5. The vibrational modes of a particular molecule are listed below. Calculate thevibrational contribution to the molar entropy at 300 K.ModeDegeneracywavenumber / cm-1v1206v2305v31083v41367USEFUL CONSTANTSR = 8.314 J/mol/K = 0.08205 Latm/mol/KkB =1.38 x10-23 J/Kh = 6.626×10-34 J sc = 3x108 m/s1 cm-1 = 1.98x10-23 JSTP = 298 K, 1bar (105 N/m²)12 3

Given : S. No. Degenracy(m) wave no (cm-1) v1 1 206 v2 1 305 v3 2 1083 v4 3 1367

5. The vibrational modes of a particular molecule are listed below. Calculate the vibrational contribution to the molar entropy at 300 K. IIT Mode Degeneracy wavenumber / cm-1 v1 1 206 v2 1 305 v3 2 1083 v4 3 1367

5. The vibrational modes of a particular molecule are listed below. Calculate the vibrational contribution to the molar entropy at 300 K. IIT Mode Degeneracy wavenumber / cm-1 v1 1 206 v2 1 305 v3 2 1083 v4 3 1367

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...

See similar textbooks

Related questions

Q: At absolute zero there are only vibrational modes of movement in a substance true or false

Q: It is possible to approximate the rotational partition function for diatomic molecules by replacing…

A: Rotational partition function gives the relationship between rotational degrees of freedom to the…

Q: 1B. Explain how a vibrationally excited molecule is able to withstand up a billion of collisions…

A: In vibration process, the two or more atoms are attached with the bonds gets vibrated on the…

Q: Why does the vibrational state of a diatomic molecule affect its rotational constant? Is there an…

A: Each vibrational level consists of several rotational levels. So the vibrational transition will…

Q: Calculate the standard molar entropy of O2(g) at 298 K from its rotational constant B=1.4457 cm and…

A: The objective of the question is to calculate the standard molar entropy of oxygen molecule…

Q: (c) A table of energies and degeneracies is given below for the lowest energy vibrational states of…

A: Here we are required to find the partition function for the given vibrational energy state.

Q: Estimate the ratio of the number of molecules in the firstexcited vibrational state of the molecule…

A: The energy delivered can be determined as follows:

Q: 4. Spectroscopic measurements indicate that the rotational constants of SO2, a non-linear molecule,…

Q: The spacing between two adjacent lines in the pure rotational spectrum of a diatomic molecule is…

Q: Estimate the ratio of the number of molecules in the first excited vibrational state of the molecule…

A: Let the number of nitrogen molecule in the first excited state be x and the number of the nitrogen…

Q: 3. Determine the internal energy of an HCl molecule having one quantum of vibrational excitation…

A: To determine the internal energy of an HCl molecule with one quantum of vibrational excitation (v-1)…

Q: The vibrational temperature of a molecule prepared in a supersonic jet can be estimated from the…

A: The ratio of populations in the two levels is given by following Boltzmann equation. The above…

Q: The four lowest electronic levels of a Ti atom are: J = 2, 3, 4 and 1, at 0, 170, 387 and 6557 cm-1,…

Q: The first excited electronic energy level of the helium atom is 3.13 ✕ 10−18 J above the ground…

A: According to the question we have, The electronic energy of the first excited state of the Helium…

Q: A system consists of three energy levels: a ground level (&o= 0, 90 = 1); a first excited level (1 =…

Q: The rotational constants of HFHF and DFDF are 20.956 cm−1 and 11.00 cm−1, respectively. 1K = 0.6950…

A: The expression of energy is shown below: E = BJJ+1 where; B = rotational constant J = energy states

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

Q: Here we calculate the heat capacity of nitrogen gas. The rotational temperature of nitrogen is Prot…

Q: Consider the of a diatomic molecule. Intensity 0 B. 2400 rotational-vibrational spectrum a. 18 cm-1…

A: In rotational vibrational spectrum of diatomic molecule, There is three type of spectrum line that…

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: sodium chloride molecule, 23NA35CI, which s present in the interstellar medium, are observed at…

A: The difference between two lines in today rotational spectroscopy is 2B Separation between 2 lines…

Q: Part D: Methane at room temperature At room temperature, the specific heat capacity (at constant…

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

Q: The H₂O molecule is an asymmetric rotor with rotational constants 27.877 cm¹¹, 14.512 cm³¹, and…

A: Given a physical problems on rotational partition function having some value of rotational constant.…

Q: What is the numerical value of the molecular partition function of a heteronuclear diatomic molecule…

Q: The following have to do with rotational partition functions. a) What are the symmetry numbers o for…

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

Q: Calculate the vibrational, rotational, and translational contributions to the constant volume heat…

Q: Please use the values in the resources listed below instead of the textbook values. Calculate the…

A: The correct solution is given below

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: Calculate the standard molar entropy of N2(g) at 298 K from its rotational constant B =1.9987cm−1…

Q: 1. Determine the number of translational, vibrational, and rotational degrees of freedom available…

A: (1) Given that, a molecule is NH3. We have to calculate the number of translational, vibrational,…

Q: 1. Consider the following diatomic molecules: H2 with a vibrational stretch mode at 4342 cm-1, Frat…

Q: 10. The first five vibrational energy levels of ¹H³5Cl are at 1481.86, 4367.50, 7149.04, 9826.48,…

Q: Calculate the value of the translational partition function for 1H 35Cl at temperature T = 406 K in…

A: The translational partition function (qtrans) for a diatomic molecule can be calculated using the…

Q: You have a diatomic ideal gas at room temperature with a rotational temperature of Orot = 2 K and…

A: In the ideal gas molecules, the interaction between them is negligible. It leads to elastic…

Q: [References] The vibrational temperature of a molecule prepared in a supersonic jet can be estimated…

Q: The frequency for the first excitation of the stretching mode in the HCl molecule was experimentally…

A: The partition function is a thermodynamic quantity that describes the number of states that a system…

Q: he lowest electronic levels for 14N 160 have the following characteristics: Calculate, for 5000 k,…

A: The objective of the question is to calculate the fraction of molecules in the 3 electronic levels,…

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: Consider 1 mol of N2(g) at room temperature. Calculate the number of molecules in the ground…

A: One mole of a gas contains Avogadro's number of molecules, which is approximately 6.022 x 10^23…

Q: The ground configuration of carbon gives rise to a triplet with the three levels 3P0, 3P1, and 3P2…

A: a) The electronic partition function of carbon at (i) 10 K, (ii) 298 K has to be given,

Q: Calculate the ratio of the rotational partition functions of 3CSCI to that of 3$C³³CI under…

Q: The rotational constant for the molecule 1H35Cl is B = 10.60 cm-1. Using Boltzmann statistics,…

A: The objective of the question is to determine the most likely rotational state J of a 1H35Cl…

Q: 4. The transition between the ground and first excited vibrational levels of the ICl molecule is…

A: The relative population of two vibrationaĺ state is given by Boltzmann equation

Q: 1. Consider water (H₂O) at high temperature. [Give some reasoning, not just values.] a. b. C. d.…

A: Note: Since you have posted a question with multiple sub-parts, we will provide the solution only to…

Q: The vibrational energy levels for XO molecule can be described by the following formula: E(n) in…

A: Energy is given by: En=n+12ωe-n+122ωexe ...... (1) where xe is the anharmonicity…

Question

5. The vibrational modes of a particular molecule are listed below. Calculate the
vibrational contribution to the molar entropy at 300 K.
Mode
Degeneracy
wavenumber / cm-1
v1
206
v2
305
v3
1083
v4
1367
USEFUL CONSTANTS
R = 8.314 J/mol/K = 0.08205 Latm/mol/K
kB =1.38 x10-23 J/K
h = 6.626×10-34 J s
c = 3x108 m/s
1 cm-1 = 1.98x10-23 J
STP = 298 K, 1bar (105 N/m²)
12 3

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

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

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

1. The energy gap between the ground state and next levels in NO is A=15.4 meV. Find the electronic contribution to the molar heat capacity at T₁ = 50 K and T₂= 500 K.
This problem explores the vibrational and rotational energy levels of the hydrogen halides. Experimental data are given below. Hydrogen halides kf (kg/s²) R (pm) HF 970.0 91.7 HCI 480.0 127.5 HBr 410.0 141.4 HI 320.0 160.9 For one mole of each HF, determine the following quantities. ΔΕ1Ο 8.29 x10-20 J b. The number of vibrational energy levels occupied at 300 K j = 2 levels c. The spacing between the two lowest rotational energy levels 7.73 x10-32 ΔΕ10 J Incorrect d. The number of rotational energy levels occupied at 300 K 5 j = levels Incorrect
The four lowest electronic levels of a Ti atom are: J = 2, 3, 4 and 1, at 0, 170, 387 and 6557 cm-1, respectively. There a many other electronic states at higher energies. The boiling point of Ti is 3287 oC. What are the relative populations of these levels at the boiling point if the degeneracy of levels is 2J + 1? Is the ground state most highly populated level?
Transitions in the rotational spectrum of the sodium chloride molecule, 23N235CI, which is present in the interstellar medium, are observed at frequencies of 247.2, 260.2, 273.2, 286.2 and 299.2 GHz. Determine the bond length of a sodium chloride molecule. A. 1.09 Å O B. 2.37 Å O C. 5.62 Å O D. 2.01 Å
Q 1. Use the equipartition principle to estimate the value of γ = Cpm/CVm for gaseous CH3COOH. Do this calculation WITH the vibrational contribution to the energy.
Plot the temperature dependence of the vibrational contribution to the molecular partition function for several values of the vibrational wavenumber. Estimate from your plots the temperature at which the partition function falls to within 10 per cent of the value expected at the high-temperature limit.
The force constant of 79Br79Br is 240 N.m−1 . Calculate the fundamental vibrational frequency and the zero-point energy of 79Br79Br.
Calculate the molecular translational partition functions in a volume of 1 cm3 at 298°K for the hydrogen molecule: H2 O 1,173 x 1025 2.750 x < 1024 6.134 x 1025 O 1.118 x 1023 6.175 x 1024
Calculate the vibrational and rotational temperatures (Ovib and Orot) for the diatomic molecular Lithium Hydride (LiH). The Li-H bond length is 0.1595 nm and the vibrational frequency (VL¡H) is 1405 cm'.
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
What is the numerical value of the molecular partition function of a heteronuclear diatomic molecule given the following conditions: (i) the characteristic length is 10 nm and the volume in which the molecules are free to move is a cube with sides of 1 mm each. (ii) Only the first four rotational levels are accessible, but for some odd reason [to keep things simple] each state in each of those levels is equally populated. (iii) all molecules are in the ground vibrational state; (iv) the molecule has a triplet electronic ground level, like O2.
Use the equipartition principle to estimate the value of γ = Cpm/CVm for gaseous N2O5. Do this calculation WITH the vibrational contribution to the energy. a. 1.07 b. 1.33 c. 1.4 d. 1.7 e. 1.5