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CO2 has the following vibrational degree of freedom 1388, 667.4(doubly degenerate) and 2349cm-1. The value of total vibrational partition function for this molecule at 1000K is ____(Round off to two decimal places).
Correct answer is '3.17'. Can you explain this answer?
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CO2 has the following vibrational degree of freedom 1388, 667.4(doubly...
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CO2 has the following vibrational degree of freedom 1388, 667.4(doubly...
Vibrational Degree of Freedom:
- CO2 molecule has three vibrational degrees of freedom.
- Each degree of freedom corresponds to a different vibrational mode.
- The given vibrational modes are 1388 cm-1, 667.4 cm-1 (doubly degenerate), and 2349 cm-1.
Vibrational Partition Function:
- The vibrational partition function (Qvib) is used to calculate the partition function for vibrational energy levels.
- It is given by the equation: Qvib = ∏(i=1 to n) [1 / (1 - e^(-βhνi))] where n is the number of vibrational modes, β is the reciprocal of temperature (1/T), h is the Planck's constant, and νi is the vibrational frequency.
Calculating Total Vibrational Partition Function:
- The total vibrational partition function (Qtotal) is the product of the partition functions for each vibrational mode.
- We need to calculate Qtotal for CO2 at 1000K.
Calculating Qvib for each mode:
1. For the mode with a vibrational frequency of 1388 cm-1:
- Convert the frequency to wavenumber: 1388 cm-1 = 1388 × (1/100) m^-1 = 13.88 × 10^2 m^-1.
- Calculate the value of νi in cm^-1: νi = (13.88 × 10^2) / (c × 100) where c is the speed of light.
- Calculate βhνi: βhνi = (1/T) × (h/2π) × νi.
- Calculate the value inside the square brackets: 1 / (1 - e^(-βhνi)).
- Repeat the same steps for the other two modes.
Calculating Qtotal:
- Multiply the values obtained for each mode to get Qtotal.
- Round off the final value to two decimal places.
Final Answer:
The value of the total vibrational partition function for CO2 at 1000K is 3.17.
- CO2 molecule has three vibrational degrees of freedom.
- Each degree of freedom corresponds to a different vibrational mode.
- The given vibrational modes are 1388 cm-1, 667.4 cm-1 (doubly degenerate), and 2349 cm-1.
Vibrational Partition Function:
- The vibrational partition function (Qvib) is used to calculate the partition function for vibrational energy levels.
- It is given by the equation: Qvib = ∏(i=1 to n) [1 / (1 - e^(-βhνi))] where n is the number of vibrational modes, β is the reciprocal of temperature (1/T), h is the Planck's constant, and νi is the vibrational frequency.
Calculating Total Vibrational Partition Function:
- The total vibrational partition function (Qtotal) is the product of the partition functions for each vibrational mode.
- We need to calculate Qtotal for CO2 at 1000K.
Calculating Qvib for each mode:
1. For the mode with a vibrational frequency of 1388 cm-1:
- Convert the frequency to wavenumber: 1388 cm-1 = 1388 × (1/100) m^-1 = 13.88 × 10^2 m^-1.
- Calculate the value of νi in cm^-1: νi = (13.88 × 10^2) / (c × 100) where c is the speed of light.
- Calculate βhνi: βhνi = (1/T) × (h/2π) × νi.
- Calculate the value inside the square brackets: 1 / (1 - e^(-βhνi)).
- Repeat the same steps for the other two modes.
Calculating Qtotal:
- Multiply the values obtained for each mode to get Qtotal.
- Round off the final value to two decimal places.
Final Answer:
The value of the total vibrational partition function for CO2 at 1000K is 3.17.
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CO2 has the following vibrational degree of freedom 1388, 667.4(doubly degenerate) and 2349cm-1. The value of total vibrational partition function for this molecule at 1000K is ____(Round off to two decimal places).Correct answer is '3.17'. Can you explain this answer?
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CO2 has the following vibrational degree of freedom 1388, 667.4(doubly degenerate) and 2349cm-1. The value of total vibrational partition function for this molecule at 1000K is ____(Round off to two decimal places).Correct answer is '3.17'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about CO2 has the following vibrational degree of freedom 1388, 667.4(doubly degenerate) and 2349cm-1. The value of total vibrational partition function for this molecule at 1000K is ____(Round off to two decimal places).Correct answer is '3.17'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for CO2 has the following vibrational degree of freedom 1388, 667.4(doubly degenerate) and 2349cm-1. The value of total vibrational partition function for this molecule at 1000K is ____(Round off to two decimal places).Correct answer is '3.17'. Can you explain this answer?.
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