A CO2 molecule has four vibrational modes with wavenumbers 1388 cm-1, 2349 cm-1, and 667 cm-1, (the last being a doubly degenerate bending motion). Calculate the total vibrational partition function at (a) 500 K, (b) 1000 K.

A CO2 molecule has four vibrational modes with wavenumbers 1388 cm-1, 2349 cm-1, and 667 cm-1, (the last being a doubly degenerate bending motion). Calculate the total vibrational partition function at (a) 500 K, (b) 1000 K.

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

Related questions

Q: Identify the molecular partition function for a molecule that has three energy levels with energies…

A: Molecular partition function q = ∑gie−Ei/kT q = goe−Eo/kT + g1e−E1/kT + g2e−E2/kT

Q: Calculate the rotational partition function for a non-linear molecule whose σ=5 at 25°C. Given A =…

A: Where Kb is Boltzmann constant, which equals to 0.695 cm-1 T = Temperature in Kelvin (K)

Q: Calculate the thermal wavelength and the translational partition function at 300. K and 3000. K of a…

Q: Q3: The ratio between the translational partition function of Hz to that of unknown gas X2 at 400 K…

A: Given: The ratio between the translational partition function of H2 to unknown gas is 70. This…

Q: Calculate (i) the thermal wavelength, (ii) the translational partition function at 300 K and 3000 K…

A: i)

Q: A certain atom has a fourfold degenerate ground level, a non-degenerate electronically excited level…

A: The conversion of energy in cm-1 to joule is done using the below equation in which h is the…

Q: Use the Boltzmann formula to calculate the low and high temperature limits of vibrational partition…

Q: Calculating Partition Functions. Consider the acetylene molecule, which is linear and has the…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Calculate the molecular translational partition functions in a volume of 1 cm³ at 298°K for the…

Q: THE THERMODYNAMICS OF GASES 5. Show that the total partition function derived from equation 7.45, on…

Q: 6) Molecular partition function a) Write down the expressions for molecular partition function over…

A: a) The molecular partition function over states is the expression for partition function in which…

Q: The diatomic molecule N2 has a rotational constant B(~) = 2.0 cm-1 and a vibrational constant v(~) =…

Q: The ground configuration of oxygen gives rise to the three levels 3P2, 3P1, and 3P0 at 0, 158.5. and…

A: Hello. Since the question contains multiple subparts the first three subparts are solved. In case…

Q: A certain atom has a triply degenerate ground level, a non-degenerate electronically excited level…

A: The conversion of energy in cm-1 to joule is done using the below equation in which h is the…

Q: system A with 100,000 molecules is at equilibrium at 400k with a boltzmann partition function of…

Q: Give an example of 2 isomers of a molecule that have different values of the rotational partition…

A: Depend on position of methyl group of ethane ,ethane has two isomer. One is staggerd and other is…

Q: 12.10 Calculate the molar entropy of nitrogen gas at 298 K. Write the overall partition function as…

A: Here we will apply the boltzmann equation to find the solution .

Q: The methyl chloride molecule, CH3Cl, has three non-degenerate vibrations with harmonic wavenumbers…

Q: P13B.5 (a) Calculate the electronic partition function of a tellurium atom at (i) 298 K, (ii) 5000 K…

A: Electronic partition function related to the diatomic molecule takes the zero of energy to be…

Q: 9. The rotational spectrum of HCN is in far-infrared region, one part is 2.96 cm", 5.92 cm", 8.87…

Q: 2. (a) What is partition function? Obtain a general relation of function with the following the…

A: The answers are given as follows:

Q: 1. Use the equipartition principle to estimate the value of γ = Cpm/CVm for gaseous N2O5. Do this…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Calculate the rotational partition function for nitric oxide (NO) at 20 K using the summation…

Q: The occupation probability of state / with an energy & is given by: exp(-ɛ¡/kµT) q p(ε₁) = where k…

A: Partition function is sum of an exponential function of all the possible energy of the system.

Q: Determine the total molecular partition function for gaseous H2O at 1000. K confined to a volume of…

A: Let qtotal be the total partition function including electronic, rotational, translational, and…

Q: The bond length of N2 is 109.75 pm. Use the high-temperature approximation to calculate the…

A: Introduction: Rotational partition function: The rotational partition function shows the…

Q: Show that bimolecular reactions between nonlinear molecules are much slower than between atoms even…

A: X +Y ----->(XY)* ---->P Transition state theory rate constant : k (q(XY*)/ q(A) q(Y)…

Q: Calculate, by explicit summation, the vibrational partition function of I2 molecules at (a) 100 K,…

Q: Calculate the values of the rotational and vibrational partition functions of CO2 at 300 K, given…

A: In the given problem, the rotational and vibrational partition function of CO2 at 300 K, The…

Q: At what temperature is the translational contribution to the standard molar entropy of CO2(g) equal…

A: The Sackar Tettrode equation for standard molar entropy is shown below: S=nRlne522πmkTh232kTP For a…

Q: In the water and nitrogen molecules, do they have the same electronic partition function? Explain it…

A: In molecules, generally only the ground electronic state is accessible, under a wide range of…

Q: Consider a system having four energy levels. Assuming the levels have energy values of (0, 1, 4, 9,…

A: Given, Energy values of the following energy levels- For level Zero (0) , E0 = 0 JFor level 1 , E1…

Q: The energy difference between consecutive vibrational states is 1.0 x 1020 J for a molecule. b. (i)…

A: According to the Boltzmann distribution number of particles in ith energy level (ni) is given as: ni…

Q: Calculate the rotational partition function for SO2 at 409 K where BA = 2.03 cm¯', BB = 0.344 cm and…

Q: Calculate the molecular rotational partition function for 14N2 at 298"K for both molecules. The…

Q: Calculate the translational partition function at (a) 300 K and (b) 600 K of a molecule of molar…

A: The given molar mass is 100 g/mol. The conversion of 100 g/mol into kg/mol is as follows:1 g = 0.001…

Q: ulate the molecular translational partition functions in a volume of 1 cm3 at 298°K for the hydrogen…

Q: Starting from the molecular partition functions of each species, calculate ASrxn at 298.15 K and…

A: The solution of the question is given below: N2 (g) →2N (g) To calculate ∆S of the recation T=…

Q: The rotational partition function for a sample of carbonyl sulfide (OCS) is found to be 25.0. Above…

A: EJ= J(J+1)

Q: NO is a well-known example of a molecular system in which excited electronic energy levels are…

Q: calculate the vibrational contribution to the entropy of chlorine molecule at 500K given the wave…

Q: An NO molecule has a doubly degenerate electronic ground state and a doubly degenerate excited state…

A: Solution- Electronic partition function (qe) is given by: qe=∑gie-βEi For NO ,degeneracy , gi=2 ,…

Q: What is overall molecular partition function Q, and how it is constructed using the partition…

Q: (b) Write an expression of the vibrational partition function. Obtain the relation of the…

A: The answers are given below:

Question

A CO₂ molecule has four vibrational modes with wavenumbers 1388 cm^-1, 2349 cm^-1, and 667 cm^-1, (the last being a doubly degenerate bending motion). Calculate the total vibrational partition function at (a) 500 K, (b) 1000 K.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 12 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.

Similar questions

Estimate the vibrational contribution to the molar entropy of the most common isotopomer of bromine, 79Br2, at 1000 K. The vibrational wavenumber for 79Br2 is 325 cm-1. You may assume that at this temperature, the equipartition theorem and the high temperature approximation for the vibrational partition function are both valid.
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.
Calculate the rotational partition function of SO2 at 298 K from its rotational constants 2.027 36 cm–1, 0.344 17 cm–1, and 0.293 535 cm–1 and use your result to calculate the rotational contribution to the molar entropy of sulfur dioxide at 25 °C.
Predict the vibrational contribution to the standard molar entropy of methanoic acid (formic acid, HCOOH) vapour at (i) 298 K, (ii) 500 K. The normal modes occur at wavenumbers 3570, 2943, 1770, 1387, 1229, 1105, 625, 1033, 638 cm−1.
Evaluate the rotational partition function at 298 K of (a) 1H35Cl. for which the rotational constant is 318 GHz, (b) 12C16O2, for which the rotational constant is 11.70 GHz.
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.
Evaluate the rotational partition function of pyridine, C5H5N, at 25 °C given that ᷉ A = 0.2014 cm−1, ᷉ B = 0.1936 cm−1, ᷉ C = 0.0987 cm−1. Take the symmetry number into account.
N2O and CO2 have similar rotational constants (12.6 and 11.7 GHz, respect ively) but strikingly different rotational partition functions. Why?
A certain atom has a triply degenerate ground level, a non-degenerate electronically excited level at 850 cm–1, and a fivefold degenerate level at 1100 cm−1. Calculate the partition function of these electronic states at 2000 K. What is the relative population of each level at 2000 K?
Estimate the rotational partition function of ethene at 25 °C given that ᷉ A = 4.828 cm−1, ᷉ B =1.0012 cm−1, and ᷉ C = 0.8282 cm−1. Take the symmetry number into account.
Calculate (i) the thermal wavelength, (ii) the translational partition function at 300 K and 3000 K of a molecule of molar mass 150 g mol−1 in a container of volume 1.00 cm3.
Calculate, by explicit summation, the vibrational partition function of I2 molecules at (a) 100 K, (b) 298 K given that its vibrational energy levels lie at the following wavenumbers above the zero-point energy level: 0, 215.30, 425.39, 636.27, 845.93 cm−1. What proportion of I2 molecules are in the ground and first two excited levels at the two temperatures?