EeqkTwhere k isThe 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 = 1c) Calculate the average energy (expectation value) of a molecule in units ofcm³¹. Make sure to use normalized probabilities.d) Plot P vs E. Make sure to use normalized probabilities.

Part (a): Convert Each Energy Level to J/moleculeThe energy levels in cm−1 are:E1=0 cm−1,E2=100…

Answered: E e q kT where k is The probability of…

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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3. Consider a 2 × 2 square lattice of spins interacting via the Ising Hamiltonian in the absence of a magnetic field: H = - ΣSi Sj, (ij) we have set J = 1. (a) Write down all the possible configurations and calculate the energy for each one of them. (b) Calculate the partition function Z, as a function of temperature, by summing over all configurations. (c) Repeat question (3a) and (3b), using periodic boundary condi- tions.
A¡H° = 86 kJ mol-1 ,A;S = – 140 JK-1 mol-1 , T = 299 K Express your answer as an integer.
P13C.8 Consider a system of N molecules with energy levels ɛ, = jɛ and j= 0, 1, 2,...(a) Show that if the mean energy per molecule is aɛE, then the temperature is given by B=-In 1+ Evaluate the temperature for a system in which the mean energy is ɛ, taking ɛ equivalent to 50 cm". (b) Calculate the molecular partition function q for the system when its mean energy is aɛ.
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
Step 1 of 7 Give the equation for the Helmholtz energy, A. (Use the following as necessary: S, T, and U.) A = U-TS U-TS Give the equation for entropy that contains the canonical partition function, Q. (Use the following as necessary: E, kB, Q, and T.) E S = kaln(Q)+ E T kB ln (Q) + 4 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 = -Tk ln(Q) + U₁ 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.) P = -(3x), ・ (a In (@)), · KB¹ KBT Step 4 of 7 For an ideal monatomic gas, the following is true. (Use the following as necessary: T, U, and V.) UT 0 Step 5 of 7 Give the equation for the canonical partition function Q. Remember that only the translational…
N2O and CO2 have similar rotational constants (12.6 and 11.7 GHz, respect ively) but strikingly different rotational partition functions. Why?
3. Calculate the residual molar entropy of a single molecule based on statistical approach if this molecule can adopt 4 orientations of equal energy at T=0K. What would be the entropy based on thermodynamic definitions?
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…
We discussed in class (several times) how the Boltzmann distribution can be used to relate the relative populations of two states differing in energy by AU. Suppose you are given a vial containing a solution of glucose in water (don't ask why this would happen). For the purpose of this question, glucose exists in one of two conformations-"chair" or "boat"-with an energy difference (AU) of 25.11 kJ mol1 between them. 1. What would be the proportion of molecules in the "boat" conformation at 310K? 2. Thinking back to our discussion of the individual sources of energy that go into the potential energy calculation for a molecule (e.g. Upond Uangle, Uelectrostatic. etc), give a plausible explanation of why the "boat" conformation is less stable. H он "Chair" OH "Вoat" но но но- HO. H. HO. HO H. HO. OH
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
2. The rotational partition function of an ethene molecule is 661 at 25°C. What is the rotational contribution to its molar entropy?
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.

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