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30. We will derive the forms of the molecular partition functions for atoms and molecules shortly in class, but the partition function that describes the translational and rotational motion of a homonuclear diatomic molecule is given by Itrans (V,T) = = 2πmkBT h² V grot (T) 4π²IKBT h² Where h is Planck's constant and I is molecular moment of inertia. The overall partition function is qmolec Qtrans qrot. Find the energy, enthalpy, entropy, and Helmholtz free energy for the translational and rotational modes of 1 mole of oxygen molecules and 1 mole of iodine molecules at 50 K and at 300 K and with a volume of 1 m³. Here is some useful data: Moment of inertia: I2 I 7.46 x 10- 45 kg m² 2 O2 I 1.91 x 101 -46 kg m² Molecular weight: 12 m = 254 g mol-1 O2 m 32 g mol-1 = Which kind of motion contributes the most to the partition function? How does the molecular weight affect the partition function? How does the energy of a diatomic molecule compare to the energy of a monatomic species like krypton or argon? Which molecule has a greater number of energy states occupied? Are more states occupied at high temperatures or at low temperatures?

30. We will derive the forms of the molecular partition functions for atoms and molecules shortly in class, but the partition function that describes the translational and rotational motion of a homonuclear diatomic molecule is given by Itrans (V,T) = = 2πmkBT h² V grot (T) 4π²IKBT h² Where h is Planck's constant and I is molecular moment of inertia. The overall partition function is qmolec Qtrans qrot. Find the energy, enthalpy, entropy, and Helmholtz free energy for the translational and rotational modes of 1 mole of oxygen molecules and 1 mole of iodine molecules at 50 K and at 300 K and with a volume of 1 m³. Here is some useful data: Moment of inertia: I2 I 7.46 x 10- 45 kg m² 2 O2 I 1.91 x 101 -46 kg m² Molecular weight: 12 m = 254 g mol-1 O2 m 32 g mol-1 = Which kind of motion contributes the most to the partition function? How does the molecular weight affect the partition function? How does the energy of a diatomic molecule compare to the energy of a monatomic species like krypton or argon? Which molecule has a greater number of energy states occupied? Are more states occupied at high temperatures or at low temperatures?

Physical Chemistry
Physical Chemistry
2nd Edition
ISBN:9781133958437
Author:Ball, David W. (david Warren), BAER, Tomas
Publisher:Ball, David W. (david Warren), BAER, Tomas
Chapter18: More Statistical Thermodynamics
Section: Chapter Questions
Problem 18.4E
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30. We will derive the forms of the molecular partition functions for atoms and molecules shortly in class, but the partition function that describes the translational and rotational motion of a homonuclear diatomic molecule is given by Itrans (V,T) = = 2πmkBT h² V grot (T) 4π²IKBT h² Where h is Planck's constant and I is molecular moment of inertia. The overall partition function is qmolec Qtrans qrot. Find the energy, enthalpy, entropy, and Helmholtz free energy for the translational and rotational modes of 1 mole of oxygen molecules and 1 mole of iodine molecules at 50 K and at 300 K and with a volume of 1 m³. Here is some useful data: Moment of inertia: I2 I 7.46 x 10- 45 kg m² 2 O2 I 1.91 x 101 -46 kg m²
Transcribed Image Text:30. We will derive the forms of the molecular partition functions for atoms and molecules shortly in class, but the partition function that describes the translational and rotational motion of a homonuclear diatomic molecule is given by Itrans (V,T) = = 2πmkBT h² V grot (T) 4π²IKBT h² Where h is Planck's constant and I is molecular moment of inertia. The overall partition function is qmolec Qtrans qrot. Find the energy, enthalpy, entropy, and Helmholtz free energy for the translational and rotational modes of 1 mole of oxygen molecules and 1 mole of iodine molecules at 50 K and at 300 K and with a volume of 1 m³. Here is some useful data: Moment of inertia: I2 I 7.46 x 10- 45 kg m² 2 O2 I 1.91 x 101 -46 kg m²
Molecular weight: 12 m = 254 g mol-1 O2 m 32 g mol-1 = Which kind of motion contributes the most to the partition function? How does the molecular weight affect the partition function? How does the energy of a diatomic molecule compare to the energy of a monatomic species like krypton or argon? Which molecule has a greater number of energy states occupied? Are more states occupied at high temperatures or at low temperatures?
Transcribed Image Text:Molecular weight: 12 m = 254 g mol-1 O2 m 32 g mol-1 = Which kind of motion contributes the most to the partition function? How does the molecular weight affect the partition function? How does the energy of a diatomic molecule compare to the energy of a monatomic species like krypton or argon? Which molecule has a greater number of energy states occupied? Are more states occupied at high temperatures or at low temperatures?
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