The properties of gases

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



2

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


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



3

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



4

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


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



5

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


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



6

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


Topic 5A The thermodynamics of reaction

5A.1 (a) 𝑄 = 𝑝CO2(g)

6

[CH3COCOOH]2𝑝O2(g)5 × (𝑐o2/𝑝o)



7

(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



8

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



9

(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



10

[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



11

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


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



12

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



13

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


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



14

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


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



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

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


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–



16

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


Topic 10A Electric properties of molecules

10A.1 −36 J mol−1



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


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



18

(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



19

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


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


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



20

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


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



21

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


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

The properties of gases

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