The number of thermally accessible states for the vibration of a molecule is often small; in fact, the vibrational partition is often just slightly more than one but still less than two. In such a case, one can approximate the infinite sum that is the partition function as just its first two terms: qV=1+e−TVTq^V=1+e^{-\frac{T^V}{T}}qV=1+e−TTV where TV = 4307 K. Assume that this form for the partition function is appropriate for this problem. (a) Calculate the vibrational contribution to the molar internal energy for HCl at 1000 K. (b) Would the vibrational partition function be larger for 2H35Cl or 1H35Cl – or perhaps the same? Think about what the partition function means – and how a mass change might make a difference.
The number of thermally accessible states for the vibration of a molecule is often small; in fact, the vibrational partition is often just slightly more than one but still less than two. In such a case, one can approximate the infinite sum that is the partition function as just its first two terms: qV=1+e−TVTq^V=1+e^{-\frac{T^V}{T}}qV=1+e−TTV where TV = 4307 K. Assume that this form for the partition function is appropriate for this problem. (a) Calculate the vibrational contribution to the molar internal energy for HCl at 1000 K. (b) Would the vibrational partition function be larger for 2H35Cl or 1H35Cl – or perhaps the same? Think about what the partition function means – and how a mass change might make a difference.
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...
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The number of thermally accessible states for the vibration of a molecule is often small; in fact, the vibrational partition is often just slightly more than one but still less than two. In such a case, one can approximate the infinite sum that is the partition function as just its first two terms: qV=1+e−TVTq^V=1+e^{-\frac{T^V}{T}}qV=1+e−TTV where TV = 4307 K. Assume that this form for the partition function is appropriate for this problem.
(a) Calculate the vibrational contribution to the molar internal energy for HCl at 1000 K.
(b) Would the vibrational partition function be larger for 2H35Cl or 1H35Cl – or perhaps the same? Think about what the partition function means – and how a mass change might make a difference.
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