i) Starting with the expression for the average vibrational energy including zero-pointenergy, derive the expression below for the contribution of vibrational motion to theconstant volume heat capacity of an ideal gas.Cv,vib = ROvib2evib/T2-Ovib/T)²ii) Determine the vibrational contribution to the heat capacity of nitrogen (ỹ =2100 cm ¹) at 375K. Compare this to the value from the high temperatureequipartition value of R, and explain why your calculated value is similar ordifferent.

To determine the expression for the contribution of vibrational motion to the heat capacity of an…

i) Starting with the expression for the average vibrational energy including zero-point energy, derive the expression below for the contribution of vibrational motion to the constant volume heat capacity of an ideal gas. Cv,vib = R -R evib T 2 e-vib/T (1 – e-Ovib/T)²

i) Starting with the expression for the average vibrational energy including zero-point energy, derive the expression below for the contribution of vibrational motion to the constant volume heat capacity of an ideal gas. Cv,vib = R -R evib T 2 e-vib/T (1 – e-Ovib/T)²

Physical Chemistry

2nd Edition

ISBN:9781133958437

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

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

Chapter2: The First Law Of Thermodynamics

Section: Chapter Questions

Problem 2.92E

See similar textbooks

Related questions

Q: A student dissolved 0.3101 g of Na2C2O4 in 30 mL of water and 15 mL of 3 mol/L H2SO4. She titrated…

Q: Balance the reaction between Cl₂ and NH3 to form CI and N₂H4 in basic solution. When you have…

Q: 3 % Transmittance 100 50- 0- 4000 singlet, 3H (a) triplet, 2H. (b) 3000 2000 2 1500 Wavenumber…

A: Molecular formula - C7H14O

Q: have an unknown volume of gas at a pressure of 730 mm Hg and a temperature of 315 K. If I raise the…

A: Initial Volume = ? No of moles = ? No of moles = ? Note: Two of the questions are exactly same. So…

Q: Write an acitivity series for the generic metals, A, B, C, D if the following observations were…

Q: How many atoms are there in 30.1 g of magnesium

A: Since, Moles is the ratio of mass to the molar mass of that atom or molecules. Also, Number of atoms…

Q: A student constructed an electrochemical cell composed of an Fe3+ (aq)/Fe(s) half-cell connected to…

A: From the given combinations , we would determine the reducing strengths one by one. Then combine all…

Q: Although water is the most common hydrogen-oxygen compound, hydrogen and oxygen form another…

A: In earlier days, hydrogen peroxide(H2O2) was used as an antiseptic which can kill the germs by…

Q: Question 14 A mixture contains 0.0100 M of both Ba2+ ions and Pb2+ ions. If NaF is slowly added to…

A: The two reactions that can take place upon adding NaF are- Ba2++ 2NaF→BaF2 +2Na+Pb2++ 2NaF→PbF2…

Q: A compound contains arsenic and oxygen as the only elements. A sample of the compound contains 75.4%…

A: Given : Sample have 75.4% arsenic by weight. And the compound is made up of only arsenic and…

Q: The preparations of two aqueous solutions are described in the table below. For each solution, write…

A: ♣ 1.1 mol of KOH is added to 1.0 L of a 1.1 M HCN solution♣ 0.2 mol of HCl is added to 1.0 L of a…

Q: (a) Determine a ductile-to-brittle transition temperature as that temperature corresponding to the…

A: The graph between temperature and the impact energy is given below: (a)The average of the maximum…

Q: How many moles of arsenic are there in 6.50 g of arsenic?

Q: ompound X has a molar mass of 316.25 g mol and the following composition: -1 element phosphorus…

A: Let 100 gram of compound

Q: To an Olympic size swimming pool was added 5.0 g of methylene blue, a dye having formula…

A: We will first convert the concentration of dye into grams/L . and eventually, we will convert…

Q: Balance the reaction between PbO2 and Fe²+ to form Pb2+ and Fe³+ in acidic solution. When you have…

A: Above reaction after balanced water appear as product and co-efficient is 2. This reaction involved…

Q: Given that K, for water is 2.4 x 10-14 at 37 °C, calculate the pH of a neutral aqueous solution at…

A: Using Kw we will find Pkw and from pkw we can find the pH of the solution. Comparing the pH of the…

Q: 1. Consider two SN1 reactions: (A) water and tert-butylbromide and, (B) water and 2- bromopropane,…

A: Note: According to our guidelines we are supposed to answer only first three subpart of question.…

Q: Question 17 Which salt would be the most soluble in an acidic solution? O Pbl₂ O PbCl₂ O Fe(OH)2 O…

Q: A chemist makes 250. mL of calcium bromide (CaBr₂) working solution by adding distilled water to…

Q: Part 3: Mass to moles. Convert mass to moles then moles to number of atoms. Use the periodic table…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: If the same amount of fuel (methane, ethane, and propane) and oxygen (excess) is subjected to…

A: Here we have to find which of the following fuel on combustion with excess of O2 will produce more…

Q: A critical reaction in the production of energy to do work or drive chemical reactions in biological…

A: we have to calculate the free energy change for the given reaction

Q: A brick has a mass of 4.0 kg and the Earth has a mass of 6.0 × 10²7 g. Use this information to…

A: 1mole brick = 6.022x1023 bricks so to find the mass of 1mole brick, we just need to calculate the…

Q: Selenium (Se) is an important trace element of human nutrition and a crucial cofactor of the enzyme…

A: To find out the concentration of Se present in 10.0 g of soil sample which is first distilled as the…

Q: Predict the major product of the following reaction. Enter the InChl code of the structure. + OCH 3

Q: compound A = 0.02 g compound B = 0.012 g If 20 ml of solvent is used, which is the best solvent to…

A: Given: mass of compound A = 0.02 g = 0.02 g × 1000 mg/g = 20 mg Mass of compound B = 0.012 g =…

Q: 1. How many milliliters of 0.250 M NaOH are required to fully neutralize the following solutions?…

A: Here we are required to find the volume of NaOH required for the neutralization reaction.

Q: 1. Spectrometry involves measurement of a) interactions between light and matter b) wave behavior of…

A: The correct options of the MCQ questions are given below-

Q: H₂O M solution of NH₂CIO (aq), arrange the species by their relative molar amounts in solution. H₂O*…

A: Molar concentration of NH4ClO4 = 1.0 x 10-2 M = 0.01 M When it is ionized, it is dissociated to…

Q: The colorless solution of an unknown solid turned red litmus blue. No odor was noted upon adding…

A: Here is your answer.........

Q: For each system listed in the first column of the table below, decide (if possible) whether the…

A: The entropy of the solution can be calculated using: ∆Smix=-Rn1lnx1+n2lnx2 where, n1, n2 are the…

Q: What wavelength (in nanometers) corresponds to the transition of an electron in a hydrogen atom from…

A: we have to calculate the wavelength for the given transition in nm

Q: Based on the information in the table, how much heat is needed to melt 10 g of ethanol? A B C D 0.01…

Q: iben terv o fouborg-voert el terW Sbetsienap eis alsoi NBS five different products hv

A: Here we have to predict five different products obtained by the free radical substitution by NBS…

Q: What are the key breakdown fragmentation pathways of the product 4-methoxyphenyl acetate?

Q: If water is added to magnesium nitride, ammonia gas is produced wen the mixture is heated. Mg3 N₂…

A: Mass of Mg3N2 needed can be figure out from the moles of chlorine gas produced.

Q: When the redox reaction Mn²+ reaction below H+ H* (aq) is (aq) + Mn2+, (aq) Bi3+ is + Bi03 (a + (aq)…

A: We have to balance the given reaction and determine the coefficients

Q: A voltaic electrochemical cell is constructed in which the anode is a Mg²+ Mg half cell and the…

A: Voltaic cell or galvanic cell: The electrochemical cell which converts the chemical energy into…

Q: For a 1.0 x 10-4 M solution of HCIO(aq), arrange the species by their relative molar amounts in…

A: Given: Concentration of HClO = 1.0×10-4 M

Q: Question 4 The molar solubility of BaF2 at 25 °C is 1.82 x 10-2 M. What is the concentration of…

Q: Potassium and chlorine react according to the balanced chemical equation shown below. If the…

Q: The preparations of two aqueous solutions are described in the table below. For each solution, write…

A: Answer: When a compound donate H+ ions in its solution it is called as acid and when a compound…

Q: 1 2 3 4 2NO₂(g) = N₂O(g) + heat Stresses Applied to an Equilibrium System 5 6 increase temperature 7…

A: According to Le Chatelier's principle, when any stress is applied to a equilibrium condition then…

Q: Aqueous hydrogen peroxide (dihydrogen dioxide) decomposes to form liquid water (dihydrogen monoxide)…

A: Hydrogen peroxide contains a peroxide linkage (Single Oxygen-oxygen bond). Peroxide bond is weak and…

Q: If the same amount of fuel (methane, ethane, and propane) and oxygen (excess) is subjected to…

A: Here we have to determine the following fuels that will produce more amount of CO2 and H2O when…

Q: Problem 6.6. Estimate the probability that a hydrogen atom at room temper- ature is in one of its…

Q: Suppose the galvanic cell sketched below is powered by the following reaction: Mn(s) + Cu(NO3)(aq)…

Q: Small pieces of copper at 100.0°C are placed in 110.0 g of water at 25.0°C in a perfectly insulated…

A: When the hot metal is dunked into the water, the heat is released by the metal and the equal heat is…

Q: What is the molar solubility of Cd(OH)2 in a solution with a pH of 11.25? O 6.75 x 10-12 M O 2.13 x…

A: We will first calculate the concentration of OH-. We can calculate this from pOH, pH is given and we…

Question

i) Starting with the expression for the average vibrational energy including zero-point
energy, derive the expression below for the contribution of vibrational motion to the
constant volume heat capacity of an ideal gas.
Cv,vib = R
Ovib
2
evib/T
2
-Ovib/T)²
ii) Determine the vibrational contribution to the heat capacity of nitrogen (ỹ =
2100 cm ¹) at 375K. Compare this to the value from the high temperature
equipartition value of R, and explain why your calculated value is similar or
different.

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

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Applications of Statistical Thermodynamics

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

Use the equipartition theorem to estimate the constant-volume molar heat capacity of (i) I2, (ii) CH4, (iii) C6H6 in the gas phase at 25 °C.
Calculate the vibrational, rotational, and translational contributions to the constant volume heat capacity (Cv) for 14N2 at 298 K. Assume this represents the high temperature limit for rotational energy and low temperature limit for vibrational energy. Given that Cv=20.81 J/K·mol for N2, state which type or types of energy contribute most to Cv for N2 and explain why those types of energy contribute most.
Use the equipartition principle to estimate the values of γ = Cp/CV for gaseous ammonia and methane. Do this calculation with and without the vibrational contribution to the energy. Which is closer to the experimental value at 25 °C?
The ground level of Cl is 2P3/2 and a 2P1/2 level lies 881 cm−1 above it. Calculate the electronic contribution to the heat capacity of Cl atoms at (i) 500 K and (ii) 900 K.
1.3 The ground level of Cl is 2P3/2 and a 2P1/2 level lies 881 cm-1 there above. Calculate the electronic contribution to the heat capacity of Cl atoms at 500 K.
How much energy does it take to raise the temperature of 1.0 mol H2O(g) from 100 °C to 200 °C at constant volume? Consider only translational and rotational contributions to the heat capacity.
Use the equipartition theorem to estimate the constant- volume molar heat capacity of (i) O3, (ii) C2H6, (iii) CO2 in the gas phase at 25 °C.
Use the equipartition principle to estimate the value of γ = Cp/CV for carbon dioxide. Do this calculation with and without the vibrational contribution to the energy. Which is closer to the experimental value at 25 °C?
What molar constant-volume heat capacities would you expect under classical conditions for the following gases: (a) Ne, (b) O_2, (c) H_2O, (d) CO_2, and (e) CHCl_3
The constant-pressure heat capacity of a sample of a perfect gas was found to vary with temperature according to the expression Cp(JK–1) = 20.17 + 0.03665(T). Calculate q, w, ΔU, and ΔH when the temperature is raised from 25°C to 300°C(a) at constant pressure(b) at constant volume
The heat capacity ratio of a gas determines the speed of sound in it through the formula cs = (γRT/M)1/2, where γ = Cp,m/CV,m and M is the molar mass of the gas. Deduce an expression for the speed of sound in a perfect gas of (a) diatomic, (b) linear triatomic, (c) nonlinear triatomic molecules at high temperatures (with translation and rotation active). Estimate the speed of sound in air at 25 °C. Hint: Note that Cp,m − CV,m = R for a perfect gas.
The constant-pressure heat capacity of a sample of a perfect gaswas found to vary with temperature according to the expression Cp/(J K−1) = 20.17 + 0.3665(T/K). Calculate q, w, ΔU, and ΔH when the temperature is raised from 25 °C to 100 °C (i) at constant pressure, (ii) at constant volume.