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Your book (page 705) shows that the pressure of a macroscopicsystem j is given by Pj(N, V) = - (dEj/dV)Nandtherefore that the average pressure <P>= Sum (nj*/N)Pj(N, V) = kBT(d lnQ/dV)N,T. Youknow that Q = q(V,T)N/N! and that q(V,T) = f(T) V, whichis true because of the translational contribution to the molecularpartition function. Show that this information is consistent withthe ideal-gas equation of state.


d = partial diff

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Sixta Kovacek
Sixta KovacekLv2
11 Sep 2019

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Calculate the following for N2O gas at 298 K: a) The characteristic rotational temperature, R. b) The characteristic vibrational temperature, V, for each if the four vibrational modes c) The molecular partition function, q. Clearly show the values and calculations for the translational, rotational, and vibrational contributions (qT, qR, and qV for each vibrational mode). d) The constant-volume molar heat capacity, CV,m. Clearly show the values and calculations for the translational, rotational, and vibrational contributions. e) The constant-pressure molar heat capacity, Cp,m (use the relationship between CV,m and Cp,m for a perfect gas) . Compare your value with that found in Table 2C.5. f) The standard molar entropy, (the molar entropy at standard pressure,). Clearly show the values and calculations for the translational, rotational, and vibrational contributions. Compare your value with that found in Table 2C.5. Molecular properties of N2O that you will need for the calculations. = 0.4190 cm-1 = 2224 cm-1 = 1285 cm-1 = 589 cm-1 (doubly degenerate)

Calculate the following for N2O gas at 298 K: a) The characteristic rotational temperature, R. b) The characteristic vibrational temperature, V, for each if the four vibrational modes c) The molecular partition function, q. Clearly show the values and calculations for the translational, rotational, and vibrational contributions (qT, qR, and qV for each vibrational mode). d) The constant-volume molar heat capacity, CV,m. Clearly show the values and calculations for the translational, rotational, and vibrational contributions. e) The constant-pressure molar heat capacity, Cp,m (use the relationship between CV,m and Cp,m for a perfect gas) . Compare your value with that found in Table 2C.5. f) The standard molar entropy, (the molar entropy at standard pressure,). Clearly show the values and calculations for the translational, rotational, and vibrational contributions. Compare your value with that found in Table 2C.5. Molecular properties of N2O that you will need for the calculations. = 0.4190 cm-1 = 2224 cm-1 = 1285 cm-1 = 589 cm-1 (doubly degenerate)

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