The approximation of calculating the partition function by integration instead of the summation of all the energy terms can only be done if the separation of the energy levels is much smaller than the product kT. Explain why.
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The approximation of calculating the partition function by integration instead of the summation of all the energy terms can only be done if the separation of the energy levels is much smaller than the product kT. Explain why.
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- The bond length of N2 is 109.75 pm. Use the high-temperature approximation to calculate the rotational partition function of the molecule at 300 K.Quantum mechanics. In translational motion, the summation is replaced by an integral when evaluating the partition function. This is correct becausea) the spacing of the translational energy levels is very small compared to the product kTb) the spacing of the translational energy levels is comparable to the product kTc) the spacing of the translational energy levels is very large compared to the product kTConsider a system of two energy levels separated by an energy equal to ε1. The lowest energy level is nondegenerate, and the second energy level has a degeneracy of 4. a) Write the expression for the partition function. b) Write the expression for E. Determine the value of E in the infinite temperature limit. c) Write the expression for S. Determine the value of S in the infinite temperature limit.
- It is possible to approximate the rotational partition function for diatomic molecules by replacing the infinite sum over states with an integral. Why might this be less accurate for H₂? OH₂ has a smaller mass so its rotational constant will be very small. OH₂ has a very high vibrational frequency so the spacings between its energy levels will be large. O the moment of inertia for H₂ is OH₂ has a shorter bond length so its rotational constant will be very small. the integral diverges for smaller-sized diatomic molecules.N2O and CO2 have similar rotational constants (12.6 and 11.7 GHz, respect ively) but strikingly different rotational partition functions. Why?2. The rotational partition function of an ethene molecule is 661 at 25°C. What is the rotational contribution to its molar entropy?
- The 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 decreasingCalculate the ratio of the translational partition functions of H2 and He at the same temperature and volume.Discuss the relation between the thermodynamic and statistical definitions of entropy.
- 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.The 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.Part 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 Answer