This problem finds an approximate expression for [Uintermol, the contribution of intermole...

This problem finds an approximate expression for [Uintermol, the contribution of intermolecular interactions to U. As the volume V changes at constant T, the average distance between molecules changes and so the intermolecular interaction energy changes. The translational, rotational, vibrational, and electronic contributions to U depend on T but not on V (Sec. 2.11). Infinite volume corresponds to infinite average distance between molecules and hence to Uintermol = 0. Therefore U(T, V) − U(T,∞) = Uintermol(T, V). (a) Verify that Uintermol where the integration is at constant T, and V’ is some particular volume, (b) Use (4.57) to show that for a van der Waals gas Uintermol = −a/Vm. (This is only a rough approximation since it omits the effects of intermolecular repulsions, which become important at high densities.) (c) For small to medium-size molecules, the van der Waals a values are typically 106 to 107 cm6 atm mol−2 (Sec. 8.4). Calculate the typical range of Uintermol,m in a gas at 25°C and 1 atm. Repeat for 25 °C and 40 atm.