Interpretation:
The ratio of the partition functions at the same volume and temperature for a
Concept introduction:
Statistical
It is used to calculate the state functions like energy, pressure, wavelength etc. of the thermodynamic system. The expressions obtained for state functions using partition functions help to determine the statistical aspect of thermodynamic system.
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- A 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_forward(1) The molecules in a thermally equilibrated isolated system are confined to just the two (non-degenerate) energy levels. lowest (a) Write down an expression for the partition function q of this system if the energy levels are separated by an amount ɛ. (b) If q = 1.142, determine the temperature of the system if the two energy levels are separated by 8 kJ/mol. (c) What is q in the limit of very high temperatures?arrow_forwardConsider a system of distinguishable particles having only two non-degenerate levels separated by an energy that is equal to the value of kT at 10 K. Calculate (a) the ratio of populations in two states at (1) 1.0 K, (2) 10 K, (3) 100 K, (b) the molecular partition function at 10 K, (c) the molar energy at 10 K, (d) the molar heat capacity at 10 K, € the molar entropy at 10 K.arrow_forward
- system 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_forward5arrow_forwardThe 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_forward
- A certain atom has a doubly degenerate ground level, a triply degenerate electronically excited level at 1250 cm-1, and a doubly degenerate level at 1300 cm-1. Calculate the partition function of these electronic states at 2000 Karrow_forward4) Consider a chemical reaction R⇒ P at 300 K. R has two states separated by 2.0x10-22 J. P has a doubly degenerate level that is 1.0x10-22 J above the ground state of P. a) Which one has a larger molecular partition function? b) Find the equilibrium constant for the reaction.arrow_forwardCalculate, by explicit summation, the vibrational partition function of I2 molecules at (a) 100 K, (b) 298 K given that its vibrational energy levels lie at the following wavenumbers above the zero-point energy level: 0, 215.30, 425.39, 636.27, 845.93 cm−1. What proportion of I2 molecules are in the ground and first two excited levels at the two temperatures?arrow_forward
- Consider a system at 250 K which has an infinite ladder of evenly spaced quantum states with an energy spacing of 0.25 kJ/mol. 1. The energy for level n=1 is kJ/mol. The minimum possible value of the partition function for this system is The average energy of this system in the classical limit is decimal] 2. 3. 4. The number of thermally populated states is kj/mol. [Answer rounded to 1 [Answer should be whole number]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_forwardN2O and CO2 have similar rotational constants (12.6 and 11.7 GHz, respect ively) but strikingly different rotational partition functions. Why?arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,