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- Use the equipartition principle to estimate the value of γ = Cp/CV for carbon dioxide. Do this calculation with and without the vibrational contribution to the energy. Which is closer to the experimental value at 25 °C?Use the equipartition theorem to estimate the constant- volume molar heat capacity of (i) O3, (ii) C2H6, (iii) CO2 in the gas phase at 25 °C.Use the equipartition theorem to estimate the constant-volume molar heat capacity of (i) I2, (ii) CH4, (iii) C6H6 in the gas phase at 25 °C.
- Use the equipartition principle to estimate the values of γ = Cp/CV for gaseous ammonia and methane. Do this calculation with and without the vibrational contribution to the energy. Which is closer to the experimental value at 25 °C?Calculate the contribution that rotational motion makes to the molar entropy of a gas of HCl molecules at 25 °C.A linear molecule may rotate about two axes. If the molecule consists of N atoms, then there are 3N- 5 vibrational modes. Use the equipartition theorem to estimate the total contribution to the molar internal energy from translation, vibration, and rotation for (a) carbon dioxide, CO2, and (b) dibromoethyne, C2Br2, at 2000 K. In contrast, a nonlinear molecule may rotate about three axes and has 3N- 6 vibrational modes. Estimate the total contribution to the molar in ternal energy from translation, vibration, and rotation for (c) nitrogen dioxide, NO2, and (d) tetrabromoethene, C2Br4,at 2000 K. In each case, first assume that all vibrations are active; then assume that none is.
- Use the equipartition theorem to estimate the molar internal energy of (i) I2, (ii) CH4, (iii) C6H6 in the gas phase at 25 °C.Calculate the work done during the isothermal reversible expansion of a gas that satisfies the virial equation of state (eqn 1C.3b) written with the first three terms. Evaluate (a) the work for 1.0 mol Ar at 273 K (for data, see Table 1C.3) and (b) the same amount of a perfect gas. Let the expansion be from 500 cm3 to 1000 cm3 in each case.Calculate the translational contribution to the standard molar entropy at 298 K of (i) H2O(g), (ii) CO2(g).
- Calculate the molar entropy of a constant-volume sample of argon at 250 K given that it is 154.84 J K−1 mol−1 at 298 K; the molar constant-volume heat capacity of argon is 3/2 R.2. Given the equation S, - S, = dq use appropriate thermodynamic equations T V. to show that S, -S, = nC, In |+ nC, In Pi V,The cohesive energy density, U, is defined as U/V, where U is the mean potential energy of attraction within the sample and V its volume. Show that U = 1/2N2∫V(R)dτ where N is the number density of the molecules and V(R) is their attractive potential energy and where the integration ranges from d to infinity and over all angles. Go on to show that the cohesive energy density of a uniform distribution of molecules that interact by a van der Waals attraction of the form −C6/R6 is equal to −(2π/3)(NA2/d3M2)ρ2C6, where ρ is the mass density of the solid sample and M is the molar mass of the molecules.