(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 &. (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?

(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 &. (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?

Physical Chemistry

2nd Edition

ISBN:9781133958437

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

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

Chapter2: The First Law Of Thermodynamics

Section: Chapter Questions

Problem 2.9E

See similar textbooks

Similar questions

Consider 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.
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?
2. The rotational partition function of an ethene molecule is 661 at 25°C. What is the rotational contribution to its molar entropy?
JustifyTrouton"s rule. What are the sources of discrepancies?
Calculate the molar entropy of a constant-volume sample of argon at 250 K given that it is 154.84 J K−1 mol−1 at 298 K; the molar constant-volume heat capacity of argon is 3/2 R.
Discuss the relation between the thermodynamic and statistical definitions of entropy.
17.12 The equilibrium bond length for HBr is 1.66 Å. (A) Calculate the value of the rotational constant for HBr, assuming that a molecule of the compound behaves as a rigid rotor whose length is equal to the HBr equilibrium bond length. (B) Compute the rotational molecular partition function for HBr at a temperature of 800 K to four significant digits. (C) Determine the most populated rotational state of HBr at 800 K. Assume that the atomic masses are the average atomic masses, (i.e., atomic weights).
4) 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.
Write down the expression for the equilibrium constant of the reaction N2(g) + 3 H2(g) ~ 2 NH3(g) in termsof the molecular partition functions of the reactants andproducts.
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
A linear molecule may rotate about two axes. If the molecule consists of N atoms, then there are 3N- 5 vibrational modes. Use the equipartition theorem to estimate the total contribution to the molar internal energy from translation, vibration, and rotation for (a) carbon dioxide, CO2, and (b) dibromoethyne, C2Br2, at 2000 K. In contrast, a nonlinear molecule may rotate about three axes and has 3N- 6 vibrational modes. Estimate the total contribution to the molar in ternal energy from translation, vibration, and rotation for (c) nitrogen dioxide, NO2, and (d) tetrabromoethene, C2Br4,at 2000 K. In each case, first assume that all vibrations are active; then assume that none is.
Calculate the contribution that rotational motion makes to the molar entropy of a gas of HCl molecules at 25 °C.