Calculate the translational partition function of a carbon dioxide, CO2, molecule in a sample of 0.250 mol of gas held in a vessel at a pressure of 1.00 bar and a temperature of 298 K.

A) 0 B) 1.0 C) 2.3 F1F1F1S1F1F1F10 1019 D) 1.8 F1F1F1S1F1F1F10 1029 A) 0 B) 1.0 C) 2.3 F1F1F1S1F1F1F10 1019 D) 1.8 F1F1F1S1F1F1F10 1029 D

The monosaccharide ribose, C5H10O5 may exist in five distinct conformations. Two of these conformations are six-membered rings and two are five-membered rings, with the remaining conformation being a straight chain. In a solution at 25 F1F1F1S1F1F1F10C, a sample of ribose was found to exist as 60% α-D-ribopyranose and 21% β-D-ribopyranose. Calculate the difference in molar energy between these two conformations, which differ only in the orientation of the anomeric hydroxyl group

A) 0.22 kJ mol-1 B) 1.2 kJ mol-1 C) 2.6 kJ mol-1 D) 4.0 kJ mol-1 A) 0.22 kJ mol-1 B) 1.2 kJ mol-1 C) 2.6 kJ mol-1 D) 4.0 kJ mol-1 C

Calculate the rotational partition function for acetylene, C2H2, at 298 K. The rotational constant of acetylene is 3.529 F1F1F1S1F1F1F10 1010 Hz.

A) 88 B) 1.0 C) 176 D) 53 A) 88 B) 1.0 C) 176 D) 53

The vibrational modes of a methane molecule, CH4, are listed below. Calculate the vibrational partition function at 1000 K. \(\begin{array}{ccc} \text { Mode } & \text { Degeneracy } & \text { Vibrational } \\ & & \text { Wavenumber } / \mathrm{cm}^{-1} \\ v_{1} & 1 & 3026 \\ v_{2} & 2 & 1583 \\ v_{3} & 3 & 3157 \\ v_{4} & 3 & 1367 \end{array}\)

A) 1.0 B) 2.04 C) 1.33 D) 17.2 A) 1.0 B) 2.04 C) 1.33 D) 17.2

Exam 12: Statistical Thermodynamics

Calculate the translational partition function of a carbon dioxide, CO₂, molecule in a sample of 0.250 mol of gas held in a vessel at a pressure of 1.00 bar and a temperature of 298 K.

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Question 1

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The monosaccharide ribose, C₅H₁₀O₅ may exist in five distinct conformations. Two of these conformations are six-membered rings and two are five-membered rings, with the remaining conformation being a straight chain. In a solution at 25 C, a sample of ribose was found to exist as 60% α-D-ribopyranose and 21% β-D-ribopyranose. Calculate the difference in molar energy between these two conformations, which differ only in the orientation of the anomeric hydroxyl group

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Water, H₂O, has a residual entropy of 3.4 J K^-1 mol^-1 at 0 K, which arises because each water molecule may be orientated in two distinct ways. Use the Boltzmann formula to predict the residual entropy of mono-deuterated water, HDO.

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Question 3

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The degeneracy of the lowest level of a Br atom is 4. The first excited electronic level lies the equivalent of 3685 cm^-1 higher in energy and has a degeneracy of 2. Calculate the electronic partition function at a temperature of 2500 K.

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Question 4

Calculate the contribution made by vibrational motion to the molar entropy of hydrogen iodide, HI, gas at a temperature of 500 K. The vibrational frequency of HI is 7.91  10¹² s^-1.

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Question 5

Calculate the rotational partition function for acetylene, C₂H₂, at 298 K. The rotational constant of acetylene is 3.529  10¹⁰ Hz.

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Question 6

Use statistical thermodynamics to derive an expression for the contribution to the molar heat capacity at constant volume of a diatomic molecule at a temperature of 298 K as a result of vibrational motion. Start by differentiating with respect to temperature the expression for the internal energy and substituting for the vibrational partition function.

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Question 7

The vibrational modes of a methane molecule, CH₄, are listed below. Calculate the vibrational partition function at 1000 K. Mode Degeneracy Vibrational Wavenumber / 1 3026 2 1583 3 3157 3 1367

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Question 8

The harmonic vibrational wavenumber of an iodine, I₂, molecule is 217 cm^-1. Treating the molecule as a harmonic oscillator, calculate the vibrational partition function at 298 K.

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Question 9

Calculate the standard molar Gibbs energy of argon gas, Ar, at a temperature of 298 K, relative to that at 0 K.

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Question 10

Showing 1 - 10 of 10

Calculate the translational partition function of a carbon dioxide, CO₂, molecule in a sample of 0.250 mol of gas held in a vessel at a pressure of 1.00 bar and a temperature of 298 K.

Water, H₂O, has a residual entropy of 3.4 J K^-1 mol^-1 at 0 K, which arises because each water molecule may be orientated in two distinct ways. Use the Boltzmann formula to predict the residual entropy of mono-deuterated water, HDO.

The degeneracy of the lowest level of a Br atom is 4. The first excited electronic level lies the equivalent of 3685 cm^-1 higher in energy and has a degeneracy of 2. Calculate the electronic partition function at a temperature of 2500 K.

Calculate the contribution made by vibrational motion to the molar entropy of hydrogen iodide, HI, gas at a temperature of 500 K. The vibrational frequency of HI is 7.91  10¹² s^-1.

Calculate the rotational partition function for acetylene, C₂H₂, at 298 K. The rotational constant of acetylene is 3.529  10¹⁰ Hz.

The vibrational modes of a methane molecule, CH₄, are listed below. Calculate the vibrational partition function at 1000 K. Mode Degeneracy Vibrational Wavenumber / 1 3026 2 1583 3 3157 3 1367

The harmonic vibrational wavenumber of an iodine, I₂, molecule is 217 cm^-1. Treating the molecule as a harmonic oscillator, calculate the vibrational partition function at 298 K.

Calculate the standard molar Gibbs energy of argon gas, Ar, at a temperature of 298 K, relative to that at 0 K.

The Propertiesof Gases

The First Law of Thermodynamics

The Second Law of Thermodynamics

Physical Transformations

Chemical Change

Chemical Kinetics

Quantum Theory

Atomic Structure

The Chemical Bond

Molecular Interactions

Molecular Spectroscopy

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Exam 12: Statistical Thermodynamics

Calculate the translational partition function of a carbon dioxide, CO2, molecule in a sample of 0.250 mol of gas held in a vessel at a pressure of 1.00 bar and a temperature of 298 K.

Water, H2O, has a residual entropy of 3.4 J K-1 mol-1 at 0 K, which arises because each water molecule may be orientated in two distinct ways. Use the Boltzmann formula to predict the residual entropy of mono-deuterated water, HDO.

The degeneracy of the lowest level of a Br atom is 4. The first excited electronic level lies the equivalent of 3685 cm-1 higher in energy and has a degeneracy of 2. Calculate the electronic partition function at a temperature of 2500 K.

Calculate the contribution made by vibrational motion to the molar entropy of hydrogen iodide, HI, gas at a temperature of 500 K. The vibrational frequency of HI is 7.91  1012 s-1.

Calculate the rotational partition function for acetylene, C2H2, at 298 K. The rotational constant of acetylene is 3.529  1010 Hz.

The vibrational modes of a methane molecule, CH4, are listed below. Calculate the vibrational partition function at 1000 K. Mode Degeneracy Vibrational Wavenumber / 1 3026 2 1583 3 3157 3 1367

The harmonic vibrational wavenumber of an iodine, I2, molecule is 217 cm-1. Treating the molecule as a harmonic oscillator, calculate the vibrational partition function at 298 K.

Calculate the standard molar Gibbs energy of argon gas, Ar, at a temperature of 298 K, relative to that at 0 K.

The Propertiesof Gases

The First Law of Thermodynamics

The Second Law of Thermodynamics

Physical Transformations

Chemical Change

Chemical Kinetics

Quantum Theory

Atomic Structure

The Chemical Bond

Molecular Interactions

Molecular Spectroscopy

Filters

Calculate the translational partition function of a carbon dioxide, CO₂, molecule in a sample of 0.250 mol of gas held in a vessel at a pressure of 1.00 bar and a temperature of 298 K.

Water, H₂O, has a residual entropy of 3.4 J K^-1 mol^-1 at 0 K, which arises because each water molecule may be orientated in two distinct ways. Use the Boltzmann formula to predict the residual entropy of mono-deuterated water, HDO.

The degeneracy of the lowest level of a Br atom is 4. The first excited electronic level lies the equivalent of 3685 cm^-1 higher in energy and has a degeneracy of 2. Calculate the electronic partition function at a temperature of 2500 K.

Calculate the contribution made by vibrational motion to the molar entropy of hydrogen iodide, HI, gas at a temperature of 500 K. The vibrational frequency of HI is 7.91  10¹² s^-1.

Calculate the rotational partition function for acetylene, C₂H₂, at 298 K. The rotational constant of acetylene is 3.529  10¹⁰ Hz.

The vibrational modes of a methane molecule, CH₄, are listed below. Calculate the vibrational partition function at 1000 K. Mode Degeneracy Vibrational Wavenumber / 1 3026 2 1583 3 3157 3 1367

The harmonic vibrational wavenumber of an iodine, I₂, molecule is 217 cm^-1. Treating the molecule as a harmonic oscillator, calculate the vibrational partition function at 298 K.