answer

watching

views

15 Nov 2019

Write an expression for the complete canonical partition function in terms of the partition functions associated with each degree of freedom. [Q = f(QKE,Qconf,â¦)]. kinetic, configurational, rotational, electronic, and vibrational energy modes, but no internal rotational degrees of freedom.

answer

watching

336

views

For unlimited access to Homework Help, a Homework+ subscription is required.

You have 0 free answers left.
Get unlimited access to 3.8 million step-by-step answers.

Get unlimited access

Already have an account? Log in

Jamar FerryLv2

28 Aug 2019

Unlock all answers

Get 1 free homework help answer.

Already have an account? Log in

Join us on Discord

Chemistry Study Group

Join now

Related questions

For which system below would quantum effects be leastnoticeable?

-The collision of two N₂ molecules in a gas, whichchanges the rotational energy of both

-Polarization of the electron density of ethanol resulting inexcitation of vibrational motions

-An electron-sized particle moving in a 1 m³ box asthe temperature decreases by 10 degrees

-A hydrogen atom being struck by a UV photon

We have dealt with two different ensembles, canonical andmicrocanonical. Which of the following statements is inaccurateregarding these ensembles?

-The canonical ensemble is always considered as a subset of alarger reservoir, which acts as the surroundings.

-The microcanonical ensemble is defined to have constant energy,volume, and composition.

-The microcanonical ensemble is a smaller subset of microstatesof the canonical ensemble.

-The canonical ensemble is generally more useful than themicrocanonical for chemical processes.

Which statement below is most correct regarding the partitionfunction of an ensemble?

-For a given temperature, the high-energy contributions to thepartition function are more heavily weighted.

-Once a partition function is defined in a specific ensemble, itis valid in all other ensembles.

-It tells us the numerical order of the energy levels for agiven system.

-It provides a measure of the energy levels available to asystem at a given temperature.

Consider a cup-carrier from your favorite take-out restaurant.The carrier can hold four cups, and you have to place two cups (onelarge, one small) into the carrier, with no preference forposition. How many microstates can you form with two cups in thefour spaces?

-12

-8

-16

-6

Boltzmann's definition of the entropy was a breakthrough inunderstanding statistical thermodynamics. What is the bestdefinition of Boltzmann's entropy?

-The Boltzmann entropy is a count of the total distinctmicrostates in a system.

-The Boltzmann entropy is a measure of the randomness of anensemble.

-The Boltzmann entropy is a count of the accessible energylevels at a given temperature.

-The Boltzmann entropy is a measure of the useful work availablein an ensemble.

Our canonical ensemble was defined such that the temperature,volume, and number of particles were each held constant. In termsof the Legendre transform, which thermodynamic potential isfundamental in the canonical ensemble?

-The Helmholtz energy

-The internal energy

-The Gibbs energy

-The enthalpy

The equipartition principle can be used to estimate the constantvolume heat capacities of gases. Under which circumstances wouldthe full equipartition heat capacity most closelyapproximate the measured value of C_V?

-A sample of N₂ gas at 373K

-A sample of propane gas (C₃H₈) at roomtemperature

-A sample of water vapor at 373K

-A sample of Br₂ vapor at room temperature

Which factor below does not contribute to the rotationalpartition function of a molecule?

-The rotational quantum number

-The nuclear and electronic spin states

-The rotational constant(s)

-The temperature of the molecule

We were able to reduce the vibrational partition function froman infinite series to a function of a single exponential, but onlyapproximately. Which approximation below was NOT used?

-We assumed that the vibrational energy can be expressed asv?_e.

-We assumed that the energy levels were close enough to allowintegration instead of summation.

-We assumed that the vibrational motion is purely harmonic.

-We assumed that the separations are relatively small, due tohigh temperature or lower vibrational constant.

The derived partition function for an ideal gas depends on allof the physical parameters listed below except for which one?

-Molecular symmetry

-The temperature of the molecules

-The volume of the sample

-Mass of the molecules

Deriving the translational partition function is more involvedthan deriving the rotational and vibrational partition functions.Which statement below is NOT a reason for this?

-There are so many possible translational energy levels, thatthe integral does not converge to a finite value.

-The integral of translational states for a single particle mustbe taken over a 6-dimensional hypervolume.

-The degeneracy of translational states is not obvious becausethey lie so close in energy.

-Translational degrees of freedom involve interactions betweenall molecules in the sample, whereas rotations and vibrations donot.

The connection between the Equipartition Principle and thetranslational partition functions helped to demonstrate that thetemperature of a system depends on the easily excited degrees offreedom. Why should this be true?

-In systems with easily excited degrees of freedom, a change inthe entropy requires energy changes on the order of thermalenergy.

-In systems with easily excited degrees of freedom, smallincreases in the pressure make excited states more accessible,

increasing the temperature.

-In systems with easily excited degrees of freedom, thepotential energy is no longer dependent on the temperature of thesystem.

-In systems with easily excited degrees of freedom, thermalenergy is sufficient to allow one to treat the energy levels as acontinuum.

The connection between the Maxwell-Boltzmann distribution andthe translational partition function allowed us to betterunderstand the distribution of speeds. Which statement below is NOTa consequence of the translational partition function?

-The population of the lowest speeds is very small.

-The pressure of the gas increases as the velocityincreases.

-An increase in the temperature will result in shifting thedistribution to higher energies.

-The population of the highest speeds is very small.

When dealing with quantum energy levels, there are severalimportant factors to consider. Which concept below is NOT importantto quantum energy levels?

-The set of quantum numbers

-Degeneracy

-The deBroglie wavelength

-The ground state

Calculate the following for N2O gas at 298 K: a) The characteristic rotational temperature, ï±R. b) The characteristic vibrational temperature, ï±V, for each if the four vibrational modes c) The molecular partition function, q. Clearly show the values and calculations for the translational, rotational, and vibrational contributions (qT, qR, and qV for each vibrational mode). d) The constant-volume molar heat capacity, CV,m. Clearly show the values and calculations for the translational, rotational, and vibrational contributions. e) The constant-pressure molar heat capacity, Cp,m (use the relationship between CV,m and Cp,m for a perfect gas) . Compare your value with that found in Table 2C.5. f) The standard molar entropy, (the molar entropy at standard pressure,). Clearly show the values and calculations for the translational, rotational, and vibrational contributions. Compare your value with that found in Table 2C.5. Molecular properties of N2O that you will need for the calculations. = 0.4190 cm-1 = 2224 cm-1 = 1285 cm-1 = 589 cm-1 (doubly degenerate)

Weekly leaderboard

Home

Homework Help 3,900,000

Chemistry 830,000

Write an expression for the complete canonical partition function in terms of the partition functions associated with each degree of freedom. [Q = f(QKE,Qconf,â¦)]. kinetic, configurational, rotational, electronic, and vibrational energy modes, but no internal rotational degrees of freedom.

Unlock all answers

Related textbook solutions

Basic Chemistry

Principles of Chemistry Molecular Approach

Chemistry: Structure and Properties

Principles of Chemistry Molecular Approach

Chemistry: A Molecular Approach

Chemistry: A Molecular Approach

Principles of Chemistry: A Molecular Approach

Chemistry: The Central Science

Related questions

Weekly leaderboard

Write an expression for the complete canonical partition function in terms of the partition functions associated with each degree of freedom. [Q = f(QKE,Qconf,â¦)]. kinetic, configurational, rotational, electronic, and vibrational energy modes, but no internal rotational degrees of freedom.

Unlock all answers

Related textbook solutions

Basic Chemistry

Principles of Chemistry Molecular Approach

Chemistry: Structure and Properties

Principles of Chemistry Molecular Approach

Chemistry: A Molecular Approach

Chemistry: A Molecular Approach

Principles of Chemistry: A Molecular Approach

Chemistry: The Central Science

Related questions

Weekly leaderboard

Write an expression for the complete canonical partition function in terms of the partition functions associated with each degree of freedom. [Q = f(QKE,Qconf,â¦)]. kinetic, configurational, rotational, electronic, and vibrational energy modes, but no internal rotational degrees of freedom.