(a)
Interpretation:
The numbers of terms for the summation of the electronic partition function for
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,
Answer to Problem 18.4E
The numbers of terms for the summation of the electronic partition function for
Explanation of Solution
The term symbol of a diatomic compound is represented as,
Where,
•
•
•
The term
From the referred Table, the state of
The total number of states of
The electronic partition function is represented as,
Where,
•
•
•
•
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
The numbers of terms for the summation of the electronic partition function for
(b)
Interpretation:
The numbers of terms for the summation of the electronic partition function for
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,
Answer to Problem 18.4E
The numbers of terms for the summation of the electronic partition function for
Explanation of Solution
The term symbol of a diatomic compound is represented as,
Where,
•
•
•
The term
From the referred Table, the state of
The total number of states of
The electronic partition function is represented as,
Where,
•
•
•
•
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
The numbers of terms for the summation of the electronic partition function for
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Chapter 18 Solutions
Physical Chemistry
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- Discuss the relation between the thermodynamic and statistical definitions of entropy.arrow_forwardCalculate the rotational partition function of SO2 at 298 K from its rotational constants 2.027 36 cm–1, 0.344 17 cm–1, and 0.293 535 cm–1 and use your result to calculate the rotational contribution to the molar entropy of sulfur dioxide at 25 °C.arrow_forwardA certain molecule can exist in either a nondegenerate singlet state or a triplet state (with degeneracy of 3). The energy of the triplet exceeds that of the singlet by ε. When ?=??(where T is a set value, i.e., ? is a constant), calculate the values of the molecular partition function, molar heat capacity, and molar entropy. Assume the molecules are distinguishable and independentarrow_forward
- Evaluate the rotational partition function of pyridine, C5H5N, at 25 °C given that ᷉ A = 0.2014 cm−1, ᷉ B = 0.1936 cm−1, ᷉ C = 0.0987 cm−1. Take the symmetry number into account.arrow_forwardsystem A with 100,000 molecules is at equilibrium at 400k with a boltzmann partition function of q=1.156518. Assume that the energy levels for system A are evenly distributed at delta U = 2Kb x T . a) calculate the probability and population distribution for the system? ( use 5 energy levels including ground state) b) calculate the entropy for the system?arrow_forwardThe H2O molecule is an asymmetric rotor with rotational constants 27.877 cm−1, 14.512 cm−1, and 9.285 cm−1. Calculate the rotational partition function of the molecule at (i) 25 °C, (ii) 100 °C.arrow_forward
- A linear molecule may rotate about two axes. If the molecule consists of N atoms, then there are 3N- 5 vibrational modes. Use the equipartition theorem to estimate the total contribution to the molar internal energy from translation, vibration, and rotation for (a) carbon dioxide, CO2, and (b) dibromoethyne, C2Br2, at 2000 K. In contrast, a nonlinear molecule may rotate about three axes and has 3N- 6 vibrational modes. Estimate the total contribution to the molar in ternal energy from translation, vibration, and rotation for (c) nitrogen dioxide, NO2, and (d) tetrabromoethene, C2Br4,at 2000 K. In each case, first assume that all vibrations are active; then assume that none is.arrow_forwardA certain atom has a fourfold degenerate ground level, a non-degenerate electronically excited level at 2500 cm−1, and a twofold degenerate level at 3500 cm−1. Calculate the partition function of these electronic states at 1900 K. What is the relative population of each level at 1900 K?arrow_forwardThe ratio between the translational partition function of H2 to that of unknown gas X2 at 400 K is 80. if the thermal de Broglie wavelength of H2 is 61.71 pm, what would be the thermal de Broglie wavelength of the unknown gas in pm assuming that both gases are confined in the same volume.arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,