Concise Physical Chemistry

c08 JWBS043-Rogers September 13, 2010 11:25 Printer Name: Yet to Come

120 A STATISTICAL APPROACH TO THERMODYNAMICS

TABLE 8.2 Some Computed Partition Functions

for Molecular and Atomic Sodium.a

Na 2 Molecules T =1300 K

Q

Total Bot 0.873633D+ 13

TotalV = 0 0.953147D+ 13 ←

Vib (Bot) 0.573265D+ 01

Vib (Bot) 1 0.573265D+ 01

Vib (V =0) 0.625441D+ 01

Vib (V =0) 1 0.625441D+ 01

Electronic 0.100000D+ 01

Translational 0.486489D+ 09

Rotational 0.313256D+ 04

Na atoms T = 1300

Q

Total Bot 0.344000D+ 09

TotalV = 0 0.344000D+ 09 ←

Vib (Bot) 0.100000D+ 01

Vib (V =0) 0.100000D+ 01

Electronic 0.200000D+ 01

Translational 0.172000D+ 09

Rotational 0.100000D+ 01

aNote thatQis unitless.

PROBLEMS AND EXAMPLES

Example 8.1 The Thermal Wavelength

Calculate the thermal wavelength of sodium atoms at 1300 K.

Solution 8.1 The calculation for Na(g) is as follows:

=

(

h^2 β

2 πm

) 1 / 2

Evaluation of theβconstant,

β= 1 /kBT= 1 / 1. 38 × 10 −^23 ·( 1300 )= 5. 570 × 1019

leads to the thermal wavelength for Na(g) atoms at 1300 K.

=

(

5. 570 × 1019 h^2

2 πm

) 1 / 2

=

(

2. 44 × 10 −^47

2 πm

) 1 / 2

=

(

2. 4 × 10 −^47

2 π· 23. 0 · 1. 66 × 10 −^27

) 1 / 2

=

(

1. 02 × 10 −^22

) 1 / 2

= 1. 01 × 10 −^11 = 10. 1 × 10 −^12 = 10 .1pm