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Calculate the value of cP at 298 K and 1 atm pressure predicted for I2(g) and...

Calculate the value of cP at 298 K and 1 atm pressure predicted for I2(g) and HI(g) by the classical equipartition theorem. Compare the predicted results with the experimental results and calculate the percent of the measured value that arises from vibrational motions.

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Answer #1

The value of Cp for any diatomic gas molecule = 9R / 2

This is because a diatomic molecule has 3 degrees of translational motion (each contributing R/2), 2 degrees of rotational motion ( each contributing R/2) and 1 degree of vibrational motion contributing R for a total of 7R /2 for value of Cv.

Cv = 7R/2

Cp = Cv +R = 7R/2 + R = 9R/2 = 37.41 J/mol.K

Neglecting the vibrational motion, the experimental value of Cp = 7R/2 = 29.10 J/mol.K

Predicted value of Cp for I2(g) = 36 J/mol.K (approx.)

Vibrational contribution = (36 - 29.10) J/mol.K = 6.9 J/mol.K

Percent of Cp due to vibration = ( 6.9 / 36) x 100% = 19.1 %

Predicted value of Cp for HI(g) = 29.2 J/mol.K

Vibrational contribution = (29.2 - 29.10) J/mol.K = 0.1 J/mol.K

Percent of Cp due to vibration = ( 0.1 / 29.2) x 100% = 0.34 %

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