THE THERMODYNAMICS OF GASES 5. Show that the total partition function derived from equation 7.45, on the assumption that the energy of the N sub-systems is E = P+ P +P+ ... + 2m' 2m' 2m P&N PyN PEN 2m ' 2m ' 2m %3D agrees with that obtained by substituting equation 7.28 in equa- tion 7.31, i.e. VN . Z = 7.47 6. Using equation 7.3 obtain a value for log Wme in terms of the energy E and the number of systems N only. (Use must be made of the values of T and a given in Chapter 2.)

THE THERMODYNAMICS OF GASES 5. Show that the total partition function derived from equation 7.45, on the assumption that the energy of the N sub-systems is E = P+ P +P+ ... + 2m' 2m' 2m P&N PyN PEN 2m ' 2m ' 2m %3D agrees with that obtained by substituting equation 7.28 in equa- tion 7.31, i.e. VN . Z = 7.47 6. Using equation 7.3 obtain a value for log Wme in terms of the energy E and the number of systems N only. (Use must be made of the values of T and a given in Chapter 2.)

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter18: More Statistical Thermodynamics

Section: Chapter Questions

Problem 18.4E

See similar textbooks

Similar questions

4. The following have to do with rotational partition functions. a) What are the symmetry numbers o for the following molecules? i) "Cl'CI ii) "CP"CI iii) triangular H3* iv) All isomers of C:H.F2 v) CH,CI vi) benzene b) Assume at = 10 the high temperature limit is reached. At what temperature does the high OR temperature limit become valid for: i) DBr (B = 4.24 cm') ii) F"CI (B = 0.516 cm') %3D iii) Csl (B = 0.236 cm) %3D e ) Obtain Jmax and / for the temperatures obtained in part b) and at 500 K.
Part A 0.344 cm-1, Calculate the rotational partition function for SO2 at 409 K where BA = 2.03 cm¯', BB and Bc = 0.293 cm-1. (Note: the Boltzmann constant k = 1.38 × 10-23 J . K-1, speed of the light c = 3.00 x 1010 cm · s', the Planck constant h J.s). -34 6.626 x 10 Express your answer to three significant figures. ΑΣφ ? |X| X•10n qR = 4.24 • 10³ %3D Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining 圓 <8
(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?
For all three of your assigned systems (Ne, Oxygen, Nitrous oxide), calculate the complete partition function (assuming a perfect gas) at T, = 2.00 and e, = 0.0500. Information on the symmetry number for your polyatomic molecules is posted in a table under the Reference section in the Content Library The symmetry number for rotational partition functions. Homonuclear diatomics: o=2 Heteronuclear diatomics: o=1 Polyatomics: Name Nitrous oxide 1
25. Calculate the values of the rotational and vibrational partition functions of CO2 at 300 K, given that the rotational constant is B = 0.391 cm' and the vibrational constants are w1 = and w3 = 2284 cm'. [Ans: qvib = 1.09] 1388 cm', w2 = 667 cm',
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]
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
6. Calculate the rotational partition function for nitric oxide (NO) at 20 K using the summation method, as well as the integrated formula. The moment of inertia is 1.65x10^-46 kg*m^2.
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.
he lowest electronic levels for 14N 160 have the following characteristics: Calculate, for 5000 k, using statistics. A) The fraction of molecules in the 3 electronic levels B) The partition functions for the 3 electronic levels Qti, Qvib, Qrot, and the total partition function. C) The energies Eti, Evib, Etot, for the 3 electronic levels and the total energy and compare with the classical prediction. D) The fraction of molecules in the state J = 2, V = 2 of the second electronic level. Eye /cm-1 Ge wavelength/cm-1 Radius /10-10 0 2 1904.04 1.15077 43845.88 1 2374.31 1.0634 45793.78 2 1037.20 1.4167
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?
What is overall molecular partition function Q, and how it is constructed using the partition functions for each energetic degree of freedom?