16.30.Boron NMR are more complex for two reasons: (a)
There are two common isotopes of B,^10 B (~20%) and^11 B
(~80%); and (b)they have different nuclear spins (3 and ^32 , re-
spectively) and different magnetogyric ratios.
16.31.154 T
Chapter 17
17.1.One per box: 4 ways. Any number per box: 24 ways.
17.2.24 ways
17.3.ln (1,000,000!) 1.281 107. Therefore, 1,000,000!
e1,281 ^10
717.5.ln (5000!) 37,591, which is the same value as given
in the text (notfrom Stirling’s approximation)
17.7.On average, there are 25 insects per month over the
course of a year.
17.8. (a)113,400 (b) 6 (c) 20
17.11.Most probable distribution: 1 ball in each of three
boxes (P0.50)
17.15.N 1 /N 0 0.38
17.17.13.2 K for 1 2 E 1 E 0 , 38.9 K for 1 1 E 2 E 0 , 122.5 K for
1 1 E 3 E 2
17.19.Gis always higher than A.
17.28.The development of statistical thermodynamic equa-
tions is based on the statistical behavior of individual particles.
Thus, the masses of those individual particles (i.e., atoms or
molecules) must be used, not the molar mass.
17.31.!(25 K) 1.745 10 ^10 m, !(500 K) 3.903
10 ^11 m
17.32.At 120 K, krypton is very close to its liquefaction tem-
perature and is not acting like a real gas.
17.33. (a)164.9 J/(molK) (b)210.2 J/(molK)
(c)174.9 J/(molK)
17.34.620 J
17.36.94,100 K
Chapter 18
18.1. (a) 1 (b) 1 (c) 2
18.4.qelect8.96 (not much change from 7.82 at 298 K)
18.5.Minimum qelect 1
18.6.qelect(Ni, 298 K) 5.971 vs. qelect(Ni, 1000 K)
5.991; qelect(Ni, 5.0 K) 4.688 vs. qelect(Ni, 298 K) 5.971
18.7.qelect5.89 1075
18.8.qelect 10128
18.9. (a)qelect13.1 (b)Room temperature has enough
thermal energy (RT) to break the He 2 “bond,” so it proba-
bly won’t exist at 300 K.
18.11.qH 2 /qD 2 1/ 2
18.12.qvib(250 K) 1.3 10 ^18 ; qvib(500 K) 1.3 10 ^9
18.13.qvib1.8 10 ^20
18.14.216 (2), 313 (3), 459, and 779 (3) cm^1 (degenera-
cies in parentheses)
18.15.Minimum qnuc1, minimum qrot1 (from equation
18.26)
18.16.T374 K
18.17.qH 2 /qD 2 1/2
18.18.Even-numbered Jstates are associated with antisym-
metric nuclear wavefunctions; odd-numbered Jstates are as-
sociated with symmetric nuclear wavefunctions.
18.20.rshould increase because centrifugal distortions will
increase the moment of inertia Iof the molecule.
18.21.qrot(NH 3 ) 74.8
18.25.For HCl, 298 K: E407.8 kJ/mol, H397.9 kJ/mol,
G456.0 kJ/mol, S186.5 J/molK
18.34. (a)35.8 N/m or 3.58 mdyn/Å (b)150 cm^1Chapter 19
19.2.6.66 10 ^21 J; 4.01 kJ/mol
19.4. (a)1305 m/s (b)285 m/s
19.6.p3.68 10 ^21 atm vavg184 m/s
19.7.213 K, 853 K, 1920 K, 3410 K, 5330 K
19.8. 3 1012 K
19.13.ratio ^32
19.14. (a)Using v15 m/s and dv10 m/s, G(v)
8.24 10 ^5. (b)Using v1005 m/s and dv10 m/s,
G(v) 5.69 10 ^4. (c)Using v10005 m/s and dv
10 m/s, G(v) 0.
19.15.T 5 10 ^7 K
19.20.2.6 1012 m
19.22.7.65 10 ^10 m
19.23.For a given gas, density and temperature are the only
variables needed to determine an average collision frequency.
19.24.z2110 s^1
19.31.2.02 1014 per second
19.32.p664 bar or 4.98 torr
19.33.2.85 10 ^6 g of Ar per second
19.36. (a)0.844 cm^2 /s814 ANSWERS TO SELECTED EXERCISES