Bundle: Physical Chemistry, 2nd + Student Solutions Manual
Bundle: Physical Chemistry, 2nd + Student Solutions Manual
2nd Edition
ISBN: 9781285257594
Author: David W. Ball
Publisher: Cengage Learning
Question
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Chapter 18, Problem 18.4E
Interpretation Introduction

(a)

Interpretation:

The numbers of terms for the summation of the electronic partition function for N2 gas at standard temperature is to be stated.

Concept introduction:

Different linearly independent wavefunctions that have same energy are called degenerate. This is expressed in terms of degeneracy. If two functions are having same energy then they are called doubly degenerate and so on. The electronic partition function is represented as,

qelect=igiei/kT

Expert Solution
Check Mark

Answer to Problem 18.4E

The numbers of terms for the summation of the electronic partition function for N2 gas at standard temperature are 46.

Explanation of Solution

The term symbol of a diatomic compound is represented as,

2S+1ΛΩ

Where,

S represents the total spin of the molecule.

Λ represents the axial component of L.

Ω represents the axial component of total angular quantum number J.

The term (Λ) of diatomic molecule is represented by Greek symbols such as Σ, Π, Δ and Φ. The term Ω is represented by either alphabet u or g.

From the referred Table, the state of 14N2 are represented as,

[ x" (1Σu+),x' (1Πu),1Πg,u5,u4,s,r,q,p,o5 1Πu,O5 (3Πu),c'n 1Σu+,cn 1Πu,cn 1Πu,o4 1Πu,O4 (3Πu),c'5 1Σu+,c4 1Πu,c4 1Πu,1Δg,1Πg,k 1Πg,1Σg-,d' 1Σu- or 1Δu,o3 1Πu,3Φu,c'4 1Σu+,c3 1Πu,b' 1Σu+,3Σu+,b 1Πu,a" 1Σg+,C' 3Πu,3Σg+,C" 5Πu,3Πu,3Δg,A' 5Σg+,1Δu,1Πg,a' 1Σu-,B' 3Σu-,3Δu,3Πg,3Σu+,1Σg+]

The total number of states of 14N2 is 46.

The electronic partition function is represented as,

qelect=igiei/kT

Where,

gi represents the degeneracy.

i represents the energy of ith microstate.

k represents the Boltzmann constant with value 1.381×1023J/K.

T represents the temperature (K).

The number of terms in the electronic partition function will be equal to the number of states. Therefore, the numbers of terms for the summation of the electronic partition function for N2 gas at standard temperature are 46.

Conclusion

The numbers of terms for the summation of the electronic partition function for N2 gas at standard temperature are 46.

Interpretation Introduction

(b)

Interpretation:

The numbers of terms for the summation of the electronic partition function for O2 gas at standard temperature is to be stated.

Concept introduction:

Different linearly independent wavefunctions that have same energy are called degenerate. This is expressed in terms of degeneracy. If two functions are having same energy then they are called doubly degenerate and so on. The electronic partition function is represented as,

qelect=igiei/kT

Expert Solution
Check Mark

Answer to Problem 18.4E

The numbers of terms for the summation of the electronic partition function for O2 gas at standard temperature are 37.

Explanation of Solution

The term symbol of a diatomic compound is represented as,

2S+1ΛΩ

Where,

S represents the total spin of the molecule.

Λ represents the axial component of L.

Ω represents the axial component of total angular quantum number J.

The term (Λ) of diatomic molecule is represented by Greek symbols such as Σ, Π, Δ and Φ. The term Ω is represented by either alphabet u or g.

From the referred Table, the state of 16O2 are represented as,

[Z  (2Πu), Y,W(3Σu+) ,V, U,R,Q,P, 1Φu,I", I', I,H (3Πu),4f,L( 3Πu),K( 1Δu),J(1Σu+),G(3Σu+),i( 1Δ2u),i( 3Δ2u),h(1Πu),g(1Πu),F*,F3Πu,E3Σu-,F 1Σu+,D( 3Σu+), e( 1Δ2u),e*( 3Δ2u),d( 1Πg),c( 3Πg),B3Σu-,A3Σu+,A3Δu,c1Σu-,b1Σg+,a1Δg,x3Σg]

The total number of states of O2 is 37.

The electronic partition function is represented as,

qelect=igiei/kT

Where,

gi represents the degeneracy.

i represents the energy of ith microstate.

k represents the Boltzmann constant with value 1.381×1023J/K.

T represents the temperature (K).

The number of terms in the electronic partition function will be equal to the number of states. Therefore, the numbers of terms for the summation of the electronic partition function for O2 gas at standard temperature are 37.

Conclusion

The numbers of terms for the summation of the electronic partition function for O2 gas at standard temperature are 37.

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Chapter 18 Solutions

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