Physical Chemistry Third Edition

1100 26 Equilibrium Statistical Mechanics. II. Statistical Thermodynamics

EXAMPLE26.10

Calculate the chemical potential and the Gibbs energy of 1.000 mol of^35 Cl 2 at 298.15 K and

1.000 atm.

Solution

We take the energy of the ground electronic state as zero. From Example 25.7,zrot 424 .7,

and from Example 25.8,zvib 1 .0720. Since the ground electronic state is nondegenerate

and since all excited states must lie high in energy,zel≈1, and the electronic contributions

toμandGare approximately equal to zero.

ztr

N



(

2 πmkBT

h^2

) 3 / 2

V

N



(

2 πmkBT

h^2

) 3 / 2

kBT

P



(

2 πM

NAvh^2

) 3 / 2

(kBT)^5 /^2

P



(

2 π(0.0699377 kg mol−^1 )

(6. 02214 × 1023 mol−^1 )(6. 6261 × 10 −^34 Js)^2

) 3 / 2

[(1. 3807 × 10 −^23 JK−^1 )(298.15 K)]5/2

101325 Pa

 2. 299 × 107

μtr−kBTln(2. 299 × 107 )− 6. 978 × 10 −^20 J

μrot−kBTln(424.7)− 2. 491 × 10 −^20 J

μvib−kBTln(1.072)− 2. 86 × 10 −^22 J

μel≈ 0

μ− 5. 35 × 10 −^20 J

GNμ(1.000 mol)(6. 02214 × 10 −^23 mol−^1 )(− 5. 35 × 10 −^20 J)

− 3. 22 × 104 J

PROBLEMS

Section 26.2: Working Equations for the Thermodynamic
Functions of a Dilute Gas

26.8Assuming the harmonic oscillator–rigid rotor
approximation, and taking the energy of the electronic
ground state to be zero:
a. Find the translational contribution to the energy of
1.000 mol of F 2 at 1.000 bar and 298.15 K.

b. Find the rotational contribution to the energy of

1.000 mol of F 2 at 1.000 bar and 298.15 K.

c.Find the electronic contribution to the entropy of 1.000

mol of F 2 at 1.000 bar and 298.15 K.

d.Find the vibrational factor in the partition function of

F 2 gas at 1.000 bar and 298.15 K.

26.9 Calculate the standard-state molar entropy of argon at
298.15 K. Compare your result with the experimental
value, 154.845 J K−^1 mol−^1. Compare your result with the

value for helium at the same temperature and comment on

the difference.

26.10 a.Calculate the value of each factor in the molecular

partition function of^16 O 2 gas at 500.0 K and a pressure

ofP◦ 1 .000 bar.

b. Calculate the standard-state molar thermodynamic

energy,Um◦, for O 2 at 500.0 K. Give the values of the

translational, rotational, vibrational, and electronic

contributions.

c.Calculate the standard-state molar thermodynamic

entropy,S◦m,ofO 2 at 500.0 K. Give the values of the

translational, rotational, vibrational, and electronic

contributions.

26.11Calculate the values ofHm◦,U◦m,A◦m,G◦m,Sm◦, andC◦V,m

for krypton gas at 298.15 K.

26.12Calculate the standard-state molar entropy of CO at

298.15 K.