Consider a system of two energy levels separated by an energy equal to ε1. The lowest energylevel 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.

Answered: Image /qna-images/answer/d4c4a2bc-f3c4-414f-9bca-2592ccedd617.jpg

Answered: Consider a system of two energy levels…

Physical Chemistry

2nd Edition

ISBN:9781133958437

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

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

Chapter17: Statistical Thermodynamics: Introduction

Section: Chapter Questions

Problem 17.41E

See similar textbooks

Similar questions

5
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]
18. Which of the following is the definition of internal energy of a system? a.it is the sum of the kinetic energy of all of its components b.it is the sum of the rotational, vibrational, and translational energies of all of its components c.lt refers only to the energies of the nuclei of the atoms of the component molecules d.It is the sum of the potential and kinetic energies of the components
1. Show that the partition function for a harmonic oscillator in the x direction only is given by: qx exp(-ẞhv) 1-exp(-ẞhv)
Prove that statement mathematically?
E e q kT where k is The probability of a molecule having energy E is P (E) Boltzmann's constant (1.38 * 10¯²³J/K) and q is the partition function. A system has three possible energy levels: 0 cm³¹, 100 cm³¹, and 250 cm³¹. The temperature is 300 K. a) Convert each energy level to J/molecule. (Double check your units!) b) Find q, the partition function (sum up the unnormalized probabilities). The degeneracy of all levels = 1 c) Calculate the average energy (expectation value) of a molecule in units of cm³¹. Make sure to use normalized probabilities. d) Plot P vs E. Make sure to use normalized probabilities.
Give the equation for the Helmholtz energy, A. (Use the following as necessary: S, T, and U.) A = U-TS - TS Give the equation for entropy that contains the canonical partition function, Q. (Use the following as necessary: E, kB, Q, and T.) E E S = k ln(Q) + B kB ln (Q) + Step 2 of 7 We only need to consider the translational translational partition function for an ideal monatomic gas, so E = U - Uo. Combine this equation with the equations for S and A from Step 1. (Use the following as necessary: KB, Q, T, U, and Up.) A = |— Tkôln(Q) + U U₁ - KBT ln(Q) Step 3 of 7 Substitute the equation from Step 2 into the given equation for P and complete the partial derivative. (Use the following as necessary: kB, Q, T, U, and Up.) -(SA), P = - a In(Q)). KBT = KBT Step 4 of 7 For an ideal monatomic gas, the following is true. (Use the following as necessary: T, U, and V.) (U) = UT - 0 Step 5 of 7 Give the equation for the canonical partition function Q. Remember that only the translational…
The answers may be one or more than one As discussed in one of the videos, the equilibrium state of a gas in a box with a movable partition is determined by maximizing Ωtotal. Choose the expressions that correctly describe Ωtotal in this situation. a. A function of the volume V1 in the left half of the box. b. A function of the total volume V of the box. c. The total number of microstates in the left half of the box. d. The total number of microstates in the system and surroundings. e. The total number of microstates available to the system. f. The total number of microstates in the right half of the box.
Calculating Partition Functions. Consider the acetylene molecule, which is linear and has the chemical structure H−C≡C−H. Calculate or determine the following: a. Symmetry number (?) and degrees of freedom b. Moment of inertia (I) and rotational temperature (Θr) c. Vibrational temperatures (Θv,i) d. Translational (qt), rotational (qr), vibrational (qv), and electronic (qe) partition functions at 298 K. e. Total partition function, (q/V). Helpful information: mass of H atom = 1.007947 amu mass of C atom = 12.01078 amu C≡C bond length = 1.203 Å C−H bond length = 1.060 Å vibrational frequencies = 1975, 3370, 3277, 729 (2), 600 (2) cm-1 (numbers in parenthesis indicate the degeneracy of that mode) ground state electronic degeneracy = 1
Please don´t use partition equation
A certain molecule can exist in either a nondegenerate singlet state or a triplet state (with degeneracy of 3). The energy of the triplet exceeds that of the singlet by ε. When ?=??(where T is a set value, i.e., ? is a constant), calculate the values of the molecular partition function, molar heat capacity, and molar entropy. Assume the molecules are distinguishable and independent
Which if the following statement describe properties of the Boltzmann expression in regards to the relative occupancy of energy states: Select one: O a. Lower temperatures favours more molecules in the higher energy levels O b. Lower the energy separation, equates to more molecules in the lower energy levels c. Lower the energy separation, equates to more molecules in the higher energy levels O d. Higher temperatures favours more molecules in the lower energy levels

SEE MORE QUESTIONS

Recommended textbooks for you

Physical Chemistry

Chemistry

ISBN:

9781133958437

Author:

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

Publisher:

Wadsworth Cengage Learning,

Chemistry by OpenStax (2015-05-04)

Chemistry

ISBN:

9781938168390

Author:

Klaus Theopold, Richard H Langley, Paul Flowers, William R. Robinson, Mark Blaser

Publisher:

OpenStax

Physical Chemistry

Chemistry

ISBN:

9781133958437

Author:

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

Publisher:

Wadsworth Cengage Learning,

Chemistry by OpenStax (2015-05-04)

Chemistry

ISBN:

9781938168390

Author:

Klaus Theopold, Richard H Langley, Paul Flowers, William R. Robinson, Mark Blaser

Publisher:

OpenStax

SEE MORE TEXTBOOKS