(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
- Estimate the vibrational contribution to the molar entropy of the most common isotopomer of bromine, 79Br2, at 1000 K. The vibrational wavenumber for 79Br2 is 325 cm-1. You may assume that at this temperature, the equipartition theorem and the high temperature approximation for the vibrational partition function are both valid.arrow_forwardA certain atom has a triply degenerate ground level, a non-degenerate electronically excited level at 850 cm–1, and a fivefold degenerate level at 1100 cm−1. Calculate the partition function of these electronic states at 2000 K. What is the relative population of each level at 2000 K?arrow_forwardThe frequency for the first excitation of the stretching mode in the HCl molecule was experimentally determined to be ? = 86.6 THz. calculate the partition function q for the stretching mode of HCL at room temperature (T=298K) assuming that it behaves as a harmonic oscillator. explain the significance of the obtained value.arrow_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_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_forwardThe methyl chloride molecule, CH3Cl, has three non-degenerate vibrations with harmonic wavenumbers 3088, 1396 and 751 cm–1 respectively and three doubly-degenerate vibrations with harmonic wavenumbers 3183, 1496 and 1036 cm–1 respectively. Calculate the vibrational partition function for the methyl chloride molecule at 1200 K.arrow_forward
- A 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 rotational partition function for a sample of carbonyl sulfide (OCS) is found to be 25.0. Above roughly what J value do we expect to see the population (the number of molecules per J level) rapidly decreasingarrow_forwardDiscuss the relation between the thermodynamic and statistical definitions of entropy.arrow_forward
- The bond length of O2 is 120.75 pm. Use the high-temperature approximation to calculate the rotational partition function of the molecule at 300 K.arrow_forwardEvaluate the translational partition function of (a) N2, (b) gaseous CS2 in a flask of volume 10.0 cm3. Why is one so much larger than the other?arrow_forwardCalculate the translational partition function at (a) 300 K and (b) 600 K of a molecule of molar mass 100 g mol-1 in a container of volume 4.20 cm3.qtr at 300 K qtr at 600 K Note: this is a measure of the vast number of accessible microstates of translation available to a molecule under these conditions.arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,