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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Physical Chemistry
- (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_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_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
- 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_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_forwardA 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_forward
- Calculate, 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_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_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
- N2O and CO2 have similar rotational constants (12.6 and 11.7 GHz, respect ively) but strikingly different rotational partition functions. Why?arrow_forwardPart A Determine the total molecular partition function for gaseous H2O at 1000. K confined to a volume of 2.20 cm³. The rotational constants for water are BA = 27.8 cm, BB = 14.5 cm¯', and Bc = 9.95 cm. The vibrational frequencies are 1615, 3694, and 3802 cm-. The ground electronic state is nondegenerate. (Note: the Avogadro's constant NA = 6.022 × 1023 mol-1). Express your answer to three significant figures. Ην ΑΣφ qtotal = Submit Request Answerarrow_forwardJustifyTrouton"s rule. What are the sources of discrepancies?arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,