1
5I.3 −212 kJ mol−1
5I.4 +7.7 kJ mol−1
Topic 5J Standard potentials
5J.1 Exercise 5I.1
(a) 0
(b) 0
(c) +0.87 V
(d) −0.27 V
(e) −0.62 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 𝐸⊕ = +1.14 V
Δr𝐺⊕ = −440 kJ mol−1
5J.3 110
5J.4 0.320 V
Answers to problems
5.1 (a) −91.14 kJ mol−1
(b) +594.6 kJ mol−1
(c) −66.8 kJ mol−1
(d) +99.8 kJ mol−1
(e) −415.80 kJ mol−1
5.2 +279 kJ mol−1
5.3 (a) −32 kJ mol−1
(b) (i) −49 kJ mol−1
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
ANSWERS TO END OF CHAPTER EXERCISES
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(ii) −67 kJ mol−1
5.4 −0.7 kJ mol−1
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 𝐾r1/𝐾r2 = 1.4 × 1046
5.11 −245 kJ mol−1
5.12 0.0958, 0.9042
5.13 𝑝NH3(g) = 1.93 bar
𝑝H3(g) = 1.10 bar
𝑝N3(g) = 0.03 bar
5.14 2.7 × 10−4bar
5.15 (a) ⌈PCl5⌉ = 0.016 mol dm−3
[PCl3] = [Cl2] = 0.013 mol dm−3
(b) 45 per cent
5.16 𝑝H2(g) ≈ 0.20 bar
𝑝N2(g) ≈ 0.20 bar
𝑝NH3(g) = 7.6 × 10−5 bar
5.17 +41.1 kJ mol−1
5.19 (a) 9.24
(b) −12.9 kJ mol−1
(c) +161 kJ mol−1
(d) +248 J K−1mol−1
5.20 −187.78 kJ mol−1
5.21 (a) +12.50 kJ mol−1
(b) +9.05 kJ mol−1
(c) −8.6 J K−1mol−1
5.22 (a) [H3O+] = 1.6 × 10−7 mol dm−3
pH = 6.8
(b) [OH−] = 1.6 × 10−7 mol dm−3
pOH = 6.8
5.23 (a) 2 D2O(l) ⇌ D3O+(aq) + OD
–(aq)
(b) 14.9
(c) 3.67 × 10−8 mol dm−3
(d) 7.43
(e) pD + pOD = p𝐾w = 14.9
5.24 ideal: pH = 0.30
𝛾H3O+ = 0.769: pH = 0.42
5.26 +57.2 kJ mol−1
𝟓.28 p𝐾a = 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 dm−3
[HOOCCO2−] = 0.07 mol dm−3
[(CO2)22−] = 6.5 × 10−5 mol dm−3
[H3O+] = 0.07 mol dm−3
[OH−] = 1.4 × 10−13 mol dm−3
5.33 [H2S] = 0.065 mol dm−3
[HS−] = 9.2 × 10−5mol dm−3
[S2−] = 7.1 × 10−15mol dm−3
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
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[H3O+] = 9.2 × 10−5mol dm−3
[OH−] = 1.1 × 10−10 mol dm−3
𝟓.35 pH = 9.2
5.36 pH = 4.8
5.38 (a) [acid]
[base]= 1.6 × 10−5
(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 𝐾a = 6.92 × 10−6
pKa = 5.16
pH = 3.38
5.44 8.00
5.46 (a) pKa = 3.08
𝐾a = 8.32 × 10−4
(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 Δs𝐺o = +241 kJ mol−1
5.50 𝑠 = 1.25 × 10−5 mol dm−3
5.51 (b) increase
5.52 (a) 2.73 g
(b) 2.92 g
5.53 0.015 mol kg−1 MgF2
𝛾±,MgF2= 0.538
𝑎Mg2+ = 0.0081
𝑎F− = 0.016
0.025 mol kg−1 NaCl
𝛾±,NaCl = 0.733
𝑎Na+ = 0.018
𝑎Cl− = 0.018
5.54 𝐵 = 2.022
5.55 13.83 mS m2mol−1
5.56 (a) 12.6 mS m2 mol−1
(b) 210 S mol1/2m1/2
5.57 1.364 × 10−5 mol dm−3
5.58 3.70
5.59 4.85
5.60 +28 mV
5.61 −1.18 V
5.62 (a) +1.23 V
(b) +1.11 V
5.63 (a) right-hand
(b) +1.06 V
5.64 (a) −1.20 V
(b) − 1.19 V
5.65 (a) −394 kJ mol−1
(b) −787 kJ mol−1
(c) +75 kJ mol−1
(d) −284 kJ mol−1
(e) −291 kJ mol−1
(f) +498 kJ mol−1
5.66 (a) 𝐸cello = −0.46 V
Δr𝐺o = +88.8 kJ mol−1
Δr𝐻o = +146.39 kJ mol−1
(b) +86.9 kJ mol−1
5.67 (a) 𝐸cello = +1.57 V
Δr𝐺o = −606 kJ mol−1
(b) −604 kJ mol−1
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
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5.70 (a) −40 kJ mol−1
(b) +29.7 kJ mol−1
(c) −313 kJ mol−1
5.71 (a) +0.324 V
(b) +0.45 V
5.72 +0.56 V
5.73 (a) 6.4 × 109
(b) 1.3 × 107
(c) 9.4 × 1043
(d) 1.1 × 1025
(e) 8.2 × 10−7
(f) 3.4 × 1013
5.75 (a) +0.94 V
(b) {1.51 + 0.041 × ln(10−pH)} V
5.76 +0.22 V
5.77 (a) −0.6119 V
(b) −0.22 V
(d) +0.41 V
(e) p𝐾a = 10.28
5.79 Δr𝑆o = −324 J K−1mol−1
Δr𝐻o = −571 kJ mol−1
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 dm−3
6A.2 A: 1.6 mol dm−3s−1
B: 0.80 mol dm−3s−1
D: 2.4 mol dm−3s−1
6A.3 0.80 mol dm−3s−1
Topic 6B Rate laws
6B.1 mol−2dm6 s−1
6B.2 𝑘r1: mol−1dm3s−1
𝑘r2: mol−1dm3
6B.3 𝑘r1: kPa−1/2s−1
𝑘r2: dimensionless
6B.4 3.7 × 106 dm3mol–1s–1
Topic 6C Integrated rate laws
6C.1 1.58 × 10−3 s−1
6C.2 1.12 × 10−4s−1
6C.5 (a) 14 Pa s−1
(b) 1.5 × 103s
6C.7 1326 s
6C.8 3100 a
6C.9 (a) 0.63 μg
(b) 0.16 μg
6C.10 (a) 0.138 mol dm−3
(b) 0.095 mol dm−3
6C.11 13.6 s
6C.12 𝑡1/2 = 5.70 h
(a) 78.4 kPa
(b) 77.6 kPa
Topic 6D The temperature dependence of
reaction rates
6D.1 7.5 × 10−14mol−1dm3s−1
6D.2 (a) 1.86 × 1023a
(b) 75.8 s
6D.3 𝐴 = 1.37 × 1015dm3mol−1s−1
6D.4 298.86 K
6D.5 52 kJ mol1
6D.6 35.9 kJ mol−1
6D.7 121 kJ mol−1
6D.8 −21.6 kJ mol−1
6D.9 (a) 27.2 kJ mol−1
(b) 54.3 kJ mol−1
6D.10 𝐴 = 1.44 × 1012 mol−1 dm3 s−1
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
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6D.11 0.8 nm2
Topic 6E The approach to equilibrium
6E.1 7.5 × 105 s−1
6E.2 23.8 ms−1
6E.3 21 ms
Topic 6F Reaction mechanisms
6F.1 39.1 d
6F.2 increase
6F.3 1.89 × 10−6 Pa−1s−1
Topic 6G Reactions in solution
6G.1 (a) 6.61 × 106 m3mol−1s−1
(b) 3.0 × 107 m3mol−1s−1
6G.2 (a) −3.1 × 1016 mol m−2s−1
(b) 1.6 × 10−11mol
6G.3 (a) 27 h
(b) 2.7 × 103 h
(c) 3.0 × 103 a
6G.4 𝑁 = 1 × 106
6G.5 17 kJ mol−1
Topic 6H Homogeneous catalysis
6H.1 5.6 × 1022
6H.2 1.62 mmol dm−3
6H.3 𝑘cat = 1.18 × 105 s−1
𝜂 = 7.9 × 106 mol−1dm3s−1
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) 𝑣 = 𝑘𝑟[ICl][H2]
(b) kr = 0.162 mol1
dm3 s1
(c) 20.6 × 10−7mol dm−3s−1
6.4 0.248 s1
6.5
(a) second order
(b) 7.80 × 10−3
dm3 mol
−1 s
−1
6.6 (a) second order
(b) 1.32 dm3 mol
–1 s
–1
6.9 second order
0.287 mol−1dm3min−1
6.10 𝐸a = 272 kJ mol−1
6.11 𝐸a = 180 kJ mol−1
A = 2.11 mol–1
dm3 s
–1
6.12
(a) 𝑓(20 ℃) = 1.7 × 10−20
(b) 𝑓(200 ℃) = 5.6 × 10−13
𝐴 = 3 × 1011 mol−1dm3s−1
6.13 (a) 126 kJ mol−1
(b) Δ𝑆‡ = 0
6.15 𝑘r,eff = 7.12 × 105 s−1
𝑘r′ = 4.00 × 1010 mol−1 dm3s−1
6.16 {𝑘b(𝑘a/𝑘a′ )1/2}[A2]1/2[B]
6.19 (a) 3 ClO(aq) ClO3(aq) + 2 Cl(aq)
(b) first step
6.26 𝐾M = 1.11 μmol dm−3
𝑣max = 2.31 μmol dm–3 s−1
𝑘cat = 1.2 × 102 s−1
6.27 𝐾M = 87 mmol dm−3
𝑣max = 16 μmol dm–3 s−1
6.28 𝛼 = 2.809 Pa−1
𝑉∞ = 0.5659 cm3
6.29 gold: zeroth order
Platinum: first order
6.33 𝑐 = 165
𝑉mon = 13.1 cm3
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
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Answers to projects
6.1 (a) 1
[A]0−[B]0ln (
[B]/[B]0
[A]/[A]0) = 𝑘r𝑡
(b) 1
[A]−
1
[A]0= 𝑘r𝑡
6.2 (b) 𝐸a = 105.1 kJ mol−1
Δr𝐺o = −26.6 kJ mol−1
Δr𝐻o = −34.3 kJ mol−1
6.6 (a) 𝐾M = 24.9 mmol dm−3
𝑣max = 4.80 mol dm−3s−1
(b) 𝐾M = 25.0 mmol dm−3
𝑣max = 4.81 mol dm−3s−1
(c) 𝐾M = 25.0 mmol dm−3
𝑣max = 4.80 mol−1 dm3s−1
Focus 7
Quantum theory
Answers to exercises
Topic 7A The emergence of quantum theory
7A.1 3.05 × 10−19 J
7A.2 8.226 × 104 cm−1
7A.3 (a) 6.6 × 10−19 J
4.0 × 102 kJ mol−1
(b) 3.3 × 10−20 J
20 kJ mol−1
(c) 1.3 × 10−33 J
7.8 × 10−13 kJ mol−1
7A.4 (a) 𝐸(750 nm) = 2.65 × 10−19 J
(b) 𝜈(250 nm) = 9.96 × 105 m s−1
7A.5 (a) 6.6 × 10−31m
(b) 6.6 × 10−39 m
(c) 99.7 pm
7A.6 1.3 × 106 m s−1
7A.7 4 × 10−36m
7A.8 (a) 1.10 × 10−27 kg m s−1
(b) 9.5 × 10−24 kg m s−1
(c) 3.31 × 10−36 kg m s−1
7A.9 2.2 × 10−24 m s−1
Topic 7B The dynamics of microscopic systems
7B.1 Δ𝑥 ≥ 0.900 nm
7B.2 Δ𝑣 ≥ 2.1 × 10−29 m s−1
7B.3 Δ𝑥 ≥ 1.1 × 10−26 m
7B.4 Δ𝑥 = 100 × 10−12 m
Δ𝑣 ≥ 5.8 × 105 m s−1
Topic 7C Translation
7C.1 (a) 𝑥 = 𝐿/2
(b) 𝑥 = 3𝐿/4
(c) 𝑥 = 5𝐿/6
7C.2 9.84 × 10−23 J
7C.3 𝐿 = 1.00 × 10−9 m
Topic 7D Rotation
7D.1 𝑛 = 0: ∞
𝑛 = 1: 628 pm
𝑛 = 2: 314 pm
7D.2 (a) 4.34 × 10−47 kg m2
(b) 1.55 mm
7D.3 6
7D.4 ml = –4, –3, –2, –1, 0, +1, +2, +3
7D.5 6.65 × 10−22 J
Topic 7E Vibration
7E.1 0.04 N m−1
7E.2 6.90 × 1013 s−1
7E.3 7.94 × 10−6 N m−1
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 × 10−4 N
(b) 6.1 × 10−10 Pa
(c) 1600 s
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
ANSWERS TO END OF CHAPTER EXERCISES
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7.5 𝑥 = ±0.5887/𝑎1/2
7.7 (a) 1.8 × 10−4
(b) 5.9 × 10−5
7.8 5h2 / 8mL
2: (1,4) (2,2)
5h2 / 4mL
2: (1,6) (3,2)
7.9 𝐿/4 , 3𝐿/4
7.10 (a) 2.2 × 10−20 J
(b) 9.2 μm
7.12 (a) 0.22
(b) 9.5 × 10−3
7.13 8.79 × 1011s−1
7.14 2.10 × 10−22 J
7.15 0.707
Answers to projects
7.1 (a) 𝑥 = 0.1 to 𝑥 = 0.2 nm:
𝑃(𝑥) = 1.84 × 10−4, 3.8 per cent
x = 4.9 to x = 5.2 nm:
𝑃(𝑥) = 2.36 × 10−4, 74.9 per cent
(b) 0.196
(c) 0.609
(d) 0.196
7.2 (a) (i) 𝜓(𝑥) = (𝑎/π)1/4e−𝑎𝑥2/2
(ii) x = 0
(b) (i) 𝜓(𝑥) = (4𝑎3/π)1/4𝑥e−𝑎𝑥2/2
(ii) x = ±1/a1/2
7.3 (a) 6.432 × 1013 s−1
(b) 2146 cm−1
(c) 𝜈 C13 O16 2098 cm−1
𝜈 C12 O18 2094 cm−1
𝜈 C13 O18 2045 cm−1
Focus 8
Atomic structure
Answers to exercises
Topic 8A Hydrogenic atoms
8A.1 4.10296 × 10−5cm = 410.296 nm
8A.2 𝑛2 = 5
8A.3 𝑛2 = 6
8A.4 1.00047
8A.5 27 cm−1
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) 61/2ℏ, 2 angular nodes,
0 radial nodes
(d) 21/2ℏ, 1 angular node, 0 radial nodes
(e) 21/2ℏ, 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) (𝑛 𝑙 1)
(b) l
(c) (𝑛 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 mol−1
Topic 8D Atomic spectroscopy
8D.1 (b), (c), (e)
8D.3 nd, ng
8D.4 (a) 𝐿 = 2, 1, 0
(b) 𝐿 = 4,3, 2, 1, 0
8D.5 S = 2, 1, 0
8D.6 (a) 1S0
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
ANSWERS TO END OF CHAPTER EXERCISES
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(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
𝐽 = 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 cm−1
He4 + 15239.3 cm−1
n = 2 1: He3 + 82288.5 cm−1
He4 + 82292.3 cm−1
8.2 122.31 eV
8.3 (a) n = 7 6 12368 nm
n = ∞ 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 cm−1
(b) n = 3 2 137170 cm−1
n = 4 2 185180 cm−1
(c) 122.5 eV
8.6 14.0 eV
8.7 0.602 𝑎0
8.8 (a) 0.262 a0, 2.530 a0
(b) 0.090 a0, 3.845 a0
8.9 (a) 1.4 × 10−5
(b) 1.1 × 10−4
8.10 (a) 1.9 𝑎0 , 7.10 𝑎0
(b) 1.87 𝑎0, 6.61 𝑎0, 15.5 𝑎0
8.11 Fe2+
8.12 2.142 meV
Answers to projects
8.1 (a) 𝑟 = 𝑎0
(b) (i) 2.69 × 10−7
(ii) 2.47 × 10−8
(iii) 0
(c) 5.24 a0
(d) 5.236 𝑎0
8.3 (a) receding, 338 km s−1
Focus 9
The chemical bond
Answers to exercises
Topic 9A Valence bond theory
9A.1 1870 kJ mol−1
9A.2 𝜓C−H = 𝜓C(1)𝜓H(2) + 𝜓C(2)𝜓H(1)
9A.3 𝜓1(σ-bond) =
𝜓2p𝑧A(1)𝜓2p𝑧B(2) + 𝜓2p𝑧A(2)𝜓2p𝑧B(1)
𝜓2(π-bond) =
𝜓2p𝑥A(1)𝜓2p𝑥B(2) + 𝜓2p𝑥A(2)𝜓2p𝑥B(1)
𝜓3(π-bond) =
𝜓2p𝑦A(1)𝜓2p𝑦B(2) + 𝜓2pyA(2)𝜓2p𝑦B(1)
9A.5 210 times
9B.2 F2−: ½
F2: 1
F2+: 1½
9B.3 O2+: 2½
O2: 2
O2−: 1½
O22−: 1
O2+ < O2 < O2
– < O2
2–
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
ANSWERS TO END OF CHAPTER EXERCISES
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9B.4
(a) H2−: 1σg
21σu1
(b) Li2: 1σg2
(c) Be2: 1σg2 1σu
2
(d) C2: 1σg2 1σu
2 1πu4
(e) N2: 1σg2 1σu
2 2σg2 1πu
4
(f) O2: 1σg2 1σu
2 2σg2 1πu
4 1πg 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 −6.26 eV
604 kJ mol−1
𝟗𝐃.2 6𝛼 + 8𝛽
9D.3 0
9D.4 (a) −2𝛽
(b) −1.24𝛽
(c) −2𝛽
Answers to problems
9.2 bond angle for SO2 is 120
9.8 CO: 1σ2 2σ2 3σ2 1π4
NO: 1σ2 2σ2 3σ2 1π4 2π1
CN−: 1σ2 2σ2 3σ2 1π4
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 −30750 cm−1
butadiene −37280 cm−1
hexatriene −44660 cm−1
octatetraene −47370 cm−1
(b) −71910 cm−1
9.14 (a) benzene: 𝛼 + 2𝛽, 𝛼 + 𝛽,
𝛼 + 𝛽, 𝛼 − 𝛽, 𝛼 − 𝛽, 𝛼 − 2𝛽
Cyclooctatetraene:
𝛼 + 2𝛽, 𝛼 + √2𝛽, 𝛼 + √2𝛽,
𝛼, 𝛼, 𝛼 − √2𝛽, 𝛼 − √2𝛽, 𝛼 − 2𝛽
(b) benzene: 2𝛽
hexatriene: 0.988𝛽
(c) cyclooctatetraene: 1.657𝛽
octatetraene: 1.516𝛽
9.15 𝛼 + √2𝛽: bonding
𝛼: non − bonding
𝛼 − √2𝛽: antibonding
9.16 (a) C6H6−: 1πu
2 2πg4 1πu
1
7𝛼 + 7𝛽
(b) C6H6+: 1πu
2 2πg3
5𝛼 + 7𝛽
Answers to projects
9.2 (c) π/4, −π/4
9.3 (b) (𝑅/𝑎0) = 2.11
(c) 𝜓1 = ±(0.356𝐴 + 0.934𝐵)
𝜓2 = ±(0.934𝐴 − 0.356𝐵)
Focus 10
Molecular interactions
Answers to exercises
Topic 10A Electric properties of molecules
10A.1 −36 J mol−1
Atkins & de Paula: Elements of Physical Chemistry, Seventh Edition
ANSWERS TO END OF CHAPTER EXERCISES
17
10A.2 (a) 1.78 D, 5.9 × 10−30C m
(b) 0.94 D, 3.1 × 10−30C m
(c) 0.76 D, 2.5 × 10−30C m
10A.3 𝜇/D = −0.89
10A.4 1.17 D
10A.5 (a) C2 m
2 J
−1
(b) (C2 m
2 J
−1) / (C
2 J
−1 m
−1) = m
3
Topic 10B Interactions between molecules
10B.1 −5.22 × 10−24 J
10B.2 𝑉(𝑟) = −1.9 × 10−27 J
𝑉m(𝑟) = −1.19 × 10−3 J mol−1
10B.3 479 pm
10B.4 𝑟 = 700 pm
𝑁A𝜖 = 12.6 kJ mol−1
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 𝜇 = 37 D
𝜃 = 11.8°
10.5 1.17 × 10−29 C m = 3.50 D
10.7 (a) 476 kJ mol−1
(b) 87.4 kJ mol−1
10.9 (a) 3.72 kJ mol−1
(b) −0.365 J mol−1
10.10 196 pm
10.11 𝑉(𝑟) = −1.6 × 10−26 J
𝑉m(𝑟) = −9.6 × 10−3J mol−1
𝟏𝟎.12 𝑉(𝑟) = −7.0 × 10−20 J,
𝑉m(𝑟) = −42 kJ mol−1
10.14 250 to 410 pm
10.16 (a) 11.6 kJ mol−1
(c) 2.12 × 1012 s−1
Focus 11
Molecular spectroscopy
Answers to exercises
11A.1 (a) 6.78 × 1014 Hz
(b) 22600 cm−1
11A.2 (a) 2.94 × 10−3 cm−1
(b) 3.41 m
11A.3 (a) 1.48 × 104 dm3 mol−1 cm−1
(b) 0.9506%
11A.4 (a) 55 dm3 mol−1 cm−1
(b) 0.048
11A.5 659.999936 nm
7.02 × 107 m s−1
11A.6 8.3 × 105 K
11A.7 (a) 53 ps
(b) 5.3 ps
(c) 160 ps
11A.8 (a) 53 cm−1
(b) 0.27 cm−1
Topic 11B Rotational spectroscopy
11B.1 3.6 × 1033
11B.2 (a) (i) 4.601 × 10−48 kg m2
(ii) 9.194 × 10−48 kg m2
(iii), (iv) 7.150 × 10−46 kg m2
(b) (i) 1.824 × 1012 Hz
60.84 cm−1
(ii) 9.126 × 1011 Hz
30.44 cm−1
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(iii), (iv) 1.174 × 1010 Hz
0.3915 cm−1
11B.3 (b) 2.66 × 109 s−1
0.0888 cm−1
11B.4 𝐼⊥ = 4𝑚B𝑟B2
𝐼∥ = 2𝑚B𝑟B2
11B.5 𝐴 = 5.149 GHz
𝐵 = 10.30 GHz
11B.6 (a) 289
(b) 17
11B.7 232.1 pm
11B.8 ½
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 cm−1
11B.14 5990749.416 MHz
11B.15 116.2 pm
11B.16 20643 cm−1
Topic 11C Vibrational spectroscopy
11C.1 (a) 4.49 × 1013 Hz
(b) 4.39 × 1013 Hz
11C.2 (a) 3
(b) 4
(c) 48
(d) 54
11C.3 329 N m−1
11C.4 (a) (i) HF: 967.4 N m−1
(ii) HCl: 515.8 N m−1
(iii) HBr: 411.8 N m−1
(iv) HI: 314.3 N m−1
(b) DF: 2930 cm−1
DCl: 2114 cm−1
DBr: 1874 cm−1
DI: 1634 cm−1
11C.6 3724.66 cm−1
11C.7 𝑥e = 0.0062
11C.8 2699.9 cm−1
Topic 11D Electronic spectroscopy
11D.1 [A] = 0.56 mol dm–3
[B] = 0.16 mol dm
–3
11D.2 1.737 × 10−15 J
11D.3 50.8 nm
11D.4 1.602 × 10−15 J
11D.5 (a) 2.04 × 10−19 J
(b) 669 km s−1
Topic 11E The decay of excited states
11E.2 0.57
11E.3 4.7 nm
Answers to problems
11.1 33 μg dm−3
11.2 (a) 162 pm
(b) 179 GHz
11.3 (b) 3.2645 GHz
(c) 237.6 pm
11.4 �̃� = 0.2029 cm−1
�̃� = 6.233 × 10−8 cm−1
11.5 ROC = 116.28 pm
RCS = 155.97 pm
11.9 (b) 126.5 pm
11.11 𝑘Q = 5.16 × 106 mol−1 dm3 s−1
11.12 kF = 1.276 1010
mol–1
dm3 s
–1
11.13 kQ =9.146 109 mol
–1 dm
3 s
–1
𝑡1/2 = 0.172 μs
11.14 407 ps
11.15 3.49 nm
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Answers to projects
11.1 (a) 4200
(b) 588 nm
11.2 𝐽max = (𝑘𝑇/ℎ𝐵)1/2 − ½
11.5 2.6 nm
Focus 12
Statistical thermodynamics
Answers to exercises
Topic 12A The Boltzmann distribution
12A.1 𝑁2
𝑁1= 0.37
12A.2 524 K
12A.3 𝑁5
𝑁0= 7.4
Topic 12B The partition function
12B.1 (a) 𝓆 = 1 + 6e−2𝜀/𝑘𝑇 + 3e−5𝜀/𝑘𝑇
(b) 𝓆 = 1
(c) 𝓆 = 10
12B.2 (a) 𝓆T = 1.45 × 1027
(b) 𝓆T = 6.49 × 1027
12B.3 (a) 𝓆T = 3.2 × 104
(b) 𝓆T = 6.2 × 1027
12B.4 (a) 𝓆R = 19.5
(b) 𝓆R = 265
12B.5 eqn 12B.6: 𝓆V = 1.39
eqn 12B.7: 𝓆V = 0.789
12B.6 𝓆E = 4.23
Topic 12C The origin of thermodynamic
properties
12C.1 �̅� = (5e−𝜀/𝑘𝑇+9e−3𝜀/𝑘𝑇
1+5e−𝜀/𝑘𝑇+9e−3𝜀/𝑘𝑇) 𝜀
12C.2 (a) 1.25 kJ mol−1
(b) 2.08 kJ mol−1
12C.3 −37.4 kJ mol−1
Answers to problems
12.1 (a) 𝑁4
𝑁2= 1.753
(b) 𝑁4
𝑁2= 2.27
12.2 (a) 𝓆𝑅 = ∑ 𝑔𝐽𝐽=0 e−𝜀𝐽/𝑘𝑇: 𝓆𝑅 = 24.816,
Using eqn 12B.5: 𝓆R = 24.474
12.4 11350 K
12.5 (a) 1.401 (at 500 K)
(b) 3.147 (at 1000 K )
12.6 1.28 × 1034
12.7 (a) qE = 5
(c) 6.730
12.8 (a) 𝓆E = 1.293 (at 10 K )
𝓆E = 7.825 (at 298 K )
12.9 𝓆V = 2.14
𝑆m = 14.6 J K−1mol−1
𝟏𝟐.10 183.1 J K−1mol−1
12.11 (a) Sꝋ(Xe) > S
ꝋ(Ne)
(b) Sꝋ(D2O) > S
ꝋ(H2O)
(c) Sꝋ(graphite) > S
ꝋ(diamond)
12.12 −54.3 kJ mol−1
12.13 𝐾 = 1.336 × 10−25
12.14 𝐾 = 1.951 × 10−11
Focus 13
Magnetic Resonance
Answers to exercises
Topic 13A Nuclear magnetic resonance
13A.1 (a) T−1 Hz
(c) A s kg−1
13A.2 𝐸3/2 = −1.949 × 10−26 J
𝐸1/2 = −6.498 × 10−27 J
𝐸−1/2 = 6.498 × 10−27 J
𝐸−3/2 = 1.949 × 10−26 J
13A.3 2.263
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13A.4 (a) 2.9 × 10−5
(c) 7.3 × 10−6
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 μT
(b) 38 μT
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 × 10−24 J
13C.2 (a) 9.02 × 10−4
(b) 2.7 × 10−3
13C.3 9.25 GHz, 32.4 mm
13C.4 2.0022
13C.5 𝑎 = 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) 𝐴′ = 1.9 Hz
𝐵′ = −1.4 Hz
𝐶′ = 6.4 Hz
(b) 109 °
13.9 2600 s−1
13.10 64 s−1
13.12 1
13.13 𝟏 0.011 mT: 0.0049
𝟏 0.172 mT: 0.0764
𝟐 0.272 mT: 0.1209
𝟐 0.450 mT: 0.2000
𝟐 0.108 mT: 0.0480
𝟑 0.112 mT: 0.0498
Focus 14
Macromolecules and aggregates
Answers to exercises
Topic 14A Biological and synthetic
macromolecules
14A.1 �̅�n = 95 kg mol−1
�̅�w = 93 kg mol−1
14A.2 3.4
14A.3 (a) 0.880 μm
(b) 31.1 nm
(c) 12.7 nm
14A.4 𝑅c = 2.74 μm
𝑅rms = 29.1 nm
14A.5 13000
14A.6 −0.042 J K−1mol−1
14A.7 8 aJ
Topic 14B Mesophases and disperse systems
14B.1 5.8 cm
14B.2 23 mN m−1
14B.3 (a) 1.4 kPa
(b) 0.14 kPa
14B.4 97 mmol m−2
Answers to problems
14.1 �̅�n = 20 kg mol−1
�̅�w = 22 kg mol−1
14.2 �̅�w/�̅�n = 1.27
14.4 ℱ = 1.37 pN
14.6 pH = 6.9
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14.7 68 μJ
Answers to projects
14.1 (a) ⟨𝑅2⟩1/2 = 10.9 nm
(b) ⟨𝑅⟩ = 10.0 nm
(c) 𝑅∗ = 8.89 nm
14.3 (a) 2.70 pN
Focus 15
Solids
Answers to exercises
Topic 15A Crystal structure
15A.1 𝑉 = 0.396 nm3
𝜌 = 2.41 × 103kg m−3
15A.2 𝑁 = 3.9
𝜌 = 4.01 × 103 kg m−3
𝟏𝟓𝐀.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 𝑎 = 363 pm
𝑐 = 564 pm
15A.8 112 pm
15A.9 1.28 mV
15A.10 66.1 pm
15A.11 𝑎 = 798 pm
Topic 15B Bonding in solids
15B.1 (a) zinc-blende
(b) zinc blende
(c) rock-salt
15B.2 ΔL𝐻ꝋ(SrO)
ΔL𝐻ꝋ(CaO)= 0.947
15B.3 3000 kJ mol−1
Topic 15C The properties of solids
15C.3 549 nm
Answers to problems
15.2 (321). (111). (122). (32̅2̅).
15.6 bcc
15.7 (b) 8.97 × 103 kg m−3
15.8 0.740
15.9 0.740 g cm−3
15.10 520 nm
15.11 (a) 424 nm
(b) 600 nm
15.12 (a) less dense
(b) 92 per cent
15.15 𝑉 = −𝑁𝑧2𝑒2π
48𝜀0𝑑
15.16 −8.16 × 10−18 J
15.18 +3500 kJ mol−1
15.19 +2421 kJ mol−1