The H₂O molecule is an asymmetric rotor with rotational constants 27.877 cm¹¹, 14.512 cm³¹, and 9.285 cm³¹. Calculate the rotational partition function of the molecule at (i) 25 °C, (ii) 100 °C. Hi! Need help with this physical chemistry question. Please explain steps and formulas thanks!

The H₂O molecule is an asymmetric rotor with rotational constants 27.877 cm¹¹, 14.512 cm³¹, and 9.285 cm³¹. Calculate the rotational partition function of the molecule at (i) 25 °C, (ii) 100 °C. Hi! Need help with this physical chemistry question. Please explain steps and formulas thanks!

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: The vibrational modes in water have spacings between levels of roughly Vi = 1600 cm. 2= 3600 cm, and…

A: Molar heat capacity that is Cv is the amount of heat required to raise the temperature of one mole…

Q: (4) Determine the vibrational contribution to Cy for one mole of HCN, where ₁ = 2041 cm ¹,₂ = 712 cm…

A: For a linear molecule such as HCN, there are 3N-6 vibrational degrees of freedom, where N is the…

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 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: The lowest excited state of a potassium (K) atom lies 2.895×10-18 J/atom above the ground state. The…

A: The Boltzmann distribution is a probability distribution that gives the probability of a system to…

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: Equilibrium constants for reactions can be determined from partition functions. For a generic…

A: The equilibrium constant for the following reaction at 298 K is needed to be determined. H2O + DCl…

Q: Calculate the residual molar entropy of a single molecule based on statistical approach if this…

A: A single molecule can adopt 4 orientations of equal energy at T = 0K. We have to calculate the…

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: Differentiate between Fermi level and Fermion.

A: Step : 1 Differentiate between Fermi level and Fermion.

Q: Calculate the vibrational and rotational contributions (with zero point energy) to the molar Gibbs…

A: To calculate the vibrational and rotational contributions to the molar Gibbs energy of a frozen…

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: Derive an expression for the mean energy of a collection of molecules that have three energy levels…

A: The expression for the molecular partition function is defined as shown below where gL is the…

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

Q: Step 5 of 7 Give the equation for the canonical partition function Q. Remember that only the…

A: To provide the partition function Q for an ideal monoatomic gas considering only the transitional…

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

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: . What is the partition function for a system with a triply degenerate level at 0 cm-1, and a doubly…

Q: Use the equipartition principle to estimate the value of γ = Cp/CV for carbon dioxide. Do this…

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

Q: Among the following statements which one is the only correct one a. The rotational partition…

A: To find which of the following statements is correct.

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

Q: P13D.2 Use statistical thermodynamic arguments to show that for a perfect gas, (@E/aV), =0.

Q: Calculate the contribution that rotational motion makes to the molar entropy of a gas of HCl…

A: Rotational motion - motion of the molecule along its axis . Entropy - it is the degree of randomness…

Q: Q1: What will degree of freedom (trans, rot & vib) for the following molecules: a) NO, b) so, c)…

A: question 1. "Since there are multiple sub-parts in this question and you have mentioned to solve all…

Q: 1. Show that the partition function for a harmonic oscillator in the x direction only is given by:…

A: We can derive the vibrational partition function in one dimension taking simple harmonic oscillator…

Q: (a) (b) (c) An atom has a non-degenerate electronic state 1000 cm-1 above a non degenerate…

A: Since you have asked multiple questions, we will answer the first one (a) for you. To get the…

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

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: Derive an expression for pressure in terms of the canonical partition function Q, and then obtain an…

A: The objective of this question is to show the theoretical foundations of statistical mechanics to…

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: Use concepts of statistical thermodynamics to describe the molecular features that determine the…

A: The equilibrium constant k of a reaction is related to the standard Gibbs energy of the reactor by…

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: What molar constant-volume heat capacities would you expect under classical conditions for the…

A: According to equipartition theorem, the contribution of degree of freedom to the heat capacity is ½…

Q: Outline the principles behind the derivation of the Boltzmann distribution.

A: To find: The principle behind the derivation of the Boltzmann distribution

Q: A,H° = 86 kJ mol-1 , A,S = - 140 JK-1 mol-1 ,T = 299 K %3D Express your answer as an integer.

Q: 12B.1 (a) Write down the expression for the partition func- tion of a molecule that has three energy…

A: (a) Write down the expression for the partition function of a molecule that has three energy levels…

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

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: 1. The energy gap between the ground state and next levels in NO is A 15.4 meV. Find the electronic…

A: Given,The energy gap of the ground state and the next levels of NO: To the electronic contribution…

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…

Question

The H2O molecule is an asymmetric rotor with rotational constants 27.877 cm¹¹, 14.512 cm²¹, and
9.285 cm ¹. Calculate the rotational partition function of the molecule at (i) 25 °C, (ii) 100 °C.
Hi! Need help with this physical chemistry
question. Please explain steps and formulas
thanks!

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 with 2 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

Gg.146.
Part A Determine the total molecular partition function for gaseous H2O at 1000. K confined to a volume of 2.20 cm³ . rotational constants for water are BA = 27.8 cm-1, BB = 14.5 cm-1, and Bc = 9.95 cm-1. The vibrational frequencies are 1615, 3694, and 3802 cm-. The ground electronic state is nondegenerate. (Note: the Avogadro's constant NA The 6.022 x 1023 mol-1). Express your answer to three significant figures. Ην ΑΣφ ? 1.29 • 1029 Itotal = Submit Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining
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.
Evaluate the translational partition function for H2 confined to a volume of 191 cm³ at 328 K . (Note: the Avogadro's constant NA 6.022 x 1023 mol-1). Express your answer to three significant figures. Hν ΑΣφ ? qT (H2) = 3.17 • 1026 Submit Previous Answers Request Answer X Incorrect; Try Again; 2 attempts remaining Part B Perform the same calculation for N2 under identical conditions. (Hint: Do you need to reevaluate the full expression for qT ?) Express your answer to three significant figures. ? qT (N2) =
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…
Nitesh
2. Calculate the total molar entropy of HF at 298K. The vibrational frequency is 3960 cm-1 and the rotational constant is 20.6 cm-1.
Differentiate between distribution ratio (D) and partition coefficient (K,).
6.
1. Write down the equation used to account for the variation of molar heat capacity of a material at constant pressure with temperature assuming that the temperature range is significant.
16.55 What are the most probable populations of the first sev- eral vibrational levels of O2(g) at 1000 K? The characteristic vi- brational temperature is 2274 K.
Don't give handwritten answers otherwise I will dislike