The expressions for the contributions to E derived in class for translational, r

Question

The expressions for the contributions to E derived in class for translational, rotational, and vibrational motions are all functions of temperature only. This means (U/V )T = 0, the ideal gas value, from which it follows that CP,m = CV,m +R. So, even for real gases, the molar heat capacities at constant V and constant P should differ by R, provided the non-interacting assumption is good. As well, all the expressions derived in class suggest it is natural to divide heat capacities by R when comparing them. In the table below are listed measured values of CP,m and CV,m at 298 K and 1 atm (in units of J K1 mol1 ) for several chemical species. a) Calculate CP,m/R, CV,m/R, and (CP,m CV,m)/R and enter these values in the appropriately labelled columns. Species CP,m CV,m CP,m/R CV,m/R (CP,m CV,m)/R C exact V,vib,m/R C cl V,vib,m/R He 20.79 12.47 H2 28.83 20.45 Cl2 33.94 25.33 CH4 35.64 27.00 H2O 33.59 25.26 C3H8 73.79 65.30 SF6 97.00 88.23 b) The deviation of (CP,m CV,m)/R from unity is a measure of non-ideal behaviour. Rationalize the trends seen in these values from the Table. 5 c) Assuming the classical limit for translation and rotation, the experimental value of CV,m/R should be equal to (C cl V,trans,m + C cl V,rot,m + C exact V,vib,m)/R. For each chemical species in the Table, calculate C exact V,vib,m/R from the measured heat capacities, and record the results in the column labelled C exact V,vib,m/R. In addition, in the column labelled C cl V,vib,m/R record the vibrational contribution to the heat capacity expected in the classical limit. Rationalize the trends in these values. Are any of the vibrational contributions close to their classical limits?

Explanation / Answer

Chemcial Specie Cp,m Cv,m Cp,m / R Cv,m / R (Cp,m - Cv,m ) / R He 20.79 12.47 2.50 1.50 1.00 H2 28.83 20.45 3.47 2.46 1.01 Cl2 33.94 25.33 4.08 3.05 1.03 CH4 35.64 27.00 4.29 3.25 1.04 H2O 33.59 25.26 4.04 3.04 1.00 C3H8 73.79 65.30 8.87 7.85 1.02 SF6 97.00 88.23 11.67 10.61 1.05

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