Interpretation:
The values of partition function with the given temperatures are to be calculated. The validation of the fact that leveling off of the value of
Concept introduction:
Statistical
Where,
•
•
•
•
It is also called as canonical ensemble partition function.
Answer to Problem 17.58E
The values of partition function at given temperatures
Explanation of Solution
The given values of temperatures are
It is given that a system has energy levels at
The degeneracy of each level is
The important quantity in the thermodynamic is partition function that is represented as,
Where,
•
•
•
•
The partition function of a system that has five different energy levels with energy
Substitute the value of energies, degeneracies,
Therefore, the value of
Substitute the value of energies, degeneracies,
Therefore, the value of
Substitute the value of energies, degeneracies,
Therefore, the value of
Substitute the value of energies, degeneracies,
Therefore, the value of
Substitute the value of energies, degeneracies,
Therefore, the value of
Substitute the value of energies, degeneracies,
Therefore, the value of
On comparing the partition function values it is observed that, the value of partition function increases with the increase in temperature. At low temperatures the increase of
The values of partition function at given temperatures
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Chapter 17 Solutions
Physical Chemistry
- Calculate 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 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_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_forward
- The 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_forwardCalculate the standard molar entropy of N2(g) at 298 K from its rotational constant ᷉ B = 1.9987 cm−1 and its vibrational wavenumber ᷉v = 2358 cm−1. The thermochemical value is 192.1 J K−1 mol−1. What does this suggest about the solid at T = 0?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
- For two nondegenerate energy levels separated by an amount of energy ε/k=500.K, at what temperature will the population in the higher-energy state be 1/2 that of the lower-energy state? What temperature is required to make the populations equal?arrow_forwardWhat do you mean by the term equilibrium partition coefficient?arrow_forwardAt what temperature is the translational contribution to the standard molar entropy of CO2(g) equal to that of H2O(g) at 298 K?arrow_forward
- Use the equipartition principle to estimate the values of γ = Cp/CV for gaseous ammonia and methane. Do this calculation with and without the vibrational contribution to the energy. Which is closer to the experimental value at 25 °C?arrow_forwardUse the equipartition principle to estimate the value of γ = Cp/CV for carbon dioxide. Do this calculation with and without the vibrational contribution to the energy. Which is closer to the experimental value at 25 °C?arrow_forwardAt what temperature is the standard molar entropy of helium equal to that of xenon at 298 K?arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,