the vibrational frequency of I2 is 214.5 cm-1.  (i) Using the harmonic oscillator model, evaluate the vibrational partition function and the mean vibrational energy of I2 at 1000K.  (ii) What is the characteristic vibrational temperature of I2? (iii) At 1000K, assuming high-temperature approximation, evaluate the vibrational partition function and the mean vibrational energy of I2.  (iv) Comparing (i) and (iii), is the high-temperature approximation good for I2 at 1000K?

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 18.31E
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 the vibrational frequency of I2 is 214.5 cm-1.  (i) Using the harmonic oscillator model, evaluate the vibrational partition function and the mean vibrational energy of I2 at 1000K.  (ii) What is the characteristic vibrational temperature of I2? (iii) At 1000K, assuming high-temperature approximation, evaluate the vibrational partition function and the mean vibrational energy of I2.  (iv) Comparing (i) and (iii), is the high-temperature approximation good for I2 at 1000K?

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