answers atkins 4e

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Atkins & De Paula: Elements of Physical Chemistry: 4eNUMERICAL ANSWERS TO END OF CHAPTER EXERCISES

Question Numerical answer

Introduction

0.5 2.6 kJ

0.10 59 J

0.14

(a) 825 Torr;

(b) 0.984 atm;

(c) 0.212 atm;

(d) 9.64 × 104 Pa

0.15 1.24 × 108 Pa ( = 1.22 × 103 atm)

0.16 1.6 × 10 −2

0.17 1.5 × 103 Pa ( = 1.5 × 10 −2 atm)

0.19 −459.67 °F

0.21 671.67 °R

0.22 3.74 × 1019 molecules

0.23 0.97 or 97%

Chapter 1

1.5 89.2 kPa

1.6 4.22 × 10 −2 atm

1.7 2.52 × 10 −3 mol

1.8 6.64 × 103 kPa

1.9 10.0 atm

1.10 418 kPa

1.11 173 kPa

1.12 29.5 K

1.13 388 K

1.14 (a) 3.6 m3; (b) 178 m3

1.15 0.50 m3

1.16 3.2 × 10 −2 atm

1.17 (a) 1.32 L; (b) 61.2 kPa

1.18 713 Torr

OXFORD H i g h e r E d u c a t i o n

© Oxford University Press, 2006. All rights reserved.




1.19 132 g mol −1

1.20 16.4 g mol −1

1.21

(a) p(H2) = 2.0 atm, p(N2) = 1.0 atm;

(b) 3.0 atm

1.22(a) (i) 693 m s −1, (ii) 1363 m s −1, (iii) 2497 m s −1;

(b) (i) 346 m s −1, (ii) 681 m s −1, (iii) 1247 m s −1

1.26 0.91%

1.27 0.065 Pa

1.28 2.4 × 106 Pa

1.29 0.97 µm

1.30

(a) 5.3 × 1010;

(b) 5.3 × 109 collisions;

(c) 5.3 × 104

1.31

(a) 6.4 × 1033 collisions;

(b) 6.4 × 1031 collisions;

(c) 6.4 × 1021 collisions

1.32 4.5 × 10

8

collisions/s1.33 (a) 6.8 nm; (b) 68 nm; (c) 7 mm

1.34 independent of temperature

1.35(a) 8.3 × 102 atm;

(b) (i) 0.99 atm, (ii) 1.7 × 103atm

1.36 4.37 MPa

1.37 ⎥⎦

⎤⎢⎣

⎡+++= ...11

2

mmm V

C

V

B

V

RT p

1.38 1.26 L2 atm mol −2

1.39 1.02 × 103 K

Chapter 2

2.5 (a) 98 J; (b) 16 J

2.6 39 J

2.7 2.6 kJ

2.8 3.03 J






2.12 −14 J

2.13 −1.0 × 102 J

2.14 (a) 895 J; (b) 899 J

2.15 (a) −88 J; (b) −167 J

2.16 +123 J

2.17 +2.99 kJ

2.18 −1.25 kJ

2.21 23.7 J K −1

2.22 42 kJ

2.23 4.4 × 104 J

2.24 38 J K −1 mol −1

2.25 6.1 × 102 s

2.26 1.86 × 103 J

2.27 773 J

2.28 −8.0 J

2.29 29.3 J

2.31 (a) 2.479 kJ mol

−1

;(b) decreased

2.32 80 J K −1

2.33 q = +2.2 kJ; ∆ H = +2.2 kJ; ∆U = +1.6 kJ

2.34 20.83 J K −1 mol −1

2.35 458 J mol −1

2.36 818 J mol −1

Chapter 3

3.6 2.53 × 104 kJ

3.8 39.8 kJ mol −1

3.9q = +39.0 kJ; w = −3.12 kJ; ∆ H = +39.0 kJ (constant pressure);

∆U = 35.9 kJ

3.10 301 kJ

3.11 478 kJ






3.16 (a) 388 kJ mol −1; (b) smaller

3.17 (a) 16 kJ mol −1; (b) −3028 kJ mol −1

3.18 −46.11 kJ

3.19 (a) −1560 kJ mol −1; (b) −2340 kJ

3.20 −4564.7 kJ mol −1

3.21 −85 kJ mol −1

3.22 −432 kJ mol −1

3.23 +79 kJ mol −1

3.24 0.769 K

3.25

(a) −2.80 MJ mol −1 ;

(b) −2.80 MJ mol −1;

(c) −1.28 MJ mol −1

3.26

(a) −1333 kJ mol −1 ;

(b) −1331 kJ mol −1;

(c) −815 kJ mol −1

3.27 +84.40 kJ mol −1

3.28 −383 kJ mol −1

3.29 +1.9 kJ mol −1

3.30 +30.6 kJ mol −1

3.31 7.5 m

3.32(a) −2205 kJ mol −1;

(b) −2200 kJ mol −1

3.33

(a) exothermic, ∆r H o = negative;

(b) endothermic, ∆ H o = positive;

(c) endothermic, ∆vap H o = positive;

(d) endothermic, ∆fus H o = positive;

(e) endothermic, ∆sub H o = positive

3.34

(a) −57.20 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






3.35 +11.3 kJ mol −1

3.36 −56.98 kJ mol −1

3.38 (a) decrease; (b) decrease; (c) increase

3.39 (a) increase; (c) increase

3.40 Higher

Chapter 4

4.4 (a) positive; (b) negative; (c) positive

4.5 0.410 J K −1

4.6 −0.12 kJ K −1

4.7 −161 J K −1

4.8 q = −45.1 kJ; ∆S = −161 J K −1

4.9 +9.1 J K −1 mol −1

4.10 2.91 L

4.11 56 J K −1

4.12 23.6 J K −1

4.13 −7.9 J K −1

4.14 0.630 T i

4.16 4.0 × 10 −4 J K −1 mol −1

4.18 5.11 J K −1

4.19 0.95 J K −1 mol −1

4.20 (a) +87.8 J K −1 mol −1; (b) −87.8 J K −1 mol −1

4.22 (a) +85 J K −1 mol −1; (b) +34 kJ K −1 mol −1

4.23

(a) −386.1 J K −1 mol −1; (b) +92.6 J K −1 mol −1;

(c) −153.1 J K −1 mol −1; (d) −21.0 J K −1 mol −1;

(e) +512.0 J K −1 mol −1

4.24 (a) −0.75 J K −1; (b) +0.15 J K −1

4.25 −5.03 kJ K −1

4.26(a) −86 kJ mol −1; (b) Yes, ∆G is negative; (c) +0.28 kJ K −1

mol −1

4.27 0.41 g






4.28 (a) Yes; (b) 0.46 mol ATP

4.29 8.1 × 1023 molecules of ATP

Chapter 5

5.2 (a) lowered; (b) raise

5.5 rhombic sulfur

5.6 No

5.7 (a) +2.03 kJ mol −1; (b) +1.50 J mol −1

5.8 +19 kJ mol −1

5.9 (a) +1.7 kJ mol −1; (b) −20 kJ mol −1

5.10 +4.3 kJ mol −1

5.11(a) )(ln f

i f

i

m p pb p

p RT G −+=∆ ;

(b) greater; (c) 0.68%

5.12 (a) yes; (b) 7 × 102 K

5.13 −5.2 kJ mol −1

5.15 (a) 2.37 kg; (b) 41.9 kg; (c) 1.87 kg

5.16 (a) −134.6 bar K −1; (b) 134.6 bar

5.18 28.85 kJ mol −1

5.20 1.53 Pa

5.21 36.7 kJ mol −1

5.22 356 K

5.23 Yes; 3 Torr or more

Chapter 6

6.55.04 g

6.6 5.04 g

6.7 0.460 g

6.8 2.41 × 10 −3

6.9 269 g sucrose

6.10 x1 = x2 = 0.500

6.11 0.451; 0.549

6.12 886.8 cm3






6.13 96 cm3

6.14 V ethanol = 53.1 mL mol −1; xethanol = 0.072

6.16

V W/(mL mol −1) = 18.067 + 6.556 × 10 −3 b2 − 1.018 × 10 −3 b3

6.18(a) ∆Gm = −1.31 kJ mol −1; spontaneous;

(b) ∆S m = +4.38 J K −1 mol −1

6.19∆Gm = −1.40 kJ mol −1; spontaneous;

∆S m = +4.71 J K −1 mol −1

6.20 4.99 kPa

6.21 2.49 kPa

6.22 6.4 × 103 kPa

6.23 4.8 × 10 −3

6.25 (a) 1.3 mmol kg −1; (b) 33 mmol kg −1

6.26 5.1 × 10 −4 mol kg −1 in N2, 27 mmol kg −1 in O2

6.27 0.101 mol L −1

6.28

p = xA p•A+ (1 − xA) p

•B

If A = toluene and B = o−xylene

xA = 0.920, xB = 0.080

The composition of the vapor is given by

yA = 0.968, yB 0.032

6.29 53.8 g mol −1

6.30 −0.27 °C

6.31 207 g mol −1

6.32 2)*(2

1

)*(1

⎟ ⎠ ⎞

⎜⎝ ⎛ −

−

−−

=

cP

PPr c

cP

PPr

K

6.33 −0.09 °C

6.34 88.3 kg mol −1

6.35 13.94 kg mol −1

6.36 (a) 0.36; (b) 0.81






6.43 (a) no

Chapter 7

7.5

(a) [G6P]

][G][Pi=Q

(b) [Gly][Ala]

Ala]-[Gly=Q

(c) ]][ATP[Mg

][MgATP-42

-2

+=Q

(d) 2

35

2

62

COCOOH]][CHCO[

]CO[

p

pQ =

7.6 −14.38 kJ mol −1

7.7

(a) 2ClCO

CCOCl

p p

p p l

(b) 32

3

SO2

O

SO2

p p

p

(c) 22 Br H

HBr 2

p p

p

(d) 2

3

O3

O2

p

p

7.8 4.46

7.9 (a) 1.2 × 109; (b) 1.8 × 102

7.10 2.42 kJ mol −1

7.11 3.01

7.13 −294 kJ mol −1

7.14 K = 1

7.15 K (G1P) = 3.5 × 103, K (G6P) = 2.3 × 102, K (G3P) = 36

7.16 (a) −48.3 kJ mol −1; (b) 66.1 kJ mol −1

7.17 6.8 kJ mol −1

7.18 397 K (124 °C)

7.19 1.5 × 103 K

7.22 (a) exergonic; (b) endergonic; (c) endergonic; (d) exergonic






7.23

(a) −91.14 kJ mol −1; (b) +594.6 kJ mol −1;

(c) −66.82 kJ mol −1; (d) +99.82 kJ mol −1;

(e) −415.80 kJ mol −1

7.24

(a) −522.1 kJ mol −1, K > 1;

(b) +25.78 kJ mol −1, K < 1;

(c) −178.6 kJ mol −1, K > 1;

(d) −212.55 kJ mol −1 , K > 1;

(e) −5798 kJ mol −1, K > 1

7.25 (a) 5.5 × 104 kJ; (b) −5.1 × 104 kJ

7.26(a) −1.4 × 104

kJ; (b) −1.57 × 104 kJ or 1.57 × 104 kJ of non

−expansion work

7.27(a) total work done = 1.68 × 104 kJ;

(b) total work done = 1.67 × 104 kJ

7.28 −49.8 kJ mol −1

7.29 817.90

kJ mol −1

7.30 −25.0 kJ mol −1

7.31 +26 kJ mol −1

7.34 −16.9 J K −1 mol −1

7.37 +12.3 kJ mol −1

7.38 xI = 0.096, xB = 0.904

7.39 x NH3 = 0.632, x N2 = 0.010, xH2 = 0.358

7.40 5.4 × 10 −4

7.41 2.6 × 10 −4 bar

7.42[PCl3] = [Cl2] = 1.58 × 10 −2 mol L −1 , [PCl5] = 2.3 × 10 −2 m

ol L −1; (b) 42%

7.43 p N2 = 0.020 bar, pH2 = 0.020 bar

7.45 −41.0 kJ mol −1

7.46 (b) and (d)

7.47 (a) +53 kJ mol −1; (b) −53 kJ mol −1

7.48 (a) 9.24, 31.08; (b) −12.9 kJ mol

−1

;






(c) +161 kJ mol −1; (d) + 248 J K −1 mol −1

Chapter 8

8.6

(a) CH3CH(OH)COOH + H2O =

CH3CH(OH)COO − + H3O+

(b) HOOCH2C(NH2)COOH + H2O =

HOOCH2C(NH2)COO − + H3O+

HOOCH2C(NH2)COO − + H20 =−OOCH2C(NH2)COO − + H3O

+

(c) NH2CH2COOH + H2O = + NH3CH2COO − +H2O

(d) −HOOCCOOH + H2O = HOOCCOO − + H3O+

HOOCCOO − + H20 = −OOCCOO − + H3O+

8.7 (a) 6.8; (b) 6.8

8.8

(a) D2O + D2O D3O + OD− ;

(b) 14.87;

(c) 3.67 × 10−8 mol L −1

(d) pD = 7.43 = pOD;

(e) pD + pOD = pK w(D2O) = 14.87

8.11

(a) 9.50 × 10 −3 mol L −1, pH = 2.02;

(b) 0.025 mol L −1, 12.40

(c) 5.35 × 10 −2 M, pH = 1.27

8.12 (a) acidic; (b) basic; (c) basic; (d) neutral; (e) acidic; (f) acidic

8.13 (a) 9.14; (b) 4.83; (c) none

8.14 (a) pK a = 3.08, K a = 8.3 × 10 −4; (b) 2.8

8.15 (a) 13.48 (b) 34 mL

8.16 (a) 1.6%; (b) 0.33%; (c) 2.4%

8.17

(a) pH = 2.00, pOH = 12.00, fraction = 0.083;

(b) pH = 4.85, pOH = 9.15, fraction = 0.10;

(c) pH = 1.1, pOH = 12.9, fraction = 0.73

8.22 2.71

8.23 (a) 6.54, (b) 2.12 (c) 1.49






8.24 pH = pK a

8.25 (a) 1.58 × 10 −5; (b) 1; (c) 5.0

8.26

(a) 0.060 mol L −1;

(b) H2S = 0.065 mol L −1,

HS − = 9.2 × 10 −5 mol L −1 = H3O+,

S2 − = 7.1 × 10 −15 mol L −1,

OH − = 1.1 × 10 −10 mol L −1

8.27 (a) 2.87; (b) 4.56; (c) 12.5 mL; (d) 4.75; (e) 25.0 mL; (f) 8.72

8.28 (a) 4.75 (b) 5.05 (c) 4.14

8.29 (a) 2 −4; (b) 3 −5; (c) 11.5 −13.5; (d) 6 −8; (e) 5 −7

8.30 pK a = 4.66, K a = 19 × 10 −5 , pH = 3.24

8.31 (a) 5.04; (b) 8.96; (c) 2.78

8.32 7.94

8.34(a) H3PO4 and NaH2PO4;

(b) NaH2PO4 and Na2HPO4

8.35

(a) K s = [Ag+] [1 −];

(b) K s = [Hg2+2] [S2 −]; (c) K s = [Fe3+] [OH −]3;

(d) K s = [Ag+]2 [CrO42 −]

8.36(a) 1.1 × 10 −10 ; (b) 6.2 × 10 −12; (c) 2.0 × 10 −39;

(d) 1.3 × 10 −18

8.37(a) 5.5 × 10 −10 mol L −1; (b) 3.2 × 10 −3 mol L −1;

(c) 1.6 × 10 −7 mol L −1; (d) 2.45 × 10 −7 mol L −1

8.38 1.25 × 10 −5 mol L −1

Chapter 9

9.5

(a) I (KCl) = b/bo

(b) I (FeCl3) = 6b/bo

(c) I (CuSO4) = 4b/bo

9.6 0.90

9.7 (a) 2.73 g; (b) 2.92 g






9.8 γ± = (γ+γ−2)1/3

9.9 0.12

9.10 2.01

9.11 13.83 mS m2 mol−1

9.12 7.63 × 10−3 S m2 mol−1

9.13 347 µm s−1

9.14

Κ m°= 12.6 mS m2 mol−1; κ = 7.30 mS m2 mol−1 M1/2

(a) 11.96 mS m2 mol−1

(b) 119.6 mS m−1

(c) 172.5 Ω

9.15 1.36 × 10−5 mol L−1

9.17 Yes

9.18 CH3COCO2 − + NADH + H+ → CH3CH(OH)CO2

− + NAD+

9.22 +1.14V, −44.0 kJ mol −1

9.23 41 mV

9.24 21 mV

9.25 Standard potential = −1.18V

9.26

(a)

R: Ag+(aq, bR ) + e − → Ag(s)

L: Ag+(aq, bL) + e − → g(s)

R −L: Ag+(aq, bR ) → Ag+ (aq, bL)

(b)

R: 2H+(aq) + 2e − → H2(g, PR )

L: 2H+(aq) + 2e − → H2(g, PL)

R −L: H2(G, PL) → H2(g, PR )

(c)

R: MnO2(s) + 4H+(aq) + 2e − → Mn2+(aq) + 2H2O

L: [Fe(CN)6]3 − = e − → Fe(CN)6]

4 −

R −L: MnO2(s) + 4H+(aq) + 2[Fe(CN6)4− (aq) →

Mn2+(aq) + 2[Fe(CN6)3− (aq)






(d)

R: Βr 2(g) +2e − → 2Br −(aq)

L: Cl2(g) +2e − → 2Cl −(aq)

R −L: Br 2(l) +2Cl − (aq) → Cl2(g) + 2Br −(aq)

(e)

R: Sn 4+ (aq) + 2e − → Sn2+(aq)

L: 2Fe3+(aq) + 2e − → 2Fe2+(aq)

R −L: Sn 4+ (aq) + 2Fe2+(aq) → Sn2+(aq) + 2Fe3+(aq)

(f)

R: −L: MnO2(s) + 4H+(aq) → Mn2+ (aq) + 2H2O(l)

L: Fe2+ (aq) + 2e − → Fe(s)

R −L: Fe(s) + MnO2(s) + 4H+(aq) → Fe2+ (aq) + Mn2+ (aq) + 2H2O(l)

9.27(a) E = E

2 − RT /F ln bL/bR

(b) E = E 2 − RT /2F ln pR / pL

9.28

(a) Fe(s)|FeSO4(aq)|PbSO4(s)|Pb(s) v=2

(b) Pt|H2(g)|H+(aq)|Hg2Cl2(s)|Hg(|) v=2

(c) Pt|H2(g)|H+(aq), H2O|O2(g)|Pt v=4

(d) Pt|H2(g)|H+(aq), H2O|O2(aq)|O2(g)|Pt v=2

(e) Pt|H2(g)|H+(aq), | −(aq)||2(s)|Pt v=2

(f) CuCl2(aq) | CuCl(aq)|Cu(s) v=2

9.29

(a) Pt|CH3CH2OH(aq), CH3CHO(aq), H+(aq)||NAD+(aq),

NADH(aq)|Pt v=2

(b) Mg(s)|ATP4 −(aq), MgATP2 −||MG2+(aq)|Mg(s) v=2

(c) Pt|Cy −c (red, aq), Cyt −c(ox,aq)||CH3CH(OH)CO2 −(aq),

CH3COCO2 −(aq)|Pt

9.30(a) 0; (b) 0; (c) + 0.87 V; (d) − 0.27 V; (e) −0.62 V;

(f) +1.67 V

9.31(a) +0.08 V; (b) +0.27 V; (c) +1,23 V; (d) +0.695 V;

(e) +0.54 V; (f) +0.366 V






9.32

(a) E o (NAD+, NADH) − E

o (CH3,CH3CH2OH);

(b) E o (Mg2+, Mg) − E

o (Mg, MgATP4−);

(c) E oCH3COCO2

−, CH3CH(OH)CO2− − E

o (Cyt−c(ox),

Cyt−c(red))

9.34 + 0.94 V

9.36

(a) E decreases, |E| increases; (b) E increases, |E| increases;

(c) E increases, |E| increases; (d) E increases, |E| decreases;

(e) E increases, |E| decreases; (f) E decreases, |E| decreases

9.37(a) decreases E; (b) decreases E; (c) increases E;

(d) decreases E; (e) decreases E; (f) has no effect on E

9.38(a) cell potential decreases; (b) cell potential increases;

(c) cell potential decreases

9.39 (a) −1.20 V (b) −1.18 V

9.40

(a) −394 kJ mol −1; (b) same as (a);

(c) +75 kJ mol −1; (d) −291 kJ mol −1;

(e) as (d); (f) −498 kJ mol −1

9.41 (a) − 44.0 kJ mol −1

; (b) 29.7 kJ mol −1

; (c) − 316 kJ mol −1

9.42 (a) + 0.324 V; (b) + 0.45 V

9.43 0.72 V

9.44 0.46 V, + 89.7 kJ mol −1146 kJ mol −1, + 87.9 kJ mol −1

9.45 −606 kJ mol −1

9.46 +0.24 V

9.47

(a) + 0.3108 V; (b) +1.14 V;

(c) E = E o − ln; (d) 207 m V; (e) 10.3

9.48 (a) 1.6 × 1 −8 [mol kg −1]; (b) + 0.12 V

9.49(a) 6.5 × 109; (b) 1.2 × 107; (c) 4 × 1069; (d) 1.0 × 1025;

(e) 8.2 × 10 −7

9.50

1.80 × 10−10 → 1.78 × 10−10,

9.04 × 10−7→ 5.1 × 10−7,






9.51 E = E o −

ln

9.52 0.78

9.53 E = 0

9.54 8.5 × 10 −17 , 9.19 × 10 −9 mol L −1

9.55 0.95 V

Chapter 10

10.9

A= 1.5 mol L −1 s −1

B = 0.73 mol L −1 s −1

D = 0.73 mol L −1 s −1

10.11

(a) (i) second-order, m3s −1

(ii) third-order, m6s −1

(b) (i) second-order, Қ Pa −1 s −1

(ii) third-order, Қ Pa −2 s −1

10.12 (a) 1; (b) 4.89 × 103 s −1

10.13 (a) 1; (b) 2.33 × 109 L2 mol −2 s −1

10.14 2.05 × 104 s; (a) 500 Torr; (b) 515 Torr

10.15 1.12 × 10 −4

s −1

10.16 4.2 × 10 −5 s −1

10.17 1.09 × 10 −3 L mol −1 s −1

10.18 1.12 × 10 −4 s −1

10.19 3.19 × 10 −6 Pa −1 s −1 (for pseudosecond-order process)

10.20 (a) 0.014 kPa s −1; (b) 1.5 × 103s

10.24 First-order, 5.6 × 10 −4 s −1

10.27 1330 s

10.28 3.1 × 103 y

10.29 (a) 0.63µg; (b) 0.16µg

10.30 (a) 0.138 mol L −1; (b) 0.095 mol L −1

10.31 2.79 × 104s

10.32 E a = 85.6 kJ mol −1;

A =

3.66 × 10

11

mol L −1

s −1






10.33 299 K

10.35 21.6 kJ mol −1

10.37 120 kJ mol −1

10.38 −21.6 kJ mol −1

10.39 48 kJ mol −1

10.40 5.4 × 104 s

10.41 1.08 × 106 L mol −1 s −1

10.42 2.1 mm2

10.43 126 kJ mol −1

10.44 4.4 J K

−1

mol

−1

Chapter 11

11.5 3.1 × 105 L mol −1 s −1

11.10 41.6d

11.12(a) 6.61 × 106 m3 mol s−1

(b) 3.0 × 107 m3 mol s−1

11.20 1.5 × 1015

11.21 First-order in H202 and in Br −, and second-order overall

11.22 rate = k eff [A2]1/2[B]

11.23

rate equation = k [A] [B]

1

21,constantratek

k k k

′=

11.24]O[]O[

]O[ rate

3221

2321

k k

k k

+′=

11.26]AH[]BH[

AH][B][ ][A32

1-

k k

k

+= +

Rate of formation of products =]AH[]BH[

[B]AH][

32

231

k k

k k

++

11.28 1.62 × 10 −3 mol L −1 s −1

11.29 [S] = K M

11.31 0.38 s −1






11.32 1.1 × 102 s −1

11.34 2/32

2/1

4

1221 ]R []R [ ⎟⎟

⎠

⎞⎜⎜⎝

⎛ −−

k

k k k

Chapter 12

12.5 1.0 × 10 −6 m

12.6 8.4 × 1011

12.7 4.5 × 103 K, this radiation is not thermal radiation

12.8 4.6 × 103 W

12.9 6.29 × 10 −34 Js

12.10 (a) 4.0 × 10

2

kJ mol

−1

; (b) 20 kJ mol

−1

; (c) 7.9 × 10

13

kJmol −1

12.11 (a) 1.7 × 1018 s −1; (b) 1.7 × 1020 s −1

12.12 6.90 × 1029 s −1

12.13 (a) no ejection occurs; (b) 4.52 × 10 −19 J, 996 km s −1

12.14 1.32 × 106 m s −1

12.15(a) 6.6 × 10 −31 m; (b) 6.6 × 10 −39 m;

(c) 99.7 pm

12.16 (a) 1.23 nm; (b) 39 pm; (c) 3.88pm

12.18(a) 9.14 × 10 −28 kg m s −1; (b) 8.8 × 10 −24 kg m s −1; (c) 3.3 ×

10 −35 kg m s −1

12.20 2.2 × 10 −24 m s −1

12.21 (a) 3.34 × 10 −6 N; (b) 3.34 × 10 −12 Pa; (c) 83 h

12.22 50.6 nm

12.23 1.11 × 10 −15 J

12.24 (a) 4.6 × 10 −5; (b) 6.0 × 10 −2

12.27 90 nm

12.28 2.1 × 10 −29 m s −1

12.29 1 × 10 −26 m

12.30 5.8 × 10 −5 m s −1

12.31 9.85 × 10 −23

J






12.32 L/4 or 3 L/4

12.33 (a) 2.17 × 10 −20 J; (b) 9.16 × 10 −6 m

12.34 4 = (1 / L)1/2

12.35 1.24 × 10 −6 m

12.36 (a) 4.34 × 10 −4T kg m2; (b) 1.55 mm

12.37 0.04 N m −1

12.38 (a) 6.89 × 1013 s −1; (b) 4.35 mm

Chapter 13

13.5 434 nm

13.6 n = 613.7 (a) 6842 cm −1; (b) 1.36 × 10 −19 J

13.8 2.24 × 103 cm −1

13.9 4 p → 2s

13.10 122.31 e V

13.11 16

13.12 n2 → 6

13.13 3092 nm

13.14 (a) 397.13nm; (b) 3.40 eV

13.15

R Li2+ = 987663 cm −1

137175 cm −1 185187 cm −1

122.5eV

13.16 r = 0.693 Å (36.7 pm)

13.17 (a) 40 pm or 13 pm; (b) 29 or 24 pm

13.18 1/6

13.19 1.1 × 10 −5

13.21(a) 2.7 × 10 −8 pm −3;

(b) 9.9 × 10 −8 pm3; (c) 0

13.22 5.2a0

13.24 (a) 101 pm and 376; (b) 99 pm, 349 ppm, and 821 pm

13.250°, 180°; 90° 270°






13.27 (a) g = 1; (b) g = 9; (c) g = 49

13.28 (a) 2; (b) 14; (c) 22

13.30 14.0 eV

13.33 Fe 2+

13.34 1F3; 3F4,

3F3, 3F2;

1D2; 3D3,

3D2, 3D1;

1P1, 3P1,

3P0

13.35 2,1 and 0

13.36 (a) 1; (b) 3; (c) 1; (d) 3

13.37(a) forbidden; (b) allowed; (c) allowed;

(d) forbidden; (e) allowed

13.38 all d and g orbitalsChapter 14

14.7 3.11 × 10 −18 J

14.12 1 − 1 = 0 [orthogonality]

14.132/1

221

1⎟

⎠ ⎞

⎜⎝ ⎛

=+=

λ λ S N

14.15 N (0.844A − 0.145Β )

14.16 978 and 22 respectively

14.17 −µ e4/12π 3ε 20ħ2

14.20 (c) 45°

14.22 (a) b = 1; (b) b = 0; (c) b = 2

14.23 (a) b = 1/2; (b) b = 3; (c) b = 2

14.24 (a) b = 3; (b) b = 5/2; (c) b = 3

14.25 C2

14.26C2 and CN stabilized by anion formation; NO, O2 and F2 stabili

zed by cation formation

14.28 no

14.29 (a) g; (b) inapplicable; (c) g; (d) u

14.30 g, u, g, u

14.31 g, u, g, u; (b) for v even, g; for v odd, u

14.33 N2






14.34 F2+ < F2 < F2

−

14.35 O2+, O, O2

−, Ο22−

14.36 (a) 7a + 7b; (b) 5a = 7b

14.37(a) C6H6

−: a22u e4

1g e12u ; E = 7α + 7 β

(b) C6H6+: a2

2u e31g ; E = 5α + 5 β

14.38 2.7 eV

Chapter 15

15.5 (a) n-type; (b) p-type

15.6 metallic conductor

15.10 3888 kJ mol −1

15.11 2258 kJ mol −1

15.12d

qNzeV

048ε

π =

15.13 1.06

15.17 (326), (11), (122), (322)

15.20 (111) = 307 pm, (211) = 217 pm, (100) = 532 pm

15.21 (123) = 0.129 nm, (236) = 0.0671 nm

15.22 66.1 pm

15.23 0.215 cm

15.24 bcc

15.25 8.97 g cm −3

15.26 (a) 0.9069; (b) 0.5236

15.28 0.740 g cm −3

15.29(a) eight nearest neighbours, 433 nm;

(b) six next-nearest neighbours, 500 nm

15.30(a) 12 nearest neighbours, 354 nm;

(b) six next-nearest neighbours, 500 nm

15.31 (a) less dense; (b) 92%

15.32V = 3.96 × 10 −28 m3;

D = 2.40 × 106 g m−3






15.33 N = 4, 4.01 g cm−3

15.34 (a) (321) = 220 pm; (b) (642) = 110 pm

15.35 rock salt structure

Chapter 16

16.5(a) 2.88 × 10−23 m−2 s−1; 5.75 × 1017 m−2 s−1

( b) 3.81 × 10−24 m−2 s−1; 7.60 × 1017 m−2 s−1

16.6 1.3 × 104 Pa

16.7 3.4 × 105 s−1

16.10 18.8 m2

16.11 (a) 0.21 kPa; (b) 22 kPa

16.13 0.37 Torr s−1

16.15 ∆ad H o = −(0.904 × 103 K) × R = −7.52kJ mol−1

16.19(a) 164, 13.1 cm3

(b) 264, 12.5 cm3

16.20 200 s

16.21 E d = 610 kJ mol−1, τ 0 = 1.13 × 10−13 s,

A = 6.15 × 1012

s−1

16.22650 kJ mol−1, (a) 1.1 × 1097 min;

(b) 2.6 × 10−6 min;

16.23 0 on gold, 1 on platinum

16.27

(a) 0.31 mA cm−2

(b) 5.41 mA cm−2

(c) −2.19 mA cm−2

16.28

(a) 4.9 × 1015 cm−2 s−1, 3.8 s−1

(b) 1.6 × 1016 cm−2 s−1, 12 s−1

(c) 3.1 × 107 cm−2 s−1, 2.4 × 108 s−1

16.29 0.38, 0.78 mA cm−2

16.30 0.50, 0.150 A m−2, 0.038 A m

16.31 j0 = 2.00 × 10−5 mA m−2, α = 0.498; R = 0.9990. There are no

significant deviations.






Chapter 17

17.5 dipole moment = 0.9D, 3.0 × 10 −30 C m

17.6 SF4 is polar

17.7(a) ortho-xylene = 0.7D; (b) meta-xylene = 0.4D;

(c) para-xylene = 0; the para-xylene value is exact by symmetry

17.8

(a) 1,2,3-trimethylbenzene = 0.8D;

(b) 1,2,4-trimethylbenzene = 0.2D;

(C) 1,3,5-

trimethylbenzene = 0; (c) should cancel exactly by symmetry

17.9 1.4D

17.10 (a) 1.50 D; (b) 2.6 D; (c) 1.13 D; (d) 1.80 D

17.11 3.10 D

17.13 (a) 100 pm = 1070 kJ mol −1; (b) 300 pm = 119 kJ mol −1

17.15(a) E = 3/2 RT = 3.7 kJ mol −1 at 298K;

(b) 0.14 J; the kinetic theory of gases is justifiable

17.17 196 pm

17.18 7.7 × 10 −5

J mol −1

17.19 4.2 × 10 −3 J mol −1

17.20 8.2 kJ mol −1

17.21 r = 21/6v

17.25 (a) V O = 11.6 kJ mol −1; (c) 4 × 1012 s −1

Chapter 18

18.10 70 kg mol−1, 71 kg mol−1,

18.11(a) 18 kg mol−1,

(b) 20 kg mol−1,

18.13 n = 244

18.14 3.4 Mg mol−1,

18.15 3500 r.p.m.

18.17 24 nm

18.18 3.08µm, 3.08 nm






18.19 1.4 × 104

18.20

(a) lN 1/2, 9.74 nm;

(b) (8 N /3π )1/2l, 8.97 nm;

(c) (2 N /3)1/2l, 7.95 nm;

18.22Serum albumin and bushy stunt virus resemble spheres; DNA

does not.

Chapter 19

19.5 (a) 4.47 × 1014 s −1; (b) 1.49 × 104 cm −1

19.6 (a) 3.07 × 10 −3 cm −1; (b) 3.26 m

19.7 75.1%

19.8 1.35 × 103 L mol −1 cm −1

19.9 log = − E m [J]0

19.10 450 L mol −1 cm −1

19.11 159 L mol −1 cm −1, 23%

19.12 (a) 0.9 m; (b) 3 m

19.130.999 999 918 × 660 mm,

green at 6.36 × 107m s −1

19.14 8.4 × 105 K

19.15 (a) 0.1 cm −1 = 53ps; (b) 5 ps; (c) 0.18ps

19.16 0.27cm −1

19.17 4 × 1033

19.18

(a) 1

H2

= 4.601 × 10 −48

kg m2

; (b) 2H2 = 9.196 × 10 −48 kg m2;

(c) 12C16O2 = 6.67 × 10 −46 kg m2;

(d) 13C16O2 = 6.67 × 10 −46 kg m2

19.19

(a) 1.825 × 1012 Hz;

(b) 9.128 × 1011 Hz;

(c) 1.26 × 1010 Hz;






(d) 1.26 × 1010 Hz

19.20 (a) I = 4mB R2; (b) 1.583 × 109 Hz

19.21 (a) I || = 4mR2, I ⊥2mR

2

19.22(a) 5.152 × 109 Hz;

(b) microwave spectroscopy could not be used

19.23 (a), (b), (c) and (d)

19.24 all

19.25 one state with J = 10

19.26 20 states and 10 energy levels

19.28(a) 636 GHz, 1272 GHz, 1908 GHz …

(b) 21.21 cm −1, 42.42 cm −1, 63.63 cm −1 . . .

19.30 lower

19.31 1.162 × 10 −10m = 116.2 pm

19.32 separation of lines = 194 GHz

19.34 R(CO) = 116.28 pm, R(CS) = 155.97 pm

19.35 (a) 12C = 16O = 4.49 × 1013Hz; (b) 13C16O = 4.39 × 1013 Hz

19.36 329 Nm −1

19.37 HF = 967.1, HCl = 515.6, HBr = 411.8. HI = 314.2

19.38 2HF = 3002, 2HCl = 2144, 2HBr = 1886, 2HI = 1640

19.39 2699.77 cm −1

19.40 (b) HCl, (c) CO2, (d) H2O, (e) CH3CH3, (f) CH4 and (g) CH3Cl

19.41 (a) 3; (b) 4; (c) 48; (d) 54

19.42 Raman active

19.43 (a) Raman active

Chapter 20

20.3 Lengthen; to blue

20.11 (a) 1.01 × 104 L mol −1 cm −1; (b) 0.965%

20.12 33 mg L −1

20.13 8.0 × 10 −19 J

20.14 2.3 × 10 −19 J






20.17 ][d

d[A]2/1

32 A

k

I k I

t ⎟⎟ ⎠

⎞⎜⎜⎝

⎛ −−=

20.18 3.3 × 1018

20.19 0.518

20.20 5.1 × 106 L mol −1 s −1,

20.22quencing rate constant = 9.2 × 109 L mol −1 s −1, half −life

1.9 × 10 −7 s

20.23 3.52 nm

20.24 (a) I abs = I 0(1–10 – ε[J]l)

Chapter 21

21.8 −1.625 × 10 −26 J × mr

21.9 (a) T −1 Hz; (b) A s kg −1

21.10 2.263

21.12 9.248 GHz

21.14 328.6 MHz

21.15 46.15 MHz

21.16 12.92 T21.17 2.66 kHz

21.18 46 mT

21.19 (a) 300 MHz = 2.4 KHz; (b) 550 MHz = 4.4 KHz

21.20 1: 7: 21: 35: 35: 21: 7: 1

21.21 (a) quintet 1: 2: 3: 2: 1; (b) septet 1: 3: 6: 7: 6: 3: 1

21.28 2.0022

21.29 2.3 mT, 2.003

21.30 (a) 1:3:3:1; (b) 1:3:6:7:6:3:1

21.31 (a) 331.9 mT; (b) 1.201 T

21.32 1

21.33

(7) ρ (3) = ρ (6) = 0.005, ρ (4) = ρ (5) = 0.076;

(8) ρ (2) = ρ (4) = 0.200, ρ (3) = 0.048. ρ (6) = 0.121;

(9) all ρ = 0.050






Chapter 22

22.7 0.37

22.8 (a) 0.9999895; (b) 0.9998955

22.9 0.99849

22.10 3.475

22.11 0.487

22.12 (a) 1 + 5e −e /kT + 3e

−3e /KT ; (b) T = 0, q = 1; (c) T = `, q= 9

22.13 (a) 1.29; (b) 7.82

22.14 (a) 9; (b) 6.731

22.15 1.072

22.16 (a) 3.2 × 104; (b) 6.2 × 1027

22.17 (a) 19.5; (b) 265

22.191/ −kT hve

Nhv

22.21(a)

T K T K

T k T K

ee

eK ReK R E

/6258/2359

/6258/2359

531

)3129()77.70(−−

−−

+++

=

(b) 339 J mol −1

22.22(a)

T K T K

T k T K

ee

eK eK R E

/3259/2280

/3259/2280

35

)3259)6840(−−

−−

+++

=

(b) 0.993 kJ mol −1

22.25 11.5 J K −1 mol −1

22.27 191.4 J K −1 mol −1

22.28 40 kJ K −1 mol −1

22.29 1.37 × 10 −25

22.30 1.97 × 10 −11

answers atkins 4e

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