Given these two equations, calculate Cv for CO2 and N2 using the velocity of sound. 6. According to statistical mechanics, the contribution to Cy due to the ith vibrational mode of a molecule is c ee;/T Cv,vib,4 = R(7) ³ (e®,/T — 1)² › where Oi = hcv./kB, h is Planck's constant, and c is the speed of light in cm s-¹. v; is the vibrational frequency of the ith vibrational mode in wavenumbers (cm-¹). The quantity O, has dimensions of temperature and is sometimes referred to as the vibrational tem- perature (of the ith vibrational mode). The total vibrational contribution to the molar heat capacity for an N-atom (linear) molecule is then Cy,vib Cv,vib,i Calculate Cy for CO₂ at 300 K, assuming that the translational and rotational con- tributions are (3/2)R and R, respectively, and use the preceding equations to obtain the vibrational contribution. Four vibrational modes for CO₂ are expected (3N- 5). How- ever, three fundamental frequencies are observed at v= 667.3, 1340, and 2349.3 cm-¹. These correspond to the bending, symmetric stretching, and asymmetric stretching modes, 3N-S i=1
Given these two equations, calculate Cv for CO2 and N2 using the velocity of sound. 6. According to statistical mechanics, the contribution to Cy due to the ith vibrational mode of a molecule is c ee;/T Cv,vib,4 = R(7) ³ (e®,/T — 1)² › where Oi = hcv./kB, h is Planck's constant, and c is the speed of light in cm s-¹. v; is the vibrational frequency of the ith vibrational mode in wavenumbers (cm-¹). The quantity O, has dimensions of temperature and is sometimes referred to as the vibrational tem- perature (of the ith vibrational mode). The total vibrational contribution to the molar heat capacity for an N-atom (linear) molecule is then Cy,vib Cv,vib,i Calculate Cy for CO₂ at 300 K, assuming that the translational and rotational con- tributions are (3/2)R and R, respectively, and use the preceding equations to obtain the vibrational contribution. Four vibrational modes for CO₂ are expected (3N- 5). How- ever, three fundamental frequencies are observed at v= 667.3, 1340, and 2349.3 cm-¹. These correspond to the bending, symmetric stretching, and asymmetric stretching modes, 3N-S i=1
Chapter27: Molecular Fluorescence Spectroscopy
Section: Chapter Questions
Problem 27.6QAP
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Transcribed Image Text:Given these two equations, calculate Cv for CO2 and N2 using the velocity of sound.
6. According to statistical mechanics, the contribution to Cy due to the ith vibrational
mode of a molecule is
c
ee;/T
Cv,vib,4 = R(7) ³ (e®,/T — 1)² ›
where Oi = hcv./kB, h is Planck's constant, and c is the speed of light in cm s-¹. v; is the
vibrational frequency of the ith vibrational mode in wavenumbers (cm-¹). The quantity
O, has dimensions of temperature and is sometimes referred to as the vibrational tem-
perature (of the ith vibrational mode). The total vibrational contribution to the molar
heat capacity for an N-atom (linear) molecule is then
Cy,vib
Cv,vib,i
Calculate Cy for CO₂ at 300 K, assuming that the translational and rotational con-
tributions are (3/2)R and R, respectively, and use the preceding equations to obtain the
vibrational contribution. Four vibrational modes for CO₂ are expected (3N- 5). How-
ever, three fundamental frequencies are observed at v= 667.3, 1340, and 2349.3 cm-¹.
These correspond to the bending, symmetric stretching, and asymmetric stretching modes,
3N-S
i=1
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